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Mathematics education :
b the voice of african american and white adolescents
h [electronic resource] /
by Sharondrea King.
[Tampa, Fla] :
University of South Florida,
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Dissertation (Ph.D.)--University of South Florida, 2010.
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ABSTRACT: Several studies have provided evidence regarding factors that contribute to the mathematics achievement gap between African American and White students. Byrnes (2003) found that 45%-50% of the difference in White and African American students' performance in mathematics was associated with socioeconomic status, exposure to learning opportunities, and motivational aspects of math while 4.5% was explained by ethnicity. The goal in this mixed method study was to examine the mathematics attitude of African American (n = 22) and White (n = 10) high school students and to allow students to voice what practices and supports they perceived enabled them to learn mathematics. The students discussed practices and supports specific to their school, home, and community. The Attitudes Toward Mathematics Inventory data were examined across race and performance levels. The performance levels, excelling and struggling, were based on each student's cumulative performance in mathematics. The attitude results yielded one positive significant differences between performance groups on the self-confidence construct. As for qualitative data, there were few differences across the racial groups. Unlike White excelling students (n=6), African-American excelling students (n=11) reported that they received limited encouragement from teachers to take advanced mathematics courses or to participate in extracurricular activities related to mathematics. In examining the students' responses, there were more similarities than differences across groups. Groups spoke of the need for teachers to be more patient and willing to provide additional support. Students reported that some teachers assumed something within them [students] was the reason that they had not grasped a concept (e.g., lack of attention during instruction). The question of why African American students' mathematics performance lags behind their White counterparts remain pertinent. Many of the reasons for the achievement gap reported in the literature were not explicitly expressed by the students in this study. However, the intent to have students express their perspectives and needs related to mathematics was accomplished. Thus, this insight can only enhance our efforts to improve African American students' mathematical experiences and success.
Advisor: Kelly Powell-Smith, Ph.D.
x Psychological & Social Foundations
t USF Electronic Theses and Dissertations.
Mathematics Education: The Voice of African American and White Adolescents by Sharondrea R. King A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Psychological and Social Foundations College of Education University of South Florida Co-Major Professor: Kelly A. Powell-Smith, Ph.D. Co-Major Professor: Michael Curtis, Ph.D. Deirdre Cobb-Roberts, Ph.D. Robert F. Dedrick, Ph.D. Gladis Kersaint, Ph.D. Date of Approval: November 9, 2009 Keywords: achievement, attitude, teacher fact ors, excelling students, struggling students Copyright 2010, Sharondrea R. King
Dedication I dedicate this research project to my family, friends, and professors who supported me to the end. I am grateful fo r a loving mother and grandmother who never gave up on my dreams or me. I am thankful for my friends who prayed and cheered me on. I give a special dedication and thanks to one friend who is no longer with me, LaKira D. Porter. LaKira saw it not robbery to offer her help while battling breast cancer. Her offer was a constant reminder of Gods power and that I can do all things through Christ who strengthens me (Philippians 4:13).
i Table of Contents List of Tables ...................................................................................................................... iii Abstract ...................................................................................................................... ........ iv Chapter I: Introduction ...................................................................................................... 1 Statement of Intent .................................................................................................. 7 Chapter II: Literature Review ............................................................................................ 12 National Mathematics Curriculum Standards ....................................................... 12 Current Status of Mathematics Achievement in the United States ....................... 15 Mathematics Performance of African American Students and White Students.... 20 Impact of Ethnicity and Socioeconomic Status ......................................... 21 Instructional Practices ............................................................................... 24 Attitudes Toward Mathematics ................................................................. 27 Other Factors that Influence th e Academic Achievement of African American Students ............................................................................................ 28 Attitude and Achievement ......................................................................... 31 Self-concept and achievement ................................................................... 35 Summary ............................................................................................................... 37 Chapter III: Method ........................................................................................................... 39 Recruitment and Selection of Participants ............................................................ 40 Participating Schools ................................................................................. 40 Selection Process ....................................................................................... 42 Participants ................................................................................................ 46 Data Collection ...................................................................................................... 49 Focus Groups ............................................................................................. 50 Interviews .................................................................................................. 52 Review of Educational History ................................................................. 52 Instrumentation ...................................................................................................... 56 Attitudes Toward Mathematics Inventory ................................................. 56 Focus Group and Interview Questions ...................................................... 57 Pilot Study ............................................................................................................. 59 Data Analysis ........................................................................................................ 60 Inventory Data ........................................................................................... 61 Focus Group and Interview Data ............................................................... 61
ii Delimitations ............................................................................................. 65 Chapter IV: Results ........................................................................................................... 66 Attitude Towards Mathematics ............................................................................. 67 Data From the ATMI ................................................................................. 67 Data from Focus Groups and Interviews ............................................................... 72 Contributing Factors to Attitude Formation .............................................. 73 Positive Attitudes Toward Mathematics ....................................... 73 Negative Attitudes Toward Mathematics ...................................... 75 Importance and Utility of Mathematics ..................................................... 77 Influence of Home/Comm unity and School Factors ................................. 78 Student Identified Sc hool-based Supports .................................... 78 Student Identified Ho me/Community Supports ............................ 80 Impact of Factors Relating to the Mathematics Classrooms ..................... 82 Factors contributing to success ...................................................... 82 Factors hindering success .............................................................. 84 Data from Interview .................................................................................. 87 Home/Community Factors ............................................................ 88 School and Mathematics Classroom Factors ................................. 88 Summary of Results .............................................................................................. 88 Chapter V: Discussion ....................................................................................................... 9 2 Attitude Towards Mathematics ............................................................................. 92 Supports and Hindrances Influencing Mathematics Performance ........................ 96 Conclusion ............................................................................................................. 99 Limitations ........................................................................................................... 102 Directions for Future Research ............................................................................ 105 References .................................................................................................................... ... 109 Appendices ...................................................................................................................... 118 Appendix A: Focus Groups and Inte rviewees Student Demographics and Activities ............................................................................................................. 119 Appendix B: Demograp hic Questionnaire ......................................................... 125 Appendix C: Focus Group and Interview Questions .......................................... 126 About the Author ................................................................................................... End Page
iii List of Tables Table 1 Percentage of Stude nts at Participating Schools ............................................... 41 Table 2 Participants Academic Information ................................................................. 47 Table 3 Participants Background In formation (excluding pilot group) ........................ 48 Table 4 Mathematics Course .......................................................................................... 49 Table 5 Data Source For Research Questions ................................................................ 59 Table 6 Statistics of ATMI: Present Study .................................................................... 68 Table 7 Cronbach Alpha: ATMI .................................................................................... 70 Table 8 F-Ratios and p -levels from Two-way Analysis of Variance for Each Subscale ( n =32 ) Present Study: ......................................................... 71 Table 9 Effect size of ATMI Subscale scor es by Performance Level and Race ............. 72
iv Mathematics Education: The Voice of African American and White Adolescents Sharondrea R. King ABSTRACT Several studies have provided evidence regarding factors that contribute to the mathematics achievement gap between African American and White students. Byrnes (2003) found that 45%-50% of the difference in White and African American students performance in mathematics was associated with socioeconomic status, exposure to learning opportunities, and mo tivational aspects of math while 4.5% was explained by ethnicity. The goal in this mixed method st udy was to examine the mathematics attitude of African American ( n = 22) and White ( n = 10) high school st udents and to allow students to voice what practices and supports they perceived enabled them to learn mathematics. The students discussed practi ces and supports specific to their school, home, and community. The Attitudes Toward Mathematics Inventory data were examined across race and performance levels. The performance levels, excelling and struggling, were based on each students cumulative performance in mathema tics. The attitude results yielded one positive significant differences between pe rformance groups on the self-confidence construct. As for qualitative data, there were few differences across the racial groups. Unlike White excelling students (n=6), African-American excelling students ( n=11)
v reported that they received limited encourag ement from teachers to take advanced mathematics courses or to participate in extr acurricular activities related to mathematics. In examining the students responses, ther e were more similarities than differences across groups. Groups spoke of the need for te achers to be more patient and willing to provide additional support. Students reporte d that some teachers assumed something within them [students] was the reason that they had not grasped a concept (e.g., lack of attention during instruction). The question of why African American students mathematics performance lags behind their White counterparts remain pe rtinent. Many of the reasons for the achievement gap reported in the literature were not explicitly expressed by the students in this study. However, the intent to have st udents express their perspectives and needs related to mathematics was accomplished. Thus this insight can only enhance our efforts to improve African American students mathematical experiences and success.
1 Chapter I Introduction The No Child Left Behind (NCLB) Act of 2001 challenges schools to improve students performance in reading, mathematics, and science. In a ddition, it focuses on improving educational outcomes for all student s. Specifically, NCLB demands an end to the achievement gap between minority and non-minority students as well as disadvantaged and advantaged students. Unfo rtunately, gaps conti nue to exist between these groups in reading, mathematics, a nd science. This study focused on the mathematics performance of African Amer ican and White students. Due to the preferences of various authors, it is important to note that the terms African American students and Black students are used interc hangeably throughout this manuscript. Reading initiatives have overshadowed the importance of mathematics competency, as teachers adopt evidence-base d reading strategies and districts focus on increasing reading test scores. Reading is a fundamental skill for all subjects; however, mathematics skills are also e ssential for academic success. This reminder is crucial because students in the United States have not been performing to their greatest mathematics potential, in comparison to other countries. Students difficulties with mathematical concepts and computation skills have been identified in results of state, national, and international assessment (Lee, Griggs, & Di on, 2007; Loveless & Coughlan, 2004; NRC, 2001).
2 According to Loveless and Coughlan ( 2004), in 1999, only 56% of 17 year olds correctly answered problems involving fractions on Nationa l Assessment of Educational Progress (NAEP) items in comparison to th e 76% in 1990. They further reported that students computation skills are lacking with respect to addition, subtraction, multiplication, division, and fractions. Th e National Research Council (NRC) believes that students are exhibiting a great deficit in their ability to apply mathematics skills to problem solving and understanding of basic mathematical concepts (NRC, 2001). Although the difference in achievement between Black and White students appeared to be decreasing during th e 1980s to early 1990s, the 2003 NAEP scores indicated a continuous disparity in achieve ment between these two groups (Holloway, 2004). This disparity was also evident in the 2007 and 2009 NAEP results. Over the last 7 years, on average, there has been an a pproximately 30-point difference between the average mathematics scores of fourth grade White and Black students and an approximately 36 point difference between th ese groups in the eighth grade (Lee et al., 2007). In 2007, only 39% of fourth graders and 32% of eighth graders performed in the Proficient achievement range on the National Assessment of Educational Progress (NAEP) (Lee et al., 2007). However, the average mathematics score for fourth and eighth graders has increased over the years. With the increase in average math scores, more students are earning scores at the Basic and Proficient achievement level (Lee et al., 2007). In an examination of students perf ormance on the 2009 NAEP, there was a 26-
3 point gap between fourth gr ade Black students average mathematics score and White students average mathematics score. For eighth graders, there was a 32-point gap between Black and White students average mathematics scores. These gaps were not significantly different from the 2007 NAEP data In addition, the average mathematics score for Black students on the 2009 NAEP was at the Basic achievement level for fourth and eighth graders. Although the White-B lack gap in mathematics performance decreased between 1990 and 2007 for four th graders and between 2005 and 2007 for eighth graders, Black students achievement level is well behind their White peers who, on average, are performing at the Proficiency achievement level in fourth and eighth grade. Existing research points to the substa ntial disparity between the mathematics achievement of African American students and White students (Butty, 2001; Byrnes, 2003; NRC 2001). In addition, this suggests that African American st udents, in general, are not mastering the mathematics skills neces sary to compete in a society that is becoming more dependent on information t echnology and do not understand the need for mathematics proficiency on the job (Anderson, 1990; Batsche, 1993; NRC, 2001). From history and research, we also know that African Americans have made gains in the educational system, despite ad versity. For example, Lee and SlaughterDefoe (2001) noted the increase in literacy among African Americans in the late 1800s, which was a time period most African American s were fighting for equality. However, as a group, African American s still have a road to travel in order for future generations to continue to be successful or, for some, to e xperience success. In our current educational
4 system, a disproportionate number of African Americans dropout of school, are suspended or expelled, and are placed in sp ecial education (Lads on-Billings, 1997; Lee & Slaughter-Defoe, 2001; NRC, 2002). These outco mes may be the result of the problems African American students face in school s and provide further support for paying attention to school-based outcome s for African Americans. Schools will not experience the positive outcomes of effective pedagogy, curriculum, and structural changes until edu cators, parents, and students understand the importance of mathematics education for personal and social advancement. Consequently, students who do not obtain adequate mathemati cal skills in grade school will not gain access to advanced mathematics courses, such as algebra (the curriculum gatekeeper) and above, and will be limited in career choices related to the science, mathematics, and technology fields as we ll as nonprofessional jobs that require mathematics and reasoning skills (Anderson, 1990; Stiff & Harvey; 1988; Tate, 2002). Mathematical literacy is considered a civil rights matter because mastery and access to higher-level mathematics is vita l to increased educational and economic opportunity for students (Ladson-Billi ngs, 1997). Successful experiences in mathematics allow individuals to have choice s with regard to car eer and other personal endeavors as well as the mathematical knowle dge to tackle, support, or modify efforts that do not support th eir community, family, and pers onal well-being (Anderson, 1990; Ladson-Billings, 1997). Sl ater (1997) states that when st udents graduate with sufficient mathematical skills, these skills also provide them with other skills necessary to analyze critically [and advocate or fight against] the justice issues in thei r own environments (p.
5 681). For instance, skills learned in mathema tics courses can help students enhance problem solving and reasoning. These skills ca n be applied to other daily living activities and subject areas, if they are taught by connecting students life experiences (or experience of those in their community) with course objectives as a way to promote generalization of skills across domains of life and schooling (DAmbrosio, 2001). Unfortunately, as a society, we have accepte d those who demonstrate inept mathematical abilities, while at the same time, we stigmatize those who are unable to read. The intent is not to suggest that individuals with limited mathematical skills be ridiculed, but we must be concerned about poor mathematics skill and encourage individuals to value reasoning and problem solving skills as much as we value other types of literacy (e.g., reading). Therefore, it is crucial that we seek and determine why African American students are not performing well and conduct re search to determine the factors that contribute to the success of African American students who are excelling in mathematics by taking into account what studen ts perceive and experience. Thus far, we are aware of factors that may impede mathematics achieveme nt such as lack of access to mathematical courses that prepare students for advanced mathematics, tracking, socioeconomic status (e.g., parent education), less ri gorous curriculum, low expect ations, and cultural capital (Byrnes, 2003; Holloway, 2004; Moody, 2004). Documenting the strengths of African American students and describing the environmen ts that have fostered their success in mathematics are important because this information may serve as a mechanism to help
6 other African American students who are not achieving at appropr iate levels. For instance, identifying the aspect s of the learning environment, as well as home, school, and community environments that contribute to mathematics achievement will provide educators and parents information that could lead to psychosocial and academic interventions to help African American students who are not doing well in mathematics. However, examining the experiences of African American students in isolation of the experiences of White students would not help researchers understand the ways in which the experiences of these groups of students differ. A comparison of the mathematics experiences of White students and African Am erican students will add insight into how such experiences may impact mathematics achievement. By revealing factors that African Amer ican and White students acknowledge as having an impact on their experiences with mathematics, additional methods can be developed to encourage students success in mathematics. This research may inform educators about the mathematical experiences of African American st udents, their beliefs and values about mathematics, their opportuni ties to learn and succeed in mathematics, and what motivates them to learn and do math ematics. Mathematical experiences include a students engagement in mathematics exer cises that include cooperative groups, direct instruction, supplemental instru ction, tutorial supports, a nd enrichment/extracurricular activities. In essence, th e knowledge of what experiences have enhanced or limited students mathematics performance and si gnificant aspects of schooling and home experiences that cause them to value mathem atics, understand mathematics concepts, and define mathematics will help transform mathematics curriculum and pedagogy.
7 Statement of Intent The intent of this study was to examin e African American and White students experiences in mathematics classrooms, fo cusing on factors that are perceived to influence their success or failure and seeking to understand the differential mathematics experiences of African American and White st udents. In addition to exploring factors that may support existing theories about raci al differences in mathematics achievement, this study used the voice of the students to provide insight into what they perceived as differences that may exist in their mathem atical experiences and possible methods to address the mathematics achievement gap. Sp ecifically, this study wa s designed to gain an understanding of the mathematics expe riences of African American and White students by allowing students to voice how school culture, family, and life experiences in and out of school have influenced thei r overall mathematics achievement. Previous research has examined the mathematics experiences of students by analyzing quantitative data gathered by standardized assessments and surveys. Quantitative data provide valuable information such as the percentage of students not achieving at grade level, what mathematical c oncepts or skills stude nts are not mastering, and information pertaining to score discrepanc ies by race, sex, gender, class, and schools (Loveless & Coughlan, 2004; Lubienski, 2002; NRC, 2001; Schmidt, Houang, & Cogan, 2002). Quantitative research on mathematics achievement also has been instrumental in determining factors that account for mathematics achievement such as exposure, motivation, and socioeconomic status (Byrnes, 2003). These findings have also stressed the need for reform (Holloway, 2004). Resu lts from such quantitative studies allow
8 researchers to determine if a problem exists and approximate its severity. However, qualitative data about students experiences can provide researchers richer understanding of the experiences of students through students words. Results obtained from qualitative studies could help educators understand how current curriculum, teaching practices, and ideology impact students achievement. In addition, insights obtained from interviews and focus groups can assist educators in determining what outside factors contribute to students mathematics experiences, what factors facilitate the understanding and acknowle dgement of students perceptions about mathematics teaching practices, and how the st udents experiences are associated with mastery of mathematical skills. These findings could inform educators as they seek to develop interventions or teaching methods that work best for Afri can American students as well as for other ethnic groups. Fo r example, by using qualitative research approaches, Martin (2002) and Moody (2004) provided educators with insights into the experiences of African American students w ho excelled in mathematics. They explored students experiences by taki ng into account the history of African Americans in the United States, society, family influences, and intrapersonal factors on mathematical achievement. Martin (2002) explored the mathematical success of African American students through ethnographic interviews, case studies and observations. Martin interviewed seventh through ninth grade stude nts at Hillsi de Junior High School. The purpose of the study was to examine how sociohistorical, co mmunity, school, and in trapersonal factors shape ones mathematical socialization and id entity. Student and teacher interviews as
9 well as case studies were us ed to gather information pertaining to the students experiences with peer pressure, personal goals motivation to learn mathematics and other subjects, beliefs about mathematics, and diffe rential treatment from peers and teachers. Martin used interviews and case studies to co llect data about the experiences of parents and community members. Moody (2004) used a phenomenological approach. Specifically, Moody used surveys, autobiographi es, and interviews to collect data. The mathematical experiences of two African Amer ican female students were used to gather data related to the impact of social and cultural factors and to identify contributing factors to the students success. The participants were adult women reflecting back on their elementary, secondary, and collegiate experien ces. Similar to th e Martin study, Moodys findings highlighted the mathematics classroom experiences as well as the social and cultural factors that impacted the mathem atics experiences and successes of African American, college females. The current study differs from the Mart in (2002) and Moody (2004) studies in several ways. First, unlike Martin and Moody studies, the current study examined the experiences of both African American and White students. Students in both groups had an opportunity to express their beliefs a bout the importance of mathematics, their experiences in the classroom related to math ematical teaching practices that worked for them, and their input about individuals and e xperiences that motivate them to do well in the area of mathematics. Information from both groups allowed the researcher to investigate commonalities and differences that existed in the perceived experiences between and among the racial groups. Da ta about within and between groups
10 experiences help to address the what, why, and how questions. Second, this study focused on high school st udents enrolled in any mathematics course. Adults participated in the Moody (2004) study in which information was gathered from elementary to college years. Martins (2002) participants were middle school students. In both Moodys and Mart ins study, data were gathered about participants early mathematics experiences. However, a focus on the early mathematics environment such as the use of ability grouping and support from teachers and parents were not explored in enough detail to understa nd the impact of these early experiences on the students mathematical performance. Although Moody addressed this area, her sample size was small and it is important to pr ovide additional data in this area that might replicate previous findings. Recall of st udents elementary, middle, and high school mathematics experiences is likely easier for high school student partic ipants. These data could help the researcher e xplore how students experiences from elementary to their present grade shaped their pers pectives about mathematics a nd mathematics achievement. Martins (2002) and Moodys (2004 ) studies are discussed in more detail in the literature review. Third, in contrast to Martin and Moody, this study used both qualitative and quantitative data to explore the mathematical experiences of African American and White students. Survey data were gathered to examine the students attitudes towards mathematics. Quantitative data have been useful in determining the existence of a problem and not as instrumental in explaining or developing reform efforts. However, qualitative information can inform educat ors regarding the follo wing: (a) what do
11 African American and White students believe ar e contributing factors to their success (or failure) in mathematics; (b) what teaching methods were perceived by the students to help them grasp a mathematical concept or skill (e.g., small group work or independent seatwork); and (c) what motivated these stude nts to do well in mathematics. Therefore, focus groups and interviews were used to gath er this information. The following research questions provide the framework in this study for exploring the mathematical experiences of African American and White students: What are the attitudes of excelling and struggling African American and White high school students toward mathematics? To what extent do excelling African American, struggling African American, excelling White, and struggling White students differ in terms of home/community factors they believe influenced their experiences in mathematics? To what extent do excelling African American, struggling African American, excelling White, and struggling White stud ents differ in terms of school and mathematics classroom factors they believe influenced their attitudes toward and their performance in mathematics?
12 Chapter II Literature Review To make a change that will impact the future, one must first have knowledge of the past. This statement is the premise of this literature review. With the current economic turmoil in our country, it is more a pparent that taking into account what we know is paramount to not ma king the same mistakes. This review includes an overview of st udents current mathematics performance and discusses the impact of race, class, a nd poverty on academic achievement in general, as well as mathematics achievement specifica lly. These impact variables will provide a context for understanding the plight of African Americans from past to present as a means to facilitate discussions related to the importance for continued dialogue, change, and action toward efforts to close the achieveme nt gap. In addition, literature pertinent to understanding the current status of students mathematics achievement is examined as a way to provide knowledge about mathematics education and determine where educators need to make changes that improve mathematics achievement. National Mathematics Curriculum Standards The current National Council of Teachers of Mathematics document, Principles and Standards (NCTM, 2000) is used to inform teaching practices and is an attempt to set comprehensive learning goals for school mathematics at the national level (NRC, 2001). Although standards outlined by NCTM ha ve not been adopted as the national curriculum, many programs use the document and previous versions of it to inform
13 teaching and the development of local a nd state standards (NRC, 2001). A national mathematics curriculum that is accessible to all students is based on a progressive scope and sequence for educators to follow regard less of geographic location and one that challenges students could help narrow the mathematics achievement gap, eliminate tracking, result in prepared and skilled teach ers, and increase mathematics literacy among all students (Schmidt, 2004). Unfortunately, a preferred and a ccepted practice in the U.S. is for states to create their curriculum and for districts to modify adopted curriculum as needed. Such practices illustrate the lack of coherence and commonality across curricula used in the U.S. These practices have a ne gative impact on students because students are expected to learn different c ontent in different settings. Such circumstances also may have a negative impact on students exposur e to the content necessary for advanced mathematics and lead to discrepancies in st udent expectations across grades (Schmidt, 2004). The NCTM (2000) emphasizes equity, curriculum, teaching, learning, assessment, and technology as principles that influence and guide the decision-making process, curriculum development, instruction, and a ssessment in mathematics education. The principles cover issues from high expecta tions and equitable access to what and how students should be taught to be proficient in mathematics. This document also emphasizes the need for a coherent and common curriculum. NCTM developed ten standards for curri cular development. These standards were designed to assist in providing all students with a co mprehensive foundation to gain mathematics understanding and competency (NCTM, 2000). Specifically, the standards
14 inform educators about what mathematics instruction should enable students to understand and apply mathematical skills. NCTM standards are divided into two overlapping parts, which include content a nd process standards. Content Standards describe the content that students should learn such as number and operations, algebra, geometry, measurement, and data analysis and probability (p. 29). Process Standards focus on the application of content know ledge through the use of problem solving, reasoning and proof, communication, connectio ns, and representation skills. Although standards are intended for all grades, variation exists at ea ch grade level regarding the amount of focus given to each of thes e areas during formal instruction. The expectations set by the NCTM delineate principles educators at national and local levels should use as cornerstones wh en developing instructional materials and instructional practices. The following are exam ples that represent hi gh standards to help meet the needs of all children, whether exce lling or struggling in mathematics (NCTM, 2000): All students should be exposed to challenging mathematics curriculum, regardless of students career goals. Students who are excelling in mathematics should be provided with opportunities for enrichment, which allows them to pursue their mathematical interests. Schools should provide differential mathem atical learning experience such as a differential pacing to allow students to acce lerate through expected curriculum to provide additional time in other mathematic content areas, curricula that emphasize a deeper understanding of targeted concepts to prepare studen ts for future experiences,
15 provide supplementary mathematics opportuni ties, and instruction in heterogeneous groups which provide differentia ted instructional support. Classroom teachers and special education staff should provide support for students with learning difficulties. Families and community members should be included in the development of curricular goals and content materials so th at expectations are consistent in school, home, and community environments. Incl usion of family and community members should involve allocated time for helpi ng participants understand, discuss, and decide upon goals. Elementary grade students should study mathematics for at least an hour under the guidance of teachers who enjoy mathematic s and are prepared to teach it well (NTCM, 2000, p. 371). Every middle-grades and high school st udent should be required to study the equivalent of a full year of mathem atics in each grade (NCTM, 2000, p. 371). In essence, NCTM has provided a blueprint to guide educators. This blueprint delineates components necessary to develop accessibl e and challenging instruction. These guidelines also are necessary for improving students mathematics achievement. Current Status of Mathematics Ac hievements in the United States Findings are mixed regarding mathematic s achievement in the United States. Existing evidence supports the claim that achiev ement levels are below what is expected for a well-developed industrial society (Schmidt, Houang, & Cogan, 2002; NRC, 2001). Both NAEP and Trends International Mathematics and Science Study (TIMSS) results
16 reveal how well students are performing base d on national and international comparisons. Researchers have used these results to hypothe size reasons for variations in mathematics achievement and to identify student performance disparity across areas and across states (Byrnes, 2003; Loveless & Coughlan, 2004; Lubienski, 2002). NAEP data were collected using two types of assessment, the main NAEP and long-term trend NAEP. The main and trend NAEP samples consisted of fourth-, eighth-, and twelfth-graders. The main NAEP is sensitive to changes in instructional practices and was designed to measure standards developed by a national assessment board. However, the main NAEP was not designed to measure change over time (Loveless & Coughlan, 2004). Unlike the main NAEP, the l ong-term trend NAEP is a reliable tool used to measure change over time because the same testing instruments have been used since the first administration (Loveless & Coughlan, 2004). In comparison to the main NAEP, the trend NAEP focuses more on the assessment of computation skills (Loveless & Coughlan, 2004). An analysis using trend NAEP data s uggests that students are having difficulty with computation skills. Specifically, a ddition, subtraction, multiplication, division, fractions, decimals and percentage skills were deficient (Loveless & Coughlan, 2004). Loveless and Coughlans (2004) analysis of trend NAEP results showed that gains observed in the 1980s slowed, leveled off, and even reversed in the 1990s (p. 56). For example, in 1999, 67% of 17 year olds correct ly answered questions assessing fractions and by 1999, only 56% responded correctly. Of the fourth-, eighth-, and 12th graders who took the 1996 NAEP, 35% scored below th e basic level of achievement and 45%
17 obtained mastery adequate for proficiency (NRC, 2001). As for the main NAEP, despite low levels of achievement, the results indicated a gain in achievement scores from 1990 to 2003. Overall, the results suggested a generally low level of performance among students in the United States (NRC, 2001, p. 55). The 2005 NAEP results revealed a decrease in the number of students whose performance indicated proficiency (Perie, Grigg, & Dion, 2005): a) For fourth graders, 80% of the students performed at or above basic level and 36% performed at or above proficiency level. b) For eighth graders, 69% of the students performed at or above basic level and 30% performed at or above proficiency level. c) For twelfth graders, 80% of the students performed at or above basic level and 36% performed at or above proficiency level. NAEP data from 2007 revealed that lo w performing students across all races made greater gains than high performing stude nts, that students across all races, on average, obtained higher mathematics scor es, and that the gap between fourth grade Black and White students narrowed in 1990 and 2007 (Lee, Grigg, & Dion, 2007). Currently, the gap between fourth grade Black and White students is 26 points. A 32point gap exists between eighth grade Black and White student s. Lee, Griggs, and Dions (2007) report also found the following: a) For fourth graders, Black students made a 35 point gain in comparison to their White and Hispanic peers who made gains of 28 points and 27 points, respectively.
18 b) For fourth graders, 82% performed at or above the basic level and 39% of those tested performed at or a bove the proficiency level. c) For fourth graders, when comparing 1990 data with 2007 data, the gap between Black and White students narrowed. In 1990, Black students average mathematics score was 188 in comparison to their White peers average mathematics score of 220. In 2007, the average mathematics score for Black students was 222 and 248 for White students. d) For eighth graders, 71% performed at or above the basic level and 32% of these tested performed at or a bove the proficiency level. e) For eighth graders, a comparison of 2005 and 2007 data revealed that the gap narrowed between Black and White st udents. In examining students performance since 1990, the gap did not decrease. While the NAEP data provide informati on about mathematics achievement in the United States, TIMSS is a cr oss-national study in which the performance of fourth, eighth, and 12th graders in the U.S. was compared to students in other countries (Schmidt, Houang, & Cogan, 2002). In addition to assess ing mathematics achievement levels, the TIMSS researchers collected data pertaining to students studies and their beliefs; teachers and school administrators beliefs, pr actices, and policies related to mathematics and science; and textbooks and curricula used to instruct students (NRC, 2001). Information about students performance data as well as information about their beliefs and learning environments is valuable. Of the 40 countries that participated in the 1995 TIMSS study, each country varied
19 with regard to educational, social, economic, historical, a nd cultural factors (NRC, 2001). Therefore, it is important to note that the variance in achievement scores is linked to differences in the classes in which student s were enrolled and to differences among schools. Differences among schools or classes explained 64% of the variance in U.S. eighth-grade mathematics achievement scores and only 7% of the variance in Japan (NRC, 2001). These differences between the U.S. and Japan were a result of one or more of the following factors: parents, teachers, and students beliefs about hard work and importance of mathematics; grouping of st udents for mathematics instruction; and availability of special schools or tutors to provide additi onal assistance for mathematics tests (NRC, 2001, p. 31). U.S. students performance varied across content domains on the 1995 TIMSS assessment. Geometry, measurement, and proportionality skills were below the international average (NRC, 2001). As for data representation, anal ysis, and probability, students performed at about the internationa l average. Differences among U.S. students and students in other countries were not observed on test s measuring fractions, number sense, and algebra (NRC, 2001). The 2007 TIMSSs data for fourth graders revealed that the average mathematics score in the United States of 529 was above the TIMSSs average mathematics of 500 (Gonzales et al., 2008). The Un ited States average mathema tics score of 529 for fourth graders (average for Black students was 482 and 550 for White students) and 508 for eighth graders (average for Black students was 457 and 533 for White students) was also above the TIMSSs average mathematics score of 500. The United States fourth graders
20 were outperformed by eight other countries. The eighth graders were outperformed by five other countries. With 95% of fourth and 92% eighth gr aders performing at or above the low benchmark, the current status of mathematic s achievement in the U.S. suggests that students need more support in mathematics (Gon zales et al., 2008). The fact that students in the U.S. are also performing below students in other countries s uggests that students preparedness to compete globally might be limited. In addition, with the mathematics gap between African Americ an and White students not changing significantly and African American students lagg ing persistently behind othe r ethnic groups, the question of what should be done to help improve the mathematics performance of African American students remains. Mathematics Performance of Af rican American and White Students Although African American students have consistently scored below their White peers on mathematic assessments, NAEP data indicated that these students rate mathematics as a favorite subject or have a positive attitude toward mathematics (Martin, 2002; Matthews, 1984). Unfortunately, this pos itivism is not reflected in outcome data for many African American students in ma thematics. Performance on the 2000 NAEP revealed that there is approximately 3.4 y ears difference between the achievement of fourth-grade African American students and their White p eers, approximately 4.3 years difference for eighth grade African American and White students, and approximately 3.7 years difference between 12th grade African American a nd White students (Lubienski, 2002). These approximations were derived using Lubienskis assumption that the
21 difference of 9 points could equate to a one year difference. Current NAEP results continue to reflect a disparity between African American and White students performance as well (Lee et al., 2007; NCES, 2009). Although the fourth grade score gap between African Amer ican and White student s has decreased from 32 in 1990 to 26 in 2007, these data imply that a gap continues to exis t and it occurs early in the education process. For African Amer ican and White eighth graders, the score gap in 1990 of 33 was not significantly different from the 2007 and 2009 score gap of 32. In addition, the factors that cont ribute to the gap also impact students preparation for advanced mathematics (Holloway, 2004). Thes e factors include ethnicity, socioeconomic status, instructional practices, attitude towards mathematics, perspective about education and achievement, and self-concept. Impact of Ethnicity and Socioeconomic Status Studies attempt to examine barriers a nd factors associated with mathematics achievement by way of survey data or other forms of quantitative analyses (e.g., standardized test scores). Byrnes (2003) used NAEP data to examine ethnic differences in mathematics achievement. His study provided insight into what affects African American students mathematics achievement as well as suggested possible interventions based on the analyses of data. Byrnes (2003) focused on the mathematics performance among 12th grade White, African American, and Hispanic students. He used the 1992 NAEP test, demographic, and survey data. Equal access to schools, tracking, course selecti on, cultural incongruity (i.e., within classroom cultural clash between teacher and student, unconscious racial
22 bias), differential experiences of students in the same classroom, and differences in home environment were factors Byrnes discusse d as those that may help explain ethnic differences in mathematics achievement. He argued that these factors alone cannot explain or account for every situation or outcome that is related to ethnic differences. It should be expected that outcomes are a resu lt of multiple antecedent factors that work in concert (Byrnes, 2003, p.316). Therefore, in tegrating these factor s to explain ethnic differences was Byrnes way of identifying ch aracteristics of stude nts and schools that were predictive of performance levels. Byrnes used various stages of sampling to examine the 1992 NAEP mathematics data. His sample consisted of 6, 410 elem entary and secondary students from White, Black, and Hispanic ethnic gr oups. His regression analyses found that parent education, ability and liking of mathematics, course work, and beliefs about the nature of mathematics were more predictive of mathematics performance than ethnicity. Approximately, 45%-50% of the variance among 12th grade students proficiency scores could be accounted for by parent education, number of parents in the home, exposure to learning, and motivation. As for ethnicity, when added to the regression analyses, the variable explained 4.5% of th e proficiency scores when pa rent education, number of parents in the home, exposure to learning, and motivation were controlled. Byrnes also reported that ethnicity accounted for 11.9% of the variance in profic iency scores when other parent education, number of parents in the home exposure to learning, and motivation were not included in the analysis These findings sugge st that educators should attend to factors within the schools that they can directly impact or change to meet
23 students needs such as curricu lum and learning opportunities. Using 1990, 1996, and 2000 NAEP fourth, ei ghth, and twelfth grade data, Lubienski (2002) examined th e Black-White mathematics ach ievement gap by analyzing achievement means at each grade and SES (socio-economic status) level and investigating differences in instructional practices. In addition to NAEP data, NAEP teacher and student survey data were used. These data pertained to demographics (i.e., socioeconomic status, performance level, numbe r of math courses), instruction delivered to students, students attitude toward math ematics, teachers educational background, and teacher report of mathematical content strands emphasized with specif ic ethnic groups. Lubenski (2002) found, in 1996, 23% of Af rican American students from high SES backgrounds took pre-calculus in comparis on to 35% of their White counterparts. However, the number of African American students (14%) from low SES backgrounds taking pre-calculus was greater than their White counterparts (11%). Thus, a possible confounding factor when examining exposure is accessibility. Lubienski (2002) used data from the 1990, 1996, and 2000 NAEP to study the issue of accessibility and how it contributed to learni ng. She examined data reported for fourth-, eighth-, and 12th graders. She found that the number and type of courses taken are primary determinants to students accessibility to math ematics instruction. African American students were found to take fewer advanced classes than White st udents. For instance, 84% of White students took geometry while only 74% of African Am erican students took geometry. The impact of SES was linked to the gap in course en rollment because the gap was more pronounced and steady between the SES groups (i.e., lowest and highest) than between the racial
24 groups (i.e., Black and White). Algebra and geometry are considered en try-level mathematics courses that are viewed as a credential that leads to advanced courses and success (Tate, 2002). Having such credentials at the begi nning of high school produces hig her expectations about how much mathematics a student will take, greate r longevity in the co llege prep track, and higher achievement results (Tate, 2002, p. 148) Pelavin and Kanes (1990) research findings indicated that 80% of African American students who completed algebra and geometry attended college. Matthewss (1984) meta-analysis indicated that the number and type of mathematics courses taken in high school are asso ciated with later achievement. Unfortunately, many African Am erican students were found to be enrolled in lower level mathematics courses (LadsonBillings, 1997; Matthews, 1984; Tate, 2002). Schools that offered more advanced classe s had fewer African Am erican students and schools populated with a large percentage of African American students offered lower level mathematics classes (Matthew, 1984; Tate, 2002). Instructional Practices One might think that a negative attitude toward mathematics would be a pervasive problem among those with substandard mathematic s ability. However, th is is not the root of the issue for African Americans. Numerous researchers (e.g., Martin, 2000; Matthews, 1984; Stiff & Harvey, 1988; Yong, 1992) have reported that the attitude of African Americans toward mathematics and mathematics educators is positive. This finding suggests that the consistent low mathema tics scores and disproportionate number of African American students in remedial or lowlevel courses is much more than a student-
25 centered problem, and is not likely a problem of attitude (Martin, 2002; Stiff & Harvey, 1988). In fact, the following practices relate d to instruction were found to contribute to differences in performance: (a) White stude nts were allowed more access to calculators for daily use and on tests; (b) African American students were more likely to be assessed with multiple-choice tests, especially at th e fourth-grade level; and (c) White students were more likely than African American stude nts to have a teacher give heavy emphasis to reasoning skills (Lubienski, 2002). Manswell-Butty (2001) found that 12th grade students who received reformed mathematics instruction obtained higher ma thematics achievement scores. Reformed mathematics instruction consisted of activities that helped students connect mathematics to their daily lives by engaging them in e xploration, peer instruction, and small group work that included problem-solving and active student inquir y. With reformed mathematics instruction, student s learn critical thinking skil ls, how to explain or show steps taken to solve a math problem, and the teacher acts as a fac ilitator. ManswellButtys sample was derived from the National Educational Longitudinal Study of 1988, in which she examined the data of African American and Hispanic students. In Evertson et al.s study (1980) the results also indicated that students mathematics achievement is associated with teaching methods such as lecture-demonstration, effective teachers who asked more process and product questions, and class discussion. In addition, Evertson et al.s (1980) results revealed a positive relationship betw een the proportion of process questions asked (calling for explanations from the students) and student achievement in mathematics.
26 In our schools, students are expected to learn mathematics through drill and practice, repetition, convergent thinking, ri ght-answer thinking, and predictability (Ladson-Billings, 1997). However, these practi ces do not take into account the diversity that exists amongst individual learners. Such practices also are not designed to support the learning styles of minority students. The learning style and academic behavior of minority students are shaped by their hom e experiences and may differ from the experience of middle class European Ameri can students, to which the curriculum, textbooks, and assessments t ypically are tailo red (Ladson-Billings, 1997). In mathematics, conventional methods have been practiced and are expected as a means for doing and learning mathematics. These conventional methods include a curriculum disconnected from African American students experiences, including such practices as individual seatwork, and recitation (DAmbrosio, 2001; Sleeter, 1997). A major misconception is that mathematics is culture free, that is, issues related to culturally responsive teaching, diversity, discrimination, and biased assessment practices are absent in mathematics instru ction or curriculum. Aspects of culture are intertwined in every discipline, behavior, and thought. The impact of culture is profound and cannot be suspended (Ladson-Billings, 1997, p.700). As it should be expected of all educators, Sleeter (1997) stresses that all mathematics teac hers should be able to do the following: (a) help students from historically lo w-achieving sociocultural groups achieve well in mathematics by using their cultural backgrounds as a pedagogical resource, (b) challenge the lower levels of mathematics that are open to such students and work to institutionalize mu ch higher mathematics, (c) recognize
27 mathematics as a cultural construct in which all people around the world engagehelp all students see mathematics as a creation of people like themselves, and (d) connect mathematical concepts with students livesto think through social issues of concern to them (p.682). Attitude Towards Mathematics Lubienski (2002) emphasized the importance of understanding how students mathematical beliefs and attitudes impact their mathematical achievement and their response to instruction. This sentiment is understood when examining African American students performance in comparison to White students performance. For example, as stated previously, Lubienski (2002) found gaps ranging from 3.4 years to 4.3 year between African American and White st udents based on 2000 NAEP data. Using 2000 NAEP data, the above statistics revealed the severity of th e gap among African American and White students (Lubienski, 2002). The lim ited gains in mathematics as well as the difference in gains between African Am erican and White students demand an understanding of students experiences from each racial group. In Manswell-Buttys (2001) study, tenth grade students with a better attitude towards mathematics had significantly higher achievement scores than those students with poor attitudes towards mathematics (p. 31) and their attitudes also affected their 12th grade mathematics performance. Although one s attitude towards mathematics is not a predictor of mathematics achievement, Mans well-Buttys findings s uggest that attitude is a factor that has relevance, in which e ducators need to be cognizant of and understand that some students mathematics performance will be impacted by their attitude towards
28 mathematics. Consequently, efforts in im proving the mathematics attitude of those students with negative attitudes should not be forgotten. Research indicates that inst ructional practice, as well as students attitudes toward mathematics, influence students mathematics achievement. Specifically, we know that students who receive instruc tion that involves teaching methods such as lecturedemonstrations, active inquiry, problem-solv ing, and small group instruction achieve higher mathematics scores (Evertson et al. s, 1980; Manswell-Butty, 2001). We also know that African American and Hispanic st udents benefit from these teaching methods (Manswell-Butty, 2001). Therefore, schools sh ould be supported and encouraged to integrate unconventional or reformed mathem atics instruction in cluding the methods listed above to increase African American students mathematic performance. The review of literature on the impact of ethnicity and SES suggested that there was more to the mathematics gap than st udent-centered variables. The authors emphasized the need to examine accessibilit y, instructional practices, and students attitudes as data to underst and the disparity in African American and White students mathematic test scores and as an avenue to find ways to close this achievement gap. This research study was designed to assist with this endeavor by looking beyond test scores. Instead, students experiences were examined as a vehicle to understand the differences in African American and White student s performance in mathematics. Other Factors that Influence the Academic Achievement of African American Students In addition to the aforementioned factor s that impact mathematics achievement, intertwined into how African American student s perform in mathematics is their attitude
29 towards education and academic self-concept. A dichotomous view of attitude and academic self-concept was defined and examin ed in this section. The importance of these two constructs is briefly expounded upon. African Americans attitudes about edu cation and academic behavior have been shaped by their experiences with achievi ng the American Dream or observance of others striving to achieve the dream (Ford, 1993; Mickelson, 1990; Ogbu, 1986). Unfortunately, some African American childre n witness the death of the American dream in their communities by observing the continue d struggle of those who have completed some form of education. An awareness or obs ervances of inequities in employment such as practices that inhibit qualified minorities in the job market affect students motivation and achievement (Ford, 1993; Mickelson, 1990). As a result, African American youth are cognizant that their educational gains may not guarantee them the same success or rewards as their White counterparts. The circumstances resulting in this death occu r as African American youth observe members of their racial-ethnic group outside of school. In addition, African American youth experiences leading up to this aforementioned death are also manifested as a result of their negative experiences in the school sy stem, which is a microcosm of the rejecting and discriminating environment many might face as adults. Researchers associate social structures that perpetuate di scriminatory practices that imply one must assimilate and accept European standards of behavior and va lues with the low academic achievement of many African American students (Ford, 1983; Gay, 2002). These discriminatory practices limit access, opport unities, and demand conformity (Ladson-Billings, 1997;
30 Ogbu, 1986; Sleeter, 1997). Therefore, when examining the achiev ement of African Am erican students, researchers must probe beyond descriptive, demographic variables such as parents education and socioeconomic status. In addition to parents educati on and whether or not a child is living in poverty, assessing and understanding the attitudes, beliefs, and experiences of the child and his/her family ar e also essential in unraveling why a child is not achieving well in school. Demographic data are important to provide necessary support to families. For instance, these data could lead to referrals for (a) parent education programs to help parents assist their children at home with academic or behavior difficulties, (b) respite or support programs for health care issues, and (c) financial assistance (i.e., agency to help find job or attain job skills). However, this information may not help educators develop strategies in which they can directly intervene to address the gap in achievement among African American students (Ford, 2005). For example, one cannot use demographi c data in isolation to explain why two African American children from the same neighborhood, a single pare nt home, and living in poverty are having different expe riences at the same school. In developing reform methods to help African American students, researchers should consider data about students perceptions related to the utility of an educational degree along with the data many educators typi cally examine such as family demographic variables (i.e., socioeconomic status, parents level of education, and family composition). Although these demographic vari ables help educators pinpoint barriers that are associated with less favorable family and student outcomes, they alone cannot
31 explain achievement and underachievement among Blacks (Ford, 1993, p. 48). In fact, Ford found that the impact of parents leve l of education, occupation, employment status, and primary caregiver on African American students perception of an education was minimal. Family achievement orientation wa s found to have a grea ter impact on African American students achievemen t orientation (Ford, 1993). Attitude and Achievement Students attitudes and the effect of family, school, and community variables have been studied in an effort to understand ach ievement among African American students. Mickelson (1990), Ford (1993), and Sanders (1998) expounded on how the experiences, attitudes, and perception of significant others affect academic achievement among African American students. Mickelson (1990) investigated the impact of abstract and concrete attitudes on academic outcomes. This study examined the significance and relevancy of abstract and concrete attit udes when predicting achievement, in which cumulative high school grade point average was used as a dependent variable. Mickelsons primary purpose was to use the data to explore the attitude-achievement paradox among African American adolescents. According to Mickelson, an individual has two belief systems, abstract and concrete. Mickelson defined abstract attitude s toward education as beliefs shared by the general population, which reflec t the American Dream. Abstra ct attitudes are based on the dominant American ideology that holds that education is the solution to most social problems (1990, p. 46). As for concrete attitude s, they are formed by the realities of life an individual experiences in regards to what education has provided for people in his/her
32 community and/or family. Simply stated, concrete attitudes are a re flection of students perceptions of their probab le returns on education from the opportunity structure (Mickelson, p. 46). Mickelson defines the attitude-achievement paradox as a discrepancy in ones attitude or belief about edu cation in comparison to ones performance. The African American community has embraced education as a valuable vehicle for achieving success as far back as slavery (Mickelson, 1990; Morgan, 1995; Perry, 2003). Sanders (1997) also supports this claim stating that, h istorically many African Americans have possessed a strong belief in and desire for lear ning that has been exhibited in an ongoing, collective struggle for educatio nal opportunity and equality (p. 84) and to also stress how African Americans desire and understa nd the significance of having an education despite achievement levels. Yet, African American students are performing below other racial groups despite this collective belief that education leads to success and a better life. Therefore to answer the ques tion, why is it that African Am erican students are lagging behind their White counterparts in academic s and are frequently identified for poor reading and mathematics performance, students experiences and the experience and attitudes of significant others must be considered. In relation to achievement, Mickelson posited that concrete attitudes significantly affect students performance in school. This hypothesis is supported by data, which revealed that the difference between abst ract attitude and performance is high among African American students. African American students belie ve that one can achieve the fruits of the American dream by excelling in their education, but their academic
33 performance is more reflective of their concre te attitudes about education. Consequently, the experiences and observations of African Am erican students, specif ically those that do not result in desirable returns, shape their beliefs and have a negative impact on their attitude toward schooling and grades (Mickelson, 1990). A significant difference between class groups was not observed (i .e., middle-class, working-class). Mickelson found that, in comparison to White students, African American students concrete attitudes about the utility of education were less hopeful. For instance, African American students unde rstood that doing well in sc hool could improve their chances of being successful. However, th eir experiences overshadow their ability to believe that an education will provide great er opportunities. This finding illustrates Neissers (1986) point that de spite African Americans desire to achieve, Blacks feel they have to work twice as hard for th e same rewards [afforded to their White counterparts]perhaps partly for this reason they have reduced their academic efforts, even though they still believe in the overall value of e ducation (Neisser, 1986, p. 46). When examining class difference across gender and racial groups, middle-class students are more positive about education than thei r working-class peers (Mickelson, 1990, p. 53). Various factors contribute to why some students succeed and others do not. These factors include resiliency and family support. Sanders (1998) found that church involvement and parental and teacher support had a significant and positive impact on the attitude and behavior of Afri can American eighth graders. She concluded that academic self-concept and school behavior influenced the academic achievement of these eighth-
34 grade students. In addition, Ogbus (1986) findings suggested that African American children are more likely to respond positivel y to the schooling experience when older people in their community usually obtain j obs, wages, and other societal benefits commensurate with their level of scho oling (Ogbu, 1986, p. 40). In conjunction, African American students who are reared in strong families enter schools with social and cultural capital that fosters school su ccess (Sanders, 1998). However, many African American students enter schools with cultural and linguistic ca pital that differs from the capital schools embrace resulting in fewer pos itive experiences and less opportunities for success. Generalizability of Mickelsons (1990) study is limited because the sample consisted of high school senior s enrolled in social studies. However, it reflects how an individual can be discoura ged when observing others, w ho did what society says you should do to be successful, continue to strugg le twice as hard for a quality of life many presume as guaranteed. In addition, it illu strates how witnessing family and friends encounter mobility barriers due to social structures can aff ect African American students persistency and will to achieve (Ogbu, 1986; Mickleson, 1990; Sanders, 1997). This study also provides data to support hypotheses and other findings that attempt to explain the achievement discrepancy between minor ity and nonminority students based on the effects of a caste system (N eisser, 1986; Ogbu, 1986). In es sence, to be born into a lower caste or castelike minorityis to grow up with the conviction that ones life will eventually be restricted to a small and poorly rewarded set of social roles (Neisser, 1986, p.4). This notion speaks to the experiences and negative reality African Americans face,
35 even today in the new millennium. These experiences exist because some individuals continue to believe that African American s are not capable, are culturally deprived, and/or disadvantaged due to their genetic makeup (Smedley, 1999). Self-concept and Achievement As noted previously, family and community variables have been associated with academic achievement as well as psychological variables such as self-concept, motivation, and attitude/beliefs. Failure and success are products of the following factors: aptitude and acquired skills; a motiva tion factor such as immediate or long-term effort; the difficulty of the task; luck; mood; and help or hindrance from others (Graham, 1988, p. 6). When examining the impact of psychological variables on academic achievement, it is imperative to consider ones need for academic competence (Jordan, 1981). To decipher why students fr om similar or disparate backgrounds achieve and some have limited success with academic experiences, researchers must consider if academic achievement is a desirable goal before equating data gathered as indicative of reasons for academic success or failure. For instance, assessing academic self-concept will provide knowledge pertaining to an individu als perception of th eir ability to learn and succeed in school (Sanders, 1998, p.392). However, assessing an individuals global self-concept will result in data that sp eaks to the totality of ones self-knowledge emanating from a history of interactions w ith others and evaluations of how one has coped with life (Jordan, p. 509). In essen ce, a correlation between global self-concept and achievement might lead to inconclusive or misleading data because one has not accounted for the unique contribution for academic self-concept and the need for
36 academic competence (i.e., competence is needed or sought by individual) (Jordan, 1981). Jordan assessed eighth graders from an urban school setting and found low positive correlations of global self-concept with academic achievement. However, he reported moderate correlations between academic self-concept and academic achievement as well as with the need for academic competence. These data were collected using self-concept scales, questi onnaires, and using composite grade point average in four subject areas, scores on sta ndardized assessments, teacher constructed tests, and teacher evaluation of student learning characteristic s. The unique proportion of variance accounted for by academic self-concept was statistically significant for male and female participants, which supports academic self-concept as a predictor of academic achievement. Such findings suggest that a stude nts belief in ones ab ility to succeed at academic tasks as well as understanding that related academic tasks are important must be addressed when tackling the issue of underach ievement and developing interventions. Academic self-concept is a construct that adds valuable information to the study of achievement. Self-concept is an all-encomp assing construct that influences aspects of learning and behavior and is sh aped by interactions with fami ly, friends, and institutions (Campbell-Whately, 2000). As home and primar y social networks si gnificantly play a role in shaping ones self-c oncept, school environments re inforce or have an adverse effect on self-image, self-esteem, and attit ude. Because many African American students are nurtured in home environments that embrace cultural, behavioral, or social perspectives and ways of doing that differ fr om the dominant culture, educators must be
37 mindful of school factors th at lead to negative self-c oncept among African American students. Summary Children in the United States are havi ng problems with fundamental mathematics skills necessary for success in mathematics (Lubienski, 2002; NRC, 2001). For instance, data gathered from the trend NAEP suggest th at students are having significant problems with computational skills. Co mputational skills are essentia l and without them students mathematical experiences are limited, impacti ng future choices (i.e., course selections and career) (Pelavin & Kane, 1990; Tate, 2002). On the whole, students are performing below the expectations of teachers and the public. Only 5% of U.S. students obtained partial mastery of knowledge and skills that are fundamental for proficient work (NRC, 2001, p. 55). Although the mathematic gains observed during the 1980s have not been evident in recent years, a gap between African Am erican students and th eir White counterparts has been persistent throughout the years. African American students are performing at least 4 years behind their White counterpar ts (Lubienski, 2002). Thus, students experiences must be taken into account when examining the gap. Various researchers have examined the gap in mathematics achievement and factors associated with overall achievement by mean s of quantitative and qualitative methods (Byrnes, 2003; Ford, 1993; Martin, 2002; Matthew, 1984; Mickelson, 1990; Moody, 2004). Exposure, motivation, and parent education were found to be more predictive of mathematic success (Byrnes, 2003). Howeve r, these factors were impacted by the
38 attitude and experiences related to mathem atics of parents an d other significant individuals in the students lif e, students attitudes toward mathematics and determination to overcome obstacles, and instructional practices (Lubienski, 2002; Matthews, 1984; Martin, 2002). Although researchers have examined issues related to the mathematics gap, an investigation of students overall schooling experiences in mathematics has not been conducted to understand why some student s are succeeding while others fail. Researchers have used quantitative data to examine reasons for and contributing factors to the mathematics gap and have used quantitative methods to assess the students present experiences or adults recollection of past experiences. However, it is important to connect the quantitative data w ith students experiences. Therefore, a goal of this study was to c onnect students achievement and personal experiences to explain factors that may contribute to understanding and closing the mathematics gap. Factors such as motivation, self-concept, attitude, and family and school influences were expl ored as the basis for unders tanding and communicating the differential mathematics experi ences, perceptions and beliefs related to mathematics, and mathematical behaviors of African-American students. In addition, studies have not probed the experiences of White students as a part of the puzzle in understanding the mathematics gap. This study was designed to investigate the mathematical experiences of African-American and White students as a means to understand the gap in mathematics achievement.
39 Chapter III Method This study used a mixed-method design to determine if Afri can American (AA) and White students have differential mathem atics experiences and what factors these students perceived influenced their attit ude toward mathematics and mathematics performance. The use of triangulation procedur es increased reliability and validity of the data. Triangulation aids in corroborating findings and reducing biases that might occur from reliance on one method (Gall, Borg, & Ga ll, 1996). Therefore, both qualitative and quantitative data were collected. The use of a mixed-methods approach a llowed the voice of African American and White students to be heard as they shared th eir experiences related to mathematics. The mixed-methods approach was aimed at unders tanding participants experiences from their perspectives. In previous research, the mathematics experiences of students have been analyzed using numbers derived from standardized assessments and surveys. Although quantitative data provid e meaningful information, th e practical significance and utility for informing practice may be limited. Therefore, focus groups, interviews, and an attitude inventory were used to address this studys research questions: 1. What are the attitudes of excelling and struggling African American and White high school students toward mathematics? 2. To what extent do excelling African American, struggling African American, excelling White, and struggling White students differ in terms of
40 home/community factors they believe influenced their experiences in mathematics? 3. To what extent do excelling African American, struggling African American, excelling White, and struggling White stud ents differ in terms of school and mathematics classroom factors they believe influenced their attitudes toward and their performance in mathematics? Recruitment and Selection of Participants Participating Schools Before entering the schools, the research er obtained approval from the University of South Floridas Institutional Review Board and the school district located on the Gulf Coast of Florida to conduct th e study. After obtaining distri ct approval, the researcher contacted schools in the distri ct, but was unsuccessful in obt aining approval from school principals to conduct the resear ch in their schools. Due to initiatives required by schools not meeting adequate yearly progress, princi pals believed their sc hools were inundated with school improvement efforts and chose not to participate. The se lected school district had a limited number of schools with diverse populations and those schools with diverse populations were overwhelmed by Federal init iatives to address student achievement, thus limiting the number of schools in which the study could be conducted. Consequently, the researcher identified another school distri ct in which to conduct the study. This change allowed for a larger pool of schools from which to select participants and an increase in the chances of finding a school to gather th e number of African American and White students needed for the participant groups.
41 Four school principals agr eed to allow their schools to participate in the study. Due to one schools schedule and space cons traints, limited teacher participation or consistency, and students not re turning parental consent forms, three of the four schools were retained in the study and served in different capacities. Tw o urban schools and one suburban school particip ated in the study. Demographic characteristics of the part icipating schools are reported in Table 1. All participating schools were identified as Title I schools and included magnet programs. Each schools population was comp rised of 50% or more students who were eligible for free or reduced lunch (i.e., econom ically disadvantaged). In addition, there were a higher percentage of African American students than any other racial group enrolled in each school. Table 1 Percentage of Students at Participating Schools ______________________________________________________________________ School School School A B C ______________________________________________________________________ Demographics White 26 14 24 Black 34 72 41 Multiracial 4 2 5 Hispanic 28 11 24 Asian Pacific Islander 7 2 6 American Indian/ Alaskan Native .26 .30 .30 Economically Disadvantaged 50 78 54 According to NCES data, School A had a student teacher ratio of about 17
42 students per teacher during 2007-2008, while Schools B and C had reported about 13 students per teacher and approximately 19 st udents per teacher, respectively (NCES, 2008). In 2009, 83% of the School A's White st udents scored at or above grade level in mathematics on the Florida Comprehensive Achiev ement Test (FCAT). It is important to note that ninth and tenth grade students ach ievement scores are used for high school FCAT reporting. As for African American students in School A, onl y 43% scored at or about grade level in mathematics on the FCAT. When reviewing these data for School B, we see that a similar percentage of the African American student popul ation scored at or above grade level in mathematics on the FC AT (43%). Since Sc hool Bs number of White student represented less than 15% of the schools pop ulation, their scores were reported by grade level. For example, 93% of ninth grade and 94% of tenth grade White students scored at or above grade level in mathematics on the FCAT. Finally, in School C, 71% of African American and 82% of White students scored at or above grade level in mathematics on the FCAT. Selection Process A purposeful sampling technique was used to select participants and to accomplish the goal of understanding the mathematical experiences of African American and White high school students (Gall, Borg, & Gall, 1996). Specifically, the type of purposeful sampling used was criterion sampli ng, in which criteria were established for selecting participants. Initially, the criteri a targeted high school students enrolled in Algebra I and those identified as excelling or struggling in mathematics. However, the criterion related to Algebra I course enro llment was broadened to include students
43 enrolled in any mathematics high school course. The following definitions detail the criteria used to identify students as excelling and struggling: Excelling students: These were students whose cumulative records indicated that they received all A or B mathematics course grades since eighth grades. For the most part, students in this group were enrolled in advanced mathematics courses or courses on target for their grade level. However, this group also included one student enrolled in a remedial mathematic s course and one student enrolled in a mathematics course below the target ed course for grade level. Struggling students: These were students whose cumulative records indicated that they received all D or F mathematics course grades since eighth grade. Students in this group primarily were enrolled in courses on target for their grade level or in remedial mathematics course. This group also included one student enrolled in an advanced mathematics course and f our students enrolled in a remedial mathematics course. Targeted course for grade level: The school districts course sequence chart illustrates students progression through mathematics over a five-year period. The map is designed for students in the eighth grade through twelfth grade. The first course on target for eighth and ninth graders is Algebra I and Algebra I Honors for those ninth grad ers on the Honors track. During the first phase of participant recruitment, the mathematics department head at each school was contac ted. The department head was asked to provide names of Algebra I teachers to participate in the nom ination process. Algebra I was selected
44 because it is considered the gatekeeper to advanced mathematics courses (Tate, 2002). Once teachers were identified, teachers were in formed of the study and the procedures for selection, and asked to assist by nominating students. Although teachers nominated a list of students for the study, part icipation was on a voluntary basis contingent upon return of parent consent forms. Participating student s were required to submit a signed parental consent form and a signed assent to partic ipate. Teachers nominated possible student participants based on current grades a nd cumulative mathematics performance. Cumulative mathematics school performance was based on grades earned from eighth grade up to the students curre nt grade level. Teachers used cumulative mathematics performance (i.e., student transcript) in c onjunction with students current grades to determine if a student should be placed in an excelling or struggling group. Using these criteria, students were alphabetized on a roster by race and gender as either excelling or struggling. The department chairs emailed thes e lists to the research er. The groups were organized as follows: African American students excelling in mathematics African American students struggling in mathematics White students excelling in mathematics White students struggling in mathematics The process of gaining parent consent was complex. When the researcher met with the students to explain the study and disse minate consent forms, they appeared to be interested in participating. The researcher visited each participating school a minimum of three times after explaining the study to the students to check if teachers had received
45 parent consent forms. During each visit, additional consent forms were distributed to students who indicated that they had lost the form, left the signed form at home, gave the signed form to a teacher, or simply forgot. As recruitment continued throughout the du ration of the study, the researcher addressed the problem with students forg etting or misplacing the form or teachers misplacing forms by mailing consent forms to interested participants. However, this change yielded few additional participants. Of approximately 60 parent consent forms mailed, two signed consent forms were receive d. The following year, the researcher implemented the original plan of dissemina ting consent forms to the interested students and increased the amount of co mpensation for participation. To increase the return of consent forms, all students were informed that if signed or unsigned forms were returned, they were eligible for a random drawing of one fifty dollar gift card. Each participan t received a ten dollar gift card to a local store. The gift card was given immediately after each of the final focus group sessions. Students were informed that the payment included thei r time for completing the inventory and participating in the focus groups or interviews. Early in the study, the decision to samp le students from Algebra I was changed due to the inability to obtain a sufficient number of White students. The researcher subsequently learned that many White st udents completed Algebra I prior to 9th grade. As a result, only a few White students enrolle d in Algebra I were available for possible participation. However, these few were either not interested in participating or did not return forms. Therefore, the sample was co mprised of students enrolled in a high school
46 mathematics course without th e Algebra I only restriction. Participants School A was used to gather pilot data School B was used to gather the study data, and School C was used to gather intervie w data. The capacity in which each school served was predetermined and originally i nvolved primary study data being collected at each school. However, the capacity was ch anged as an outcome of the number of students available to participate. The number of each schools participants was based on the number of students who returned consent forms. The composition of participants included students from a pilot study and the primary study. The final participant sample included 32 students enrolled in mathematics courses in three high schools. Demographic characteristics of the sample are reported in Tables 2 and 3. The sample was comprise d of 22 African Amer ican students and 10 White students. As shown in Table 2, there were more African American participants and students enrolled in grades 9 and 10 th an grades 11 and 12. Amongst the African American group, there was an equal number of excelling and struggling students. Although fewer White students participated, the majority of particip ants from this group were excelling students and those en rolled in grades 9 and 10.
47 Table 2 Participants Academic Information ______________________________________________________________________ African Americana Whiteb ______________________________________________________________________ Gender Female 12 5 Male 10 5 Grade 9th 10th 18 7 11th 12th 4 2 Performance Excelling 11 6 Struggling 11 4 Math Courses 1-2 17 5 3-4 3 2 5-6 2 2 Note The table represents data reported by participants on Demographic Questionnaire bOne student did not report grade level or number of math courses taken. The participants included students receiving services in the exceptional student education program and illustrated in Table 3. Four African American students were identified as having specific learning disabilities and/or spee ch and language difficulties. Two White students qualified for services in the gifted program. Data about exceptional student educational services were no t collected for p ilot study students.
48 Table 3 Participants Background Information (excluding pilot groups) ______________________________________________________________________ African American White ______________________________________________________________________ Grade Point Average A/B 4 6 C 2 0 D/F 7 0 Exceptional Student Education Servicesa 4 2 Retained 2 0 _______________________________________________________________________ Note These data were gathered from the pa rticipants cumulative files. Students fr om the pilot study are not represented. aThe services include gifted services. The extracurricular activitie s of the participants were included to understand the students interests outside of mathematics. Th ese data are reported in Appendix A. When examining the types of activities in which st udents were involved, the African American struggling students were less involved in clubs or organizations with an academic/vocational focus. These students we re either not involve d in activities or involved in athletic focused activities. Five out of 11 African American students indicated participation only in athletic focused activities. Furthermore, there were four out of 11 who did not particip ate in school activities. The remaining three African Americans and four Whit e excelling students indi cated participation in academic/vocational focused activities or a combination of academic/vocational focused and athletic activities. The range of mathematics courses taken by African American and White excelling students, which included 9th through 12th graders, was two to five. The White
49 struggling students, which comprised 9th graders only, indicated th at they had taken one course. The African American st ruggling students, which included 9th through 10th graders, had taken 1-2 cour ses (with the exception of one student, who had taken 3 courses). Table 4 lists the students enroll ed in various mathematics classes from intensive mathematics classes to AB Calculus. Table 4 Mathematics Course ________________________________________________________________________ African American White ____________________________________________________ Course Excelling Strugg ling Excelling Struggling ________________________________________________________________________ Course Intensive Math 1 4 Algebra I 7 5 4 Geometry 1 Algebra II Honors 1 2 Trigonometry 2 AP Stats 1 1 AB Calculus 1 Note These data do not include pilot study participants. Data Collection The qualitative data were gathered usi ng the demographic questionnaire, focus groups and interviews. Quantitative data we re gathered via an attitude inventory, specifically, the Attitudes Toward Mathema tics Inventory (ATMI). Before each focus group, the researcher administered the ATMI and demographic questionnaire to all participants. Questions addressed in focus groups and interviews were designed to have students discuss constructs measured by the ATMI and their mathematical experiences. These ATMI constructs were self-confiden ce, value of mathematics, enjoyment of
50 mathematics, and motivation. The demogra phic questionnaire was used to gather information about parents in the home, the number of mathematics courses taken by participants, and participants extracurricula r activities and favorite school subjects. The ATMI and demographic questionnair e were administered using a group administration format. Prior to the focus group discussion, the ATMI was distributed to each student so that a group of individua ls could complete the inventory and demographic questionnaire at one time. The format allowed the res earcher to read the instructions and each item of the inventor y to limit the impact of possible reading disabilities, difficulties, confus ion, or other impairments. However, this was offered as an option and not a requirement for each group. To link ATMI data to interview da ta while still maintaining student confidentiality a coding procedure was used. The researcher created a four-column list that included students names in the first colu mn and then in the second, third, and fourth columns the unique number assigned to each name This list was printed on labels. The first label remained on the student list a nd the second number label was put on the ATMI and the third number label was put on the in terview notes. This information was kept confidential. Focus Groups Eight focus groups were conducted to allo w students to share their thoughts and describe their experiences. Each group cons isted of 4-6 participants. Due to student absence, two focus groups contained only two participants (i.e., pilot group and primary study group). The students were separated into the excelling or struggling group to
51 address the aforementione d research questions. The purpose of having homogeneous groups, based on performance and race, was to give the students an opport unity to openly share their experiences in a group with peers who may share similar cultural and mathemati cal experiences. The assumption was that students grouped by common characteristics would allow for uninhibited dialogue amongst the participants. The intent was to al so limit the possibility of peer pressure, which may influence how students respond to questions. The groups were labeled as AA students excelling in mathematics, AA students struggling in mathematics, White students excelling in mathematics, and White students struggling in mathematics. During the focus group, a name card was used to identify each student. The name card allowed the researcher to direct questi ons to students. To prevent students from disclosing identifiable information, the name car ds used student initi als in reverse along with middle initial. For example, a stude nt named Kisha Mahogany Jones, would have JMK written on her name card. The researcher facilitated the focus group discussion. The facil itators role was to direct the discussion and take notes (Krueg er & Casey, 2000). A research assistant was present during the focus group discussion to ope rate audio and video tape and attend to unexpected interruptions (Krueger & Case y, 2000). The research assistants, one undergraduate and one graduate, worked sepa rately. Prior to collecting data, both research assistants were given a review of how focus groups are conducted, a list of the guiding questions, and an explan ation of her role as descri bed above. In addition, both research assistants were given an opportunity to ask questions pert aining to the study and
52 procedures. Interviews As a means to provide readers with an in -depth understanding of the experiences students discussed during the focus groups, tw o interviews were conducted. The intent was to use randomly selected participants from the focus groups to illustrate a comprehensive picture of a few students e ducational triumphs and battles endured to excel in mathematics as well as a depiction of the struggle, if applicable. The researcher also planned to use a semi-structured inte rview approach using open-ended questions based on follow-up inquiry from the focu s group sessions. Although semi-structured interviews were conducted, the in terview participants were not focus group participants. The interview participants were two White excelling stude nts from School C. This choice was made because there were a limited number of White part icipants in the study and the researcher determined that their voi ces needed to be heard and would add to the knowledge obtained from the White excelli ng focus group. The interviewees ATMI surveys and interview data were encompassed with the White excelling group. The principal investigator used pr obing techniques to prompt partic ipants to elaborate and to obtain a deeper understanding of the individu als experiences and perspectives. For example, as a probing tactic, the researcher as ked the student to tell me more about that when a student gave an unclear or terse response. Review of Educational History To provide additional data about each st udents educational history, a review of student records was conducted. Information such as grades in all subjects, standardized
53 test scores, and number of mathematic s courses taken was used as background information to describe the students and a dd information pertinent to the students experiences. The permission of each schools principal was obtained before the researcher reviewed students records. This re view process also was disclosed as part of the parental consent and st udent assent process. Historical, demographic, and extracurricula r activity data were used to describe and understand the dynamics of each focus group and interviewee (see Tables 4 and 5). These data were gathered from cumulati ve records review and the demographic questionnaire. The groups will be referred to by number in order to provide a composite overview of each group (e.g., Group 1). The composites are as follows: Group 1: This group was comprised of four White female students from School A. The students were identified as struggling. These 9th grade students were enrolled in Algebra I and had only taken one course at the time of the study. Students ex tracurricular activities range d from participation in programs with a focus on college preparation for low-income students, programs with a military focus, and programs with a focus for on the job training. Group 2: This group included four Wh ite male students from School B. These students were identified as excelling students in grades 10th and 11th. The students were enrolled in Al gebra II Honors, Advanced Placement Statistics, or Advanced Placement Calcul us. Each student in this group had taken two to five courses. Accordin g to the school districts mathematics
54 sequence chart, the classes were advanced classes for their grade level. Their extracurricular activities included programs with a focus on military skills, academic achievement, foreign language enrichment, and robotic or technological design. Group 3: African American male and female students identified as excelling in mathematics comprised this group. There were two students, a 9th and 10th grader. Each student had taken two cour ses prior to the study. At the time of the study, the students were enrolled in Algebra I at School A. Unlike the 10th grade male enrolled in a mathematics course below the targeted mathematics courses for his grade level, the 9th grade female student was enrolled in a mathematical course targeted for her gr ade level. The male student indicated that football was his only extracurri cular activity. The female student indicated that she did not participate in extr acurricular activities. Group 4: This group was comprised of African American students identified as excelling. There were five student s, three males and two females. The students were enrolled in Algebra I at Sc hool B. There were four 9th graders; these students had taken one course prio r to the study and were enrolled in a targeted mathematics course for their grade level. This group included an eleventh grade student who had taken four mathematics courses prior to the study and was enrolled in a mathematics course below courses targeted for his grade level. The 9th grade female and male indicat ed that their extracurricular activities included sports. The othe r three students did not indicate
55 participation in extracurricular activities. Group 5: Four African Americans comp rised this group from School B. The group included three females and one male Three of the students were in 12th grade and one in the 9th grade. The 12th grade students had taken four to five courses prior to the study and were in a mathematics course targeted for their grade level or a more advanced clas s (e.g., two students in trigonometry and one student in advanced placement statistics). The 9th grade student had taken two courses prior to the study and was in intensive mathematics, which was below the targeted mathematics courses for 9th graders. Their extracurricular activities ranged from sports to computer technology. Group 6: African American struggling students from School A were included in this group. The group included four 9th graders and one 10th grader. Each student had taken one to two courses prior to the study. The students were enrolled in Algebra I at th e time of the study. The 10th grade student was the only one in a mathematics course below the targeted mathematics courses for 10th grade. Group 7: This group consisted of four African American struggling students from School B. The students were 9th graders enrolled in Intensive Mathematics and each student had taken two courses prior to the study. Thus, the students were enrolled in a course below the targeted mathematics courses for their grade level. One student indicated participation in an extracurricular
56 activity that focused on college prepar ation for low-income students. Group 8: This group was comprised of two 10th grade African American students identified as struggling in math ematics. There was one male and one female student. The male student was enrolled in geometry, which was a targeted mathematics course for his grad e level. The female was enrolled in Algebra II honors, which was an advan ced mathematics course. The students had enrolled in two to three mathem atics courses prior to the study. The female students extracurricular activ ities included sports and the male students activities included band. Interviewees: Two student s were interviewed from School C. These were White students identified as excelling in mathematics. They had taken one to two courses prior to the study. At the time of the study, the 9th grade students were enrolled Algebra I honors, which was an advanced, targeted mathematics course for their grade level. The fema le students extracurricular activities consisted of participation in clubs gear ed toward a health occupation and sign language. The male student participated in sports and clubs geared toward industrial organizations. Instrumentation Attitudes Toward Mathematics Inventory In an effort to collect quantitative data to supplement the qualitative data, the Attitudes Toward Mathematics Inventory (ATMI) was used to assess students
57 perceptions, motivation, and values related to mathematics. The ATMI is an instrument designed to assess the attitudes of secondary school students, specifically those in grades 8 through 12 (Tapia & Marsh, 2004). The i nventory measures the following four constructs: self-confidence, value of mathematics, enjoyment of mathematics, and motivation. The ATMI consists of 40 items and uses a Likert-type response scale format. Students were asked to rate items on a five-point scale from strongly agree (5) to strongly disagree (1). The ATMI takes appr oximately 10 to 20 minutes to complete. Tapia and Marsh (2004) used the ATMI to assess 545 high school students. The only student characteristic discussed in th eir study was gender ( 302 boys and 243 girls). Information pertaining to race/ethnicity or socioeconomic status was not provided. To determine the four factors the authors used an exploratory factor an alysis that involved extraction and a varimax, orthogonal rotation (Tapia & Marsh, 2004). Tapia and Marsh used the Kaiser-Guttman criterion and Cattells scree test to determine what factors to retain. By connecting items to variables, content validity was measured using a fourfactor model. The scores for items measur ing Factor I (self-confidence) had a Cronbach alpha of .95, items for Factor II (value) had a Cronbach alpha of .89, items for Factor III (enjoyment) had a Cronbach alpha of .89, and items for Factor IV (motivation) had a Cronbach alpha of .88. After Tapia and Mars hs a four-month follow-up with 64 students from the previous administration, test-retest re liability resulted in the following Pearson correlation coefficients: self-confidence (.88), value (.70), enjoyment (.84), and motivation (.78) (Tapia & Marsh, 2004). As a result, Tapia and Marsh (2004) concluded that the ATMI yielded reliabl e subscale scores. The following are the items associated
58 with each construct: (a) Self-confidence: Items 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, and 40 (b) Value: Items 1, 2, 4, 5, 6, 7, 8, 35, 36, and 39 (c) Enjoyment: Items 3, 24, 25, 26, 27, 29, 30, 31, 37, and 38 (d) Motivation: Items 23, 28, 32, 33, and 34 Focus Group and Interview Questions In Table 5, the questions used in this study were designed to prompt discussion about students experien ces related to beliefs and attitude s, curriculum, in structional and remedial strategies, peer relationships as well as parental, community and teacher support. For instance, partic ipants were asked to share information about obstacles, strategies used to succeed, experiences in school, likes and dislikes pertaining to mathematics instruction and available cour ses. Appendix C ha s a list of guiding questions that were used to gather data for both focus groups and interviews. In addition, Appendix C includes a pool of questions that were used for additional probing for both focus groups and interviews.
59 Table 5 Data Source for Research Questions Research Question Data Source Research Question 1 Attitudes Toward Mathematics Inventory (ATMI) Appendix C: Questions: Question 4and probing questions Question 7and probing questions Question 8 and probing questions Research Question 2 Appendix C: Questions: Question 1 and probing questions Question 6 and probing questions Research Question 3 Appendix C: Questions: Question 2 and probing questions Question 3 and probing questions Question 5 and probing questions Question 6 and probing questions Pilot Study The pilot groups were from School A. A pilot study was conducted to evaluate the procedures as well as the wording of focus group questions. The pilot study was conducted after students were identified and grouped by race and by performance (i.e., struggling and excelling). Three pilot focus groups were conducted (1 AA excelling group with 2 members, 1 AA struggling group with 5 members, and 1 White struggling group with 4 members). Due to consent fo rms not being returned, a White excelling
60 group was not a part of the pilot study. The procedures outlined unde r the data collection section were implemented. In addition to the researcher eval uating the procedures, the pilot study participants input was valued and gathered to inform procedures for the primary study. Upon completion of the ATMI and focus groups and before students were dismissed, they were asked questions pertaining to th eir understanding of focus group and interview questions and their understanding of inventory directions and statements. Participants input regarding the grouping system also was gathered (i.e., African American and White students separated in groups). Based on student feedback and active part icipation, data collection procedures proposed were modified only slightly. Instead of two or three focus group sessions for 90 minutes, the pilot study partic ipants participated in one focus group, which provided enough time to collect data within 30-50 minutes Therefore, the subsequent groups that were involved in the primary study met for one focus group session. Students commented that the studys questions and expectations were unde rstood and rephrasing, deletion, or the addition of ne w questions was not required. Thus, it was determined that the proposed amount of time needed for the focus group could be reduced from approximately 90 minutes over one to two sessions to 30 minutes in one session. Principals and teachers perceived this as a favorable change. Data Analysis This section describes the data analysis procedures used to address the research questions. First, the analysis of the quantitati ve data is discussed. Then, the analysis of
61 qualitative data is explained. Inventory Data Descriptive analysis of the ATMI data was conducted to examine the four constructs. The information consisted of th e mean, standard deviation, range, skewness, and kurtosis. These data were used to desc ribe scores for each set of variables and to integrate the data with the qua litative analysis. For instan ce, a particular groups (e.g., excelling AA) mean score for the motivati on construct was linked to focus group and interview discussions related to motivating factors which fostered their success in mathematics. The scores were examined within and across groups. For example, a within-group analysis of scores for the st udents in the African American excelling group was conducted as well as for each of the othe r groups. In addition, the scores across groups were analyzed. Lastly, these data were summarized by gr oup and across groups to reveal students attitudes toward math. The ATMI data addre ssed research question one by providing a measure of students att itudes toward mathematics. In addition, during focus groups and interviews, student s expounded on their at titudes measured on the ATMI and the influential factors relate d to their mathematical experiences. Focus Group and Interview Data The focus group and interview data addr essed research que stions one through three, in which students provided informati on on mathematical experiences and factors that shaped their attitudes and performance. The researcher used analysis processes described by Creswell (2005), Bogdan and Bi klen (1998), and Mertens (1998). These anecdotal data were analyzed from the focus groups and interviews by determining core
62 themes. The researcher transcribed record ings from both focus groups and interviews by hand. To ensure reliability of transcripti on, an accuracy check was completed with a research assistant to verify transcription with participants spoken statements. For example, 20% of an audiotape or videotap e was played, the segment on the tape was located on the transcript, and then the research assistant determined whether the participants statement was writ ten as it was spoken. The transcript with pilot study data and primary study data totaled 25 typed singlespaced pages. Once transcriptions were prepared, member checking was used to confir m whether or not indi viduals experiences were accurately documented (i.e., thoughts, comments) (Gall, Borg, & Gall, 1996). The researcher returned to participating school s to conduct member ch ecking. During a oneon-one session with the resear cher, the participant was given an opportunity to review draft versions of the transc ript specific to his/her co mments during the focus group or interview. Since participants did not comment or request changes, revisions were not necessary. The principal investigator and resear ch assistant used recommended coding processes to identify core themes within th e transcripts (Creswell, 2005; Mertens, 1998). The research assistant was a graduate student in the College of Education with research interests in academic achievement. Due to the assistants limited experience with qualitative data analysis, the research assistant was provided guidance on the coding procedure. The guidance involved the researcher using selected portions of the transcript to describe what comprised a thought unit (a statement made by the participant) and how to categorize a thought unit using the list of existing themes derived from the literature.
63 Once the procedure was explained, a portion of the transcript was used to check for understanding. The research assistant was provided opportunities to ask questions. The coding of data occurred in several phases. The first phase involved the researcher and research assi stant reading through the tran scripts. During the second phase, a sampling of the pilot groups transcri pt was used to practice the process of questioning the meaning in a persons statemen t. The researcher and research assistant collaborated to ensure understa nding of this task. Once this process was understood, the process of coding thought units was accomp lished by assigning a code or phrase that generalized the meaning or the thoug ht expressed in a thought unit. The next phase involved determinin g agreement on the coded pilot groups transcripts. Once the procedure was explai ned, the researcher provided the research assistant with a sample to determine agreement and disagreement between coders to check comprehension and accuracy. The rese arch assistant was given opportunities to ask questions. Agreement was established by comparing the coded t hought units of the researcher and the research assistant. This agreement procedure was completed using the pilot group data in order to provide numerous opportunities for accuracy checking. The following formula was used to calculate agreement: agreement / agreements + disagreement x 100 = % of agreement (Coope r, Heron, & Heward, 1987). The agreement obtained was 80% or higher to indicate accura te and reliable coding. The criterion was met after using several samples of an entire pilot transcript. These phases aided in increasing the reliability of data coding so that the resulting data accurately reflected the students experiences as they related to the research que stions. Once reliability was
64 obtained, the researcher and the research as sistant worked independently on coding the themes. Next, the researcher and research assistan t, individually, used the transcripts to code thought units. Again, thought units (e.g., statements made by participants) were used to categorize information. Phrases or codes were used to provide an overall meaning of the unit (i.e., a students perspec tive about teachers will ingness to help). Once thought units were coded, the research er and the research assistant read through and compared coded units. The di scussion led to consensus building on the meaning of thought units and the development of existing and emergent themes. Existing themes were those derived from the literature on mathematics and the educational experience of African American students. The following existing themes were identified in the analysis: beliefs about importance of education; attitude toward mathematics; differential treatment by teachers; support fr om family, community and teachers related to academics; support from family, community, and teachers related to mathematics; and factors students report as contributing or hindering their success in mathematics. Additional or emergent themes were derived during the analysis of the data by grouping related thought units together to create a ca tegory that best fit the related units. Using this process the following themes were id entified: resourcefulne ss, goals/aspiration, anxiety, benefit of good grades, and guidance. For example, the impact of race on teacher and student interactions was a them e derived from the focus group or interview discussions.
65 Delimitations There were factors that were imposed by the researcher and those imposed by the school district that narrowed the studys targ eted sample. These f actors could have had an impact on the results and conclusions dr awn from the data. Thus, the delimitations were criteria used to define excelling and struggling students and the fluidity of the school districts student progression sequence chart in mathematics courses. The definitions related to excelling a nd struggling students did not delineate success based on level of mathematics cour se (e.g., intensive mathematics versus advanced placement calculus). For exam ple, the excelling group included students enrolled in advanced mathematics, targeted mathematics course for grade level, and remedial mathematics. Since the defin itions did not exclude students enrolled in remedial courses from the excelling group, the excelling group analysis of data included remedial students voice in an excelling gr oup. Thus, this delimitation could impact the internal and external valid ity of data, specifically cred ibility and generalizability. The second delimitation, districts mathema tics course sequence chart and fluidity of course offerings in the high school, restri cted the number of students accessible for a representative sample of White students enrolled in Algebra I at the high school level. This delimitation impacts external va lidity, specifically generalizability.
66 Chapter IV Results This chapter presents the results gathered from the attitude surveys, focus groups, and interviews. Descriptive statistics and reliability coefficients for the ATMI derived from its use in this study are presented. Students experiences from each of the four groups (e.g., African American excelling, White struggling) and interviewees are presented in the sections that follow. However, the interview data are discussed separately from the focus group data. Although p ilot study data are typically used to test procedures and to determine necessary change s to improve data co llection, the quality and the depth of information provided by pilot study participan ts rendered that information as valuable as the information fr om participants in th e actual study. To not include pilot study participants' experiences would have eliminated a great deal of insight about students mathematical experiences. Th erefore, pilot study data are included in the results for this study. The results are discussed by common themes or factors. These common themes and factors are based on findings from the liter ature as well as from themes or factors derived from the analysis of the focus group data. These data highlight what students voiced about their attitude toward mathematics and the factors that led to negative or positive mathematic experiences.
67 Attitude Towards Mathematics Insight into students at titude toward mathematics was provided through an analysis of the ATMI survey data as well as focus group and interview data. The ATMI results are presented first, followed by the relevant focus group and interview data. These data are aggregated by r ace and performance level. Data from the ATMI Tapia and Marsh (2004) designed the ATMI to gather data regarding students level of self-confidence, value, enjoyment, and motivation in the area of mathematics. It is important to note that the self-confidence c onstruct also measured feelings of anxiety related to mathematics. To understand th e meaning of the survey data, Tapia and Marshs scale ranking is used to depict how students rated themselves along each of the constructs measured using the ATMI. Tapi a and Marsh based the means on a scale from 1 to 5, in which 1=strongly disagree, 3=neutral, and 5=strongly agree. In this study, as shown in Table 6, th e ATMI data were analyzed using the Statistical Package for the Social Scien ces (SPSS). Means, st andard deviations, skewness, kurtosis, and reliability were de rived for each subscale of the ATMI. A twoway ANOVA was used to determine between and within group differences related to race, gender and performance (i.e., excelling or struggling). An alpha level of .05 was used for all statistical tests. As for variability, the standard deviati on for each subscale indicated that the scores fell close to the mean. The score di stribution for self-confidence (skew = 0.29) was positively skewed, while the value (skew = -0.99), enjoyment (skew = -0.38), and
68 motivation (skew = -0.37) subscales had nega tively skewed score distributions. The negative kurtosis of the self-c onfidence (kurtosis = -0.14), en joyment (kurtosis = -0.55), and motivation (kurtosis = -0.07), subscales indicated that there were fewer extreme scores than what is found in a normal distribution. Table 6 Statistics of Attitudes Toward Mathematics Inventory: Pres ent Study (n = 32) _____________________________________________________________________ Subscale _____________________________________________________________________ Self-confidence Mean 3.50 SD 0.72 Skewness 0.29 Kurtosis -0.14 ______________________________________________________________________ Value Mean 3.80 SD 0.63 Skewness -0.99 Kurtosis 1.80 _______________________________________________________________________ Enjoyment of Mathematics Mean 3.39 SD 0.88 Skewness -0.38 Kurtosis -0.55 _______________________________________________________________________
69 Table 6 (Continued) Statistics of Attitudes Toward Mathematics Inventory: Pres ent Study (n = 32) ________________________________________________________________________ Motivation Mean 3.40 SD 0.76 Skewness 0.37 Kurtosis -0.07 ________________________________________________________________________ The reliability results for each subscale on the ATMI are presented in Table 7. Reliability coefficients (Cronbachs alpha) ranged from .75 to .92, with the self-concept scale being the highest and the motivation s cale having the lowest reliability. These results were similar to the Cronbach alpha coefficients Tapia a nd Marsh (2004) reported for each subscale: self-confidence (.95), va lue (.89), enjoyment (.89), and motivation (.88).
70 Table 7 Cronbach Alpha: Attitudes Toward Mathematics Inventory ______________________________________________________________________ Tapia and Marshs Present Studya Studyb ( N =545) ( N =32) ______________________________________________________________________ Subscale Self-confidence .95 .92 Value .89 .84 Enjoyment of Mathematics .89 .91 Motivation .88 .75 ________________________________________________________________________ Note The values represent the reliability for each subscale. abThere were 40 items on the inventory. A two-way ANOVA was used to analyze the main effects and interaction effects of each subscale across race and performance. One statistically significant main effect was found between the performance groups (e .g., excelling and str uggling) on the selfconfidence construct. The e ffect size comparing the two groups on the self-confidence construct was large ( d = 0.85). The self-confidence of the excelling group was higher. There were no other statistically significant main effects or interaction effects for the other variables on the ATMI constructs. T hus, performance differences on the value, enjoyment, and motivation constructs were not dependent on the race variable. In
71 addition, race differences on attitude cons tructs were not dependent on level of performance. Results from the two-way ANO VAs are presented in Table 8 and effect sizes for mean score main effects in Table 9. Table 8 F-Ratios and p -levels from Two-way Analysis of Variance for Each Subscale ( n = 32 ) Present Study: _____________________________________________________________________ Variable Performance Race P x R Level _____________________________________________________________________ Self-confidence 6.08 0.76 1.18 ( p = .02) ( p = .39) ( p = .29) ______________________________________________________________________ Value 0.44 0.82 2.32 ( p = .51) ( p = .37) ( p = .14) ______________________________________________________________________ Enjoyment of Mathematics 1.94 0.12 0.06 ( p = .18) ( p = .73) ( p = .81) ______________________________________________________________________ Motivation 3.14 1.10 0.03 ( p = .09) ( p = .31) ( p = .87)
72 Table 9 Effect size of ATMI Subscale scores by Performance Level and Race ___________________________________________________________________ Variable Performance Race ___________________________________________________________________ Self-confidence 0.85 -.046 ____________________________________________________________________ Value 0.65 -0.35 ____________________________________________________________________ Enjoyment of Mathematics 0.58 -0.21 ____________________________________________________________________ Motivation 0.77 -0.49 ____________________________________________________________________ Data from Focus Groups and Interviews Several themes were derived from the focus group data. The identified themes were: (1) that students e xpressed mixed attitudes with various factors identified as shaping their positive and negative mathematic attitudes; (2) the importance and utility of mathematics; (3) the influence of home/communityand school-based supports; and (4) the impact of mathematics classroom factor s, including those that students believed contributed to success and thos e that students believed hinde red their success. These themes encompass the experiences shared by the high school students. Thus, the following sections will highlight the students voices and support for the aforementioned themes. When examining the data from the excelling groups, data from cumulative review and demographic questi onnaires revealed that thr ee of the African American
73 excelling groups had one student in each group enro lled in a remedial course or a course below the targeted mathematics cour se for his/her grade level. Contributing Factors to Attitude Formation The students expressed mixed attitudes toward mathematics. Their responses varied in identifying whether they had a positive or negative at titude. Factors that shaped their attitudes shifted or remained constant and included students perception of their student-teacher relationships, students j udgment of teachers instructional ability, teachers temperament, students mastery of mathematics concepts, and students past performances in mathematics. Positive attitudes toward mathematics. Students in the White excelling group reported having positive attitudes about mathem atics. These students attributed their attitude to teachers ability to instruct, to encouragement from teachers, and to the harmoniousness of student-teacher relationships. Of the four students in the White struggling group, one indicated having an overa ll positive attitude while the others indicated a more negative attitude. For ex ample, the student in the White struggling group expressed a positive attitude towards mathematics that was rooted in ones confidence in his/her mathematic abilities. WT (White struggling group): Yes, pos itive, but my teacher doesnt explain things well. [For example]my teacher doe snt explain things well. He teaches a different method than the way I learned it in eighth grade. So I just do it my way. The African American excelling students, generally, expressed a positive attitude
74 in mathematics. Positivism was attributed to how well they performed in mathematics based on perceived innate abilities, the amount of effort he/she put forth, or comments teachers and parents made about their abilit y. Students reported feeling confident because of comments made by parents and/or teachers about their abilities. Students in the excelling group were also forthcoming a bout enjoying mathematics. Similar to some of the students in the White focus groups, so me African American students attitudes were influenced by self-confid ence in their mathematical abilities. For example: GZ (African American excelling group): I was always good at math. I like doing math. It was always easy for me. DG (African American excelling group): It is easy. I like to argue about formulas. Some of the African American excelling students i ndicated that their goals influenced their outlook on mathematics. Some students expressed a positive attitude in mathematics that was shaped by what they as pired to do in the future. The meaning of the future varied, in that it meant performan ce on the next test or in the next mathematics course. For others in this group, the futu re was adulthood and working. For example: BJ (African American excelling group): PositiveI know I will have to use math when I am older. So why not learn it now because when I get older I dont want to mess up with my money. Those students in the African American struggling group with positive attitudes spoke about becoming successful in life and/or were focused on overcoming obstacles to do better in mathematics such as difficulty pa ying attention. A focus on goals appeared
75 to be the root of their positive view towards mathematics, despite performing below their other peers. The following quote depicts this mindset: McClo (African American struggling group): It [mathematics] was difficult, but as I got in eighth grade it got better. I like it. Since I want to be a hairdresser, then I have to do all of my work. I need to know how to count my money. Negative attitudes toward mathematics. The students shared that unexpected poor performance in a mathematics class, strain ed student-teacher relationships, perceived ineffectiveness of instruction, and difficulty of mathematics content contributed to negative attitudes. For stude nts in the White struggling group, many indicated that their attitudes were shaped by their middleand high-school experiences. A student from the struggling group, who had a negative attit ude, attributed this mindset to being unsuccessful in a subject in wh ich she was once successful. LL (White struggling group): I have a ne gative attitude beca use Im used to having an A and now I have a D. Math used to be so easy, but now the math teacher we have cant teac h. So I dont understand it. A White student from the excelling group attributed his negative mindset to his attitude and the relationship he had with his teacher: RXA (White excelling group): My experien ces have been like a roller coaster because it is all about the relationship with the teache r and my attitude about the classwhether or not I want to be there or not. As for students in the African American excelling group who reported negative attitudes, they linked their attitudes to negative experiences due to ineffective teacher
76 instruction or disappointment re garding performance in a previous class. For example, a student from the excelling group reflected on a time when she had negative feelings about her mathematics class. She attributed her ne gativity to poor perfor mance in a past class and being around others who were excel ling in the particular class. Unanimously, all of the students in on e of the African American struggling groups reported negative attitudes in mathem atics because of the complexity of the subject. Students from a different African American struggling group expressed negative attitudes towards mathematics that surf aced from experiences in their current mathematics class. The students believed th eir negative attitude was a result of their teachers inability to teach. It was later found that the teacher was an international teacher with a strong accent, which made it difficult for the students to understand instruction. In the other Afri can American struggling group, th e majority of the students frustration was due to their pe rception that mathematics went from a subject they could understand to a challenging subject. For example: WC (African American struggling group): We really didnt do a lot of math in elementary school. We went from 1 + 1 to a + b. It went from fun to boring. BN (African American struggling group): It went from easy to hard. In sum, The African American and White excelling student s expressed having positive attitudes; similarly, these studen ts perceived themselves as good at mathematics. White excelling students focuse d more on how effective instruction shaped their positive attitudes. Ho wever, African American exce lling and strugg ling students and White struggling students expressed that the cause of their negative attitudes,
77 whether pervasive or specific to a particular mathematics class, was the ineffectiveness of the teachers instruction. Importance and Utility of Mathematics Another theme identified through the co llection of focus group data was the importance and utility of mathematics. Students, across both racial and performance groups, spoke of the importance and utility of mathematics as it rela ted to their present and future goals. In the White excelling group, students indicated that mathematics was important for bargain shopping, scheduling, sa ving money, and attaining a career. One student in this group viewed the amount of mathematics needed to be successful dependent upon ones career path. As fo r the White struggling group, they believed mathematics would be important for mana ging bills, furthering their education, and preparation for their careers. However, one student in the White struggling group viewed the use of mathematics limited to basic mathematic skills. For example: MD (White excelling group): It is import ant to a pointafter that it is more about specialization. RXA (White excelling group): I was thinking of an example of a sale two for five dollars. You have to know if you are saving money or not. Similar to the White students, African American students related the importance and utility of mathematics to everyday life and careers. Many of the students in the African American excelling gr oup believed that they would need mathematics for taxes, cooking, careers, school, and to survive in the world. One student shared how a shoe store gave him a mathematics test before he was hired. A second student indicated
78 needing to use mathematics when older as a reas on to learn as much as she could now. In the African American struggling group, st udents stated reasons mathematics was important, but one student questione d the utility of some of the skills they were taught in school. For example: BJ (African American excelling group): Wh y not learn it now because when I get older I dont want to mess up my money. I want to learn all the math I can. KG (African American excelling group): Everything requires math. Even if I wanted to throw a ball to you along with science. It is good for accuracy. DG (African American excelling group): For your taxes and cooking to measure stuff. DN (African American struggling group): For me I want to be a physical therapist. You cant do physical therapy without having science under your belt. You cant really do chemistry or anything without math. CW (African American struggling group): You may need it for your job, other than that math is not that useful. Influence of Home/Community and School Factors Focus group data also were used to understand how home/community and school factors influenced students mathematics attitudes and performance in mathematics. Across race and performance le vel, students expressed support s related to the impact of school and home/community. The common themes in this area guide the discussion that follows. Student identified schoo l-based supports. The students from each group reported
79 tutoring services in mathematics being available at their schools. These services were available after school and struggling students as well as African American excelling students took advantage of these services. Many students indicated that transportation was a limitation to access after school services. For example, in response to questions that inquired about where students get help for mathematics, students said: CC (White struggling group): I would see if I could get tutoring. LL (White struggling group): Yes, you have to sign up and go everyday and some people cant stay every day. WT (White struggling group): So people c ant get a ride every day. Like me, I cant get a ride. KK (African American excelling group): Ask my teacher and to the after school program. NB (African American struggling group): I go to the parkor ELP (extended learn program) after school tutoring. Students identified elementary and middl e school teachers and principals as persons who provided support through encourag ement and guidance. This sentiment was expressed across all groups. During their hi gh school years, a few White struggling and African American excelling a nd struggling students had diffi culty identifying teachers who provided an increased level or a commens urate level of support as elementary and middle school teachers. For example, in res ponse to questions inquiri ng about the type of help students received from their teachers, students said: WT (White struggling group): My eighth grade teacher was really nice. If you
80 dont get something, she would calmly explain it to you. We had it on the computers because we had to learn everything on the computers, but if you dont get it she would explain it. My teacher now, he is like come on you have to know this and you got it. But I dont get it. S (African American struggling group): I hat e to ask for help. In my class, he asks why are you not understanding or have you not been paying attention. LA (African American excelling group): In middle school it [teacher support] was. I still see my basketball coaches. White and African American excelling st udents were able to identify high school teachers who encouraged and supported their enthusiasm in mathematics. However, only White excelling students voiced teacher encourag ement to participate in extracurricular or enrichment activities relate d to mathematics. This group was the only one to express that teachers informed them about ways to a dvance their mathematic skills. For example: AR (White excelling group): With me, I had a teacher who encouraged me to join the math team. GZ (African American excelling group): A lo t of my teachers told me I was pretty good at math. KK (African American excelling group): My teachers have influenced me and that makes it seem easy. Student identified hom e/community support. Among all groups, the majority of students from each group identified one or more parents as contributing to their success. The type of parental support changed once st udents were enrolled in advanced classes or
81 classes beyond basic mathematics. For some students, the support cons isted of assistance with assignments along with encouragement in their earlier years with mathematics. When students enrolled in advanced classe s or classes beyond basic mathematics, students reported continued encouragement from parents with little assistance on difficult assignments. This was expressed by excelling African American and White students. For example: MD (White excelling group): My parents are really not the best in math so they cant really help me and if I am doing bad they encourage me to do better. RA (White excelling group): Now, one of the problems in my home is that I am more advanced in math when before they [parents] could help me but not so much now. GD (African American excelling group): My parents try to help, but I pretty much know more than they do. Each African American and White stude nt identified school and home supports that influenced their attitude toward mathematics and their mathematics performance. It was evident that each particip ant had one or two parents in the home to encourage their efforts in mathematics. There were two students among the African American and White groups that noted a non-relative as primar y support outside of school. The most significant difference was the absence of teacher encouragement for African American excelling students to participate in extracurr icular or enrichment activities related to mathematics.
82 Impact of Factors Relating to the Mathematics Classroom A final theme identified through focus groups data was the impact of mathematics classroom factors on their succes s in mathematics. These results are discussed first in relation to those factors students identified as contributing to su ccess. Lastly, those factors students identif ied as hindering their success are presented. Factors contributing to success. All students reported th at hands-on activities, the use of manipulatives and visual s, use of note-taking skills, use of group work, practice of giving step by step instruction, use of flashcards, and use of calculators contributed to success in the classroom. Specifically, White excelling students stated that hands-on activities allowed them to visualize a concep t and that teachers willingness to provide one-on-one assistance had a positive impact on their mathematics performance. These students viewed learning in groups as a common ground, mean ing, they were learning the same information as the other students. They viewed groups as a way to master a skill (i.e., helping others in the group fostered the helpers mastery of the skill) or as a way to challenge each others minds (i.e., working together and coming up with different ideas to solve a problem). White excelling students who participated in gifted classes during elementary and middle school expressed that having more than one teacher or a smaller class was helpful (i.e., low student to teacher ra tio). In this setting, teachers were more available to assist if they had difficulties with a problem. These students indicated that, in this setting, teachers spent extra time with students, which allowed for more encouragement from teachers and students obser ved that teachers displayed interest in their successes. As for White struggling stud ents, they preferred working in groups and
83 perceived it as a supplemental method when a teacher could not at tend to all of their questions and needs. Consequently, the support from their peers who understood the skill or concept sufficed. For example: Researcher: We talked a little bit about things or pe ople who have helped you in math. Describe that a little more. RXA (White excelling group): What has always helped me out is to be very hands on. In math it has always been about me be being able to see it and have it right in front of me. RA (White excelling group): Teachers who provided more one-on-one help has helped me. Researcher: How do you prefer to practice math skills such as group, independent, one on one? CC (White struggling group): A group so that we can help each other. LL (White struggling group): Yeah, so meone might get it better than you. Similar to the White excelling group, Af rican American struggling and excelling students expressed what worked for them in mathematics. Students indicated that learning songs, classroom competitions, using flash cards, using manipulatives, and stepby-step instructions were key in helping th em learn mathematics. One-on-one with the teacher and group work were also preferre d methods. African American struggling students stressed the following as beneficial: the use of the board to explain and provide examples, the teachers willingness to break dow n a concept, and the task of taking notes to use as references. For example:
84 Researcher: Did working in groups help you? HN (African American excelling group): A lot because somebody might know what they are doing. LA (African American excelling group): Yes and they [students in groups] can explain it better than the teacher. Researcher: What about different things teachers did in the classroom? Were there things they did for you to have a positive attitude in math or influence your performance? BJ (African American excelling group): Some taught you songs and stuff to help you. Researcher: What helps you learn math be tter such as activities or strategies? CW (African American struggling group): When it is step by step. NB (African American struggling): On the board and explaining and examples. Factors hindering success. Across race and performance level variables, students reported a teachers negative demeanor or la ck of willingness to provide supplemental instruction (e.g., breaking down instruction) as a hindrance to their success. In comparison to the White excelling group, the White struggling group s experiences with high school teachers who did not explain material or provide supplemental instruction overshadowed their overall mathematics experien ces. This group consistently reiterated how they were struggling due to teachers not having the patience to explain in detail or re-teach a concept. These students readily identified hindrances to their mathematics success such as teachers impatience and unwillingness to re-teach. For example:
85 WT (White struggling group): I might ask the teacher but he is so impatient with you. TT (White struggling group): They [teach ers] just tell you what to do and dont explain it. RXA (White excelling group): They [teachers] would put the math up on the board and hope they [students] understand it. Two of the students in the African American excelling group discussed the use of computers in eighth grade as a hindrance. On e out of six of these students viewed the use of computers as a great learning tool. The students comment illustrated his positive view of the use of computers for mathematics: HN (African American excelling group): Y ou get to move at your own pace. It teaches you first and makes you take notes then you take qui zzes, and at the end you take a test (talking about his experience with 8th grade math on computers). Many disliked the use of computers because it limited access to the teacher. This was true for excelling students as well as struggling students. For example: JL (African American excelling group): It is better with a teacher (talking about his experience with eighth grade math on computers). NB (African American struggling group): Yeah, when you are on the computers, math is kind of hard instead of being taught. African American students in both groups also reported that a hindrance outside of the classroom was their schools focus on wh at they did wrong such as arriving late to school and wearing clothing viewed by the scho ol staff as inappropr iate for school. For
86 example: Researcher: What are things that might hold you back from be ing successful in your community or school? LA (African American excelling group): Te achers at school. They suspend us for tardies or wearing the wrong clothes to sc hool. They want us to come to school, but suspend you for tardiness or wearing the wrong clothes. HN (African American excelling group): Yeah, or they suspend us for talking in class, not having your id, or absences. LJ (African American excelling group): They are always talking about the bad stuff. Across racial and performance groups, stude nts voiced that asking for help was a hindrance. Those students were apprehensive because of teac hers response to questions or peers response. Students reported that these issues lim ited their ability to take the initiative to ask for problems to be clarifie d. In these cases, students either relied on peers for assistance or dealt with the conseque nces of not asking for help. For example: LK (African American excelling group): because you think you might sound retardedyou dont want to hear other peoples [students] mouths. KW (White excelling group): Students w ould be afraid to ask questions if they didnt understandI havent be en able to ask a teacher if I dont understand it. CC (White struggling group): If you don t get it, they [tea chers] get fed up. Another hindrance was parents level of support. A few students reported that their parents expressed a dislike for ma thematics or a limited understanding of
87 mathematics. For those students, their pare nts dislike or limited understanding reduced the level or amount of support with ma thematics assignments. For example: Researcher: What kind of help have you r eceived from your parents to help you learn math? S (African American struggling group): Well, my mom never liked mathNo, so I dont get much help. WT (White struggling group): My dad dropped out in 11th grade. So he doesnt know. LA (African American excelling group): Theyll [parents] say we didnt do this. Data from Interviews The interviewees were two White students identified as excelling in mathematics from School C. The 9th grade students included one male and one female student. These students shared similar experiences to the students in the White excelling group from School B. The students expressed a positive att itude towards mathematics. When talking about her positive attitude, the female stude nt stated, I like math, its fun, and I do well. The male student was unable to give a ny specifics about his pos itive attitude other than, I just like math. When examining student statements regarding importanc e and utility of mathematics, the female student indicated that mathematics is important to get what you want in life. For this student, she indicated that she believes mathematics will help her get into college and become a veterinarian. As for the male student, he expressed that mathematics is needed to understand taxes and to get into college.
88 Home/community factors The female student indicated that her mother being a teacher pushed her to do good in math as well as people who dropped out of school as support and contributing factors to her succ ess in mathematics. The male student indicated that his mothers support influenced his mathematic experiences. He shared that his mother would scaffold support by making him figure out how to do problems and not tell him the answers. He describes this as his mother making it look like she was helping me. He indicated the questioning techniques his mother used helped him remember how to solve mathematic problems. School and mathematics classroom factors. The students shared that pictures or fun posters that help them understand concepts, strategies that help them remember steps, and group work were helpful in learning mathematics concepts. As for groups, the male student expressed that groups were helpful to learn other ways of doing math problems. The female student shared that groups were helpful because her peers could help her through a problem. The female student also st ated, good teachers help you want to do mathematics. She later added, I had really good teachers in 8th grade. We always worked in groups with mixed abilities. Ne ither of the students interviewed expressed hindrances to their mathematics success. Summary of Results The ATMI data and qualitative data we re analyzed to learn about students attitudes toward mathematics and what fact ors were perceived to contribute to their success or lack of success in mathematics. The identified themes derived from the qualitative data were: (1) that students expressed mixed attitudes with various factors
89 identified as shaping positive and negative mathematic attitudes; (2) the importance and utility of mathematics; (3) the influence of home/communityand school-based supports; and (4) the impact of mathematics classroom factors, including those that students believed contributed to success and those that students believed hindered their success. The students voices provided examples of how they perceived their mathematical experiences. In addressing research question one, thes e data indicated that African American and White excelling students agreed with statements on the ATMI that supported having self-confidence in mathematical abilities, valuing mathematics, enjoying mathematics, and being motivated to take more mathematic courses. However, except for students in the White struggling group reporting a simila r level of moderate agreement in valuing mathematics, African American and White stru ggling students ratings were more neutral in response to statements on the ATMI th at suggested self-confidence in ones mathematics abilities, enjoyment of mathem atics, and motivation to participate in mathematic courses beyond those required. The students responses on the ATMI were supported by comments regarding their attitude about their experiences. For th e majority of African American and White excelling students in focus groups and intervie ws, they reported a positive attitude about mathematics. As for the African American and White struggling students, the responses were mixed with some students having a posit ive attitude while ot hers had a negative attitude. In examining student s responses, their attitudes an d experiences were impacted by relationships with teachers, teachers at titude, and students confidence in their
90 mathematical abilities. It is important to note that three of the African American excelling groups had one student in each group enrolled in a remedial course or a course below the targeted mathematics course for his/her gr ade level. Thus, this finding may have impacted overall mean scores on the ATMI for each group. However, it is uncertain because the students were identified as ex celling and may have had positive mathematics experiences based on current perf ormance at the time of the study. As for the importance of mathematic s, students across groups reported that mathematics was important for their presen t and future endeavors such as for the advancement to other mathematics courses, careers, and daily living. Although the ratings of students in the African Amer ican struggling group on the ATMIs value construct were neutral, collec tively students identifie d a need for mathematics. However, few students across groups questioned the ut ility of mathematics beyond basic skills. In addressing research question two and three, the data from the other themes such as influence of home /community and school factors and fact ors that supported or hindered students success were instrumental in uncovering what students perceived as vital in learning mathematics. The perceive d level of teacher support was a catalyst to students positive or negative experiences. Stud ents in the struggling group indicated that the level of teacher support decreased over th e years, while excelling students reported a constant presence of teacher support. However, in comparison to their White excelling peers, the absence of encouragement to take a dvanced courses appeared to be a reality for African American excelling students. Across groups, students indica ted the availability of supports in the school and community such as tutoring. The level of parental support
91 decreased as students advan ced through the mathematics curriculum. However, many students expressed support in the form of encouragement when the mathematics content was beyond parents level understanding. As for interview participants, they expressed continued assistance and support in th e home for mathematics achievement. It was evident that supplemental inst ruction was a common component focus group students identified as missing to s upport learning and applying mathematical concepts. Student responses indicated that instruction that provided hands-on opportunities or provided steps would incr ease the likelihood of their success in mastering mathematic skills. Interviewees indi cated that visuals in the form of classroom posters, memory strategies, and group work foster mathematics success. The data represented in this section de pict students experi ences as expressed during focus groups, interviews, and reporte d on the ATMI. The aggregated data provided the basis for examining experiences across race and performance levels to highlight similarities and difference among and between groups.
92 Chapter V Discussion In this study, the differences and simila rities amongst groups were explored in an effort to understand the mathematics achieveme nt gap. Specifically, the experiences of African American and White hi gh school students were examin ed to learn about factors that shaped their attitudes towards mathematics and their perceptions about their experiences related to mathematics. It is important to note that the differences among or between the groups were not statistically significant. However, the qualitative data provided insight into what students perc eived as supports and hindrances to their mathematics achievement. Attitude Towards Mathematics Although the difference between White a nd African American excelling students was not statistically significant, the moderate effect size of -0.69 indicated that White excelling students had slightly more self-confidence in their mathematics abilities and performance than African Americans students. The ratings of African American excelling students suggested a level of confidence; however, their mean score was about 0.58 points lower than the White excelling students. The students in both groups indicated having positive mathematics experien ces. Focus group data indicated that the White excelling group attributed their experi ences to good teachers, whereas, the African-American excelling students, attributed feelings of confidence to teachers and parents. The White excelling group discussed repeated experiences related to teachers
93 encouraging them to take more advanced classes as well as to participate in mathematics clubs and organizations. These students attributed these ex periences to their level of confidence, which was related to their abili ty and performance. The White excelling interviewees attributed their attitude to math ematics to fun or just liking math. In this study, African-American excelling students sh ared the common experience of being encouraged by teachers. Teacher encouragemen t is a factor reported in the research in which many successful African American mathematic students attributed to their success (Moody, 2004; Sheppard, 2006). Of the African-American excelling student s, one student mentioned being pushed by middle-school teachers to take advanced clas ses. However, the other students in this group did not speak of teachers pushing them to join mathematics clubs or organizations. Although it is unknown why these st udents believed they were not encouraged to take advanced classes, previous research has at tributed teachers neglect in encouraging African American students to take more advan ced classes or engage in other mathematics learning opportunities to teachers low expectations of African American students (Anderson 1990; Flores, 2007). Having opportun ities to take advanced mathematics classes and exposure to challenging mathema tics experiences contribute to students success in mathematics (Byrnes, 2003; Flores, 2007). Regardless of the explanation for why students did not pursue advanced classes, finding a means to encourage those pursuits is important because doing so will help to create equ ity in schools. Such equity will help children receive the level of suppor t necessary to not only be A students, but also to be competitive and well prepared for whatever endeavors they choose to pursue
94 for educational and economic ga in (Ladson-Billings, 1997). The African American and White struggli ng groups rated their level of selfconfidence as slightly greater than neutral. This finding suggests th at these students were less certain than excelling stude nts about their math abili ties and performance. In addition, both groups, overall, provided mixed responses to questions regarding their math attitude and math experiences. Approximately six students from the White and African American groups were de finite in stating that they had a positive or negative attitude. However, they were the fe w who also had both negative and positive experiences in math. During the focus group discussion specifically related to their negative or positive attitudes, the White struggling students discussed how teachers influenced their attitudes, in addition to how the complexity of content and their past successes shaped their attitudes. However, the African American students focused more on the complexity of the content. For ex ample, in response to the probe prompting students to tell about their mathematic expe riences from elementary, middle, and high school, one student from the str uggling group stated: we went from 1 + 1 to a + b. In addition, African American students also focu sed on personal attributes or goals that influenced their attitude. This sentiment was expressed by one student who stated, when I started to get into higher gradesit became difficult and harder for me to pay attention. The struggling stude nts perception about teachers and personal attributes as hindrances are discussed in more detail later. On the other ATMI constructs, African American and White excelling students ratings continued to be more similar than di fferent for value, enjoyment of mathematics,
95 and motivation. Although differences were not statistically significan t, African American excelling students ratings were slightly highe r than White excelling students for value of mathematics (see Table 9). As for the Af rican American and White struggling group, they also tended to be more similar than different. The struggling students rating on the value construct was similar to what was shared during the focus group. All groups expressed valuing and knowing the utility of mathematics. Across all performance groups, the value and utility of mathematics app eared to be influenced by career goals. The students viewed its value and utility as it related to attaining th eir dream of going to college and career goals. When examining the information gather ed across performance groups (excelling and struggling) and constructs, the differen ces suggested both Af rican American and White excelling students were more certain a bout their attitudes rela ted to mathematics than the struggling students. This finding was unexpected due to the assertive attitude most of the African American and White st ruggling students exhi bited during the focus group. If it were not for the teachers groupi ng the students into th e performance groups, one would not be able to detect this indeci siveness in conversati on. The ratings of the African American and White struggling students were genera lly in the neutral to agree range with respect to the enjoyment of math ematics and motivation constructs, whereas, African American and White excelling students rating ranged from moderately agree to agree on the enjoyment and motivation construc ts. The assertive behavior of African American and White struggling students could be explaine d by the theory of social desirability and the knowledge of anonymity. Social desirabi lity theory suggests that a
96 participant may respond in a manner favorable to peers in a group or to a researcher (Trichom, 2006). Likewise, the knowledge of anonymity allowed for a student to speak freely and respond to the questionnaire withou t concerns regarding teacher, parent, or peer verification of what he/s he shared during the study. Supports and Hindrances Influencing Mathematics Performance Research on the African American-White mathematics achievement gap indicates that factors resulting in the gap are related to the value placed on mathematics, unequal access, racism, teacher competency in ma th and culture, limited exposure, low expectations, pedagogy, motivation, and other factors (Anderson, 1990; Byrnes, 2003; Flores, 2007; Lubienski, 2002; Stiff & Harvey, 1998). In this study, the African American and White struggling students expressed a valuing of mathematics and a desire to be professionals in society such as teachers or doctors. However, these students performed below grade level expectations in mathematics. In spite of their expressed desire to become successful professional s, both racial groups communicated shared experiences in regards to teachers low expect ations, and their perspective that teachers lack competency in teaching mathematics. Teachers receptiveness to students in need of help was considered a hindrance and students were less likely to ask for hel p. One White student shared, if you dont get it, they [teachers] get fed up. Likewise, one African American student stated he [teacher] asks why are you not understanding or have you not been paying attention. The struggling students overwhelmingly voiced that when they did not understand, the teacher either got upset, refused to explain further, or suggested that it was something
97 wrong within them as to why they did not understand (i.e., paying attention). A difference amongst the groups was whether or not they received encouragement and/or assistance. Many of the White struggling student s indicated having family members in the home such as brothers, moth ers, and fathers to assist with math. Although the African American students had encouragement from family members, the assistance with math was limited to those who had someone in the home who enjoyed the subject. Secondly, another difference was that African American struggling students were able to go beyond teacher temperament and working in groups when asked about classroom strategies that assisted or hindere d them in math. The students named several classroom activities or instruc tional methods that helped them in elementary school that could have been beneficial in middle school and in high school such as step-by-step instruction, the use of the board to explain and provide examples, the use of flashcards, the use of calculators, the use of strategies that helped them check work, and notes-taken next to sample problems as a reference. Based on the students accounts of their ex periences, it appears that the students communication and learning styl es and their need for more supplemental instruction either limited or enhanced their experiences In Stiff and Harvey s (1988) discussion on identity in the classroom, they concluded th at African American students find themselves weighing the need to cooperate in the manner teachers expect or expressing themselves. They found that directness, elaborate synt actical demonstrations, conciseness, and competition are the valued attributes of a successful mathematics student (Stiff & Harvey, 1988, p.198).
98 If students felt empowered, ta lking with their teachers about their needs would be of benefit to teachers and the students. Even when the White struggling students were asked about sharing their needs w ith teachers, they did not find talking with their teachers as a viable solution given their experiences in pa st attempts to talk to their teachers. In addition, allowing students to express what they believe helps them will provide teachers insight into what approaches or supports might work best fo r the students. In essence, this effort could lead to in structional scaffolding, which could assist with students acquisition of knowledge and a pplication of math skills (Ladson-Billings, 1997). African American and White excelling students voiced that working in groups was helpful to them in learning math. They both viewed group work as a way to learn from others. All the students in the White excelling group and one student from the African American excelling gr oup saw group work as way to challenge their minds (i.e., coming up with different solutions to a prob lem). Students from the African American excelling groups shared that they enjoyed the tasks of determining alternative ways to solve math problems and this was one reason why they liked math. As for factors that impeded success, the White excelling group considered teaching style as a hindrance to mathematic success. For example, a student explained that teachers must give ade quate time to those who do not understand instead of focusing on students who do understand. In addition, they expressed th e same concern with the amount of explanation given to content as th e African American struggling groups. They preferred for teachers to provide detail with respect to whatever is written on the board without assuming ease of understanding.
99 Both excelling groups expre ssed anxiety related to asking questions. Each group expressed a different catalyst that resulted in anxiety. For instance, a student from the White excelling group had a negative experien ce with a teacher w ho yelled and that resulted in his reluctance to ask questions In the African Amer ican excelling group, a student spoke about his apprehension due to c oncerns about what his peers might think. For example, this student said you mi ght sound retardedyou dont want to hear other peoples [students] mouths. Conclusion This study was designed to examine the common and different mathematics experiences of African American and White students. The motivation behind this study was to understand the White and African American mathematics achievement gap. Previous studies have provided evidence regarding factors that cont ribute to the gap. Byrnes (2003) found that 45%-50% of the difference in White and African American students performance in math is due to pare nt education, number of parents in the home, exposure to learning opportunities, and motivational aspe cts of math and 4.5% is explained by ethnicity when added with the other variables. Ot her researchers have investigated the impact of factors related to curriculum and instruction, teacher experience, parent support, se lf-concept, learning style and socio-cultural factors (Butty, 2001; Ladson-Billings, 1997; Moody, 2004; Rech & Stevens, 1996; Sleeter, 1997; Stiff & Harvey, 1988). In this study, students themse lves had the opportunity to voice what worked for them in the mathematics classroom and express their pe rceptions and attitudes about mathematics.
100 When examining the results and conclusion drawn from the data, the participating schools in this study were similar in dem ographics. Thus, the results cannot be generalized to schools with differing de mographic characteristics because the composition of participating students was not a proportionate representation of the population. It is likely that schools with different demogr aphic characteristics would result in a more or less representative sample of students by race and/or performance level. In addition, school differences such as willing participation of school staff may have impacted results. Of the three part icipating schools, two of the administrators demonstrated a willingness to participate by expressing their approva l of assisting in the study to mathematics department heads. T hus, the department heads were accessible. However, this did not lead to increased teacher access. As a result, the limited access to teachers resulted in less student pa rticipation than was desired. The varying schools climates were anot her difference that was noted among each school. In the participating schools, one walked away with the belief that the participating teachers had eith er (a) given up on trying to r each all students or (b) that teachers were still fighting to reach each student. This was evident by negative comments made by department heads or teache rs. For example, across the schools, there were a few teachers who expressed negative statements about their students. These negative attitudes could have impacted teach ers efforts in nominating students and maintaining necessary paperwork for students to participate in the study (e.g., collecting consent forms). In fact, there were student s at one of the participating schools that
101 consistently reported turning in forms to te achers. However, teachers were unable to locate forms after students first or second submission of consent forms. A few differences were found across th e racial groups when examining focus group data. Unlike White excelling student s, African-American excelling students reported a lack of encouragement from teachers to go beyond mathematics in the classroom. African American st ruggling students expressed a need for more explicit and supplemental instruction. Thes e students expressed the need and identified instructional methods they believed would be helpful. In terestingly, students in the White excelling group expressed a similar need in that they preferred hands-on ac tivities and explicit instruction. In this study, more similarities than di fferences were found in what the students expressed across groups. All groups spoke to th e need for teachers to be more patient, willing to provide support, and for teachers to not assume that something within them (students) is the reason why they have not gr asped a concept (i.e., lack of attention during instruction). Whether or not parents liked math or completed their education impacted students across both racial groups. Parents w ho did not complete their education or had limited math skills were not available to help their children. Howeve r, students reported that such parents were encouraging, excep t for a student whose mother did not like mathematics. Given the similarities, an overall conclu sion is that the students expressed what supplemental learning strategies teachers used and how student-teacher relationships fostered an enjoyment and a desire to do math. However, the question of why is it that
102 this group of African American students mathematics performance lags behind the performance of their White pe ers remains. This studys results and the reality of the achievement gap indicate a need to better equi p teachers to be sensitive to the identified needs of these students. In particular, pr oviding secondary mathematics teachers training that results in greater compassion and patie nce being evident in their teaching may be helpful. In the age of accountability and sc hool sanctions, we must assess what teachers need to be effective mathematics teachers. Fi rst, teachers must be competent in their own mathematics skills in order to teach others Overwhelming, African American and White students who struggled expressed the need for teachers to break down information. Interestingly, those students who were ex celling also expressed the same need. In addition, teachers must be cognizant and pur poseful of what they do and say. The majority of students, whether identified as excelling or struggling, expressed a difference between the treatment by and pa tience of elementary teacher s and secondary teachers. Limitations As with any research study, limitations that may have impacted the results should be considered. In this study, one limitation wa s the small pool of students from whom to select participants. This limitation was in part due to school principals and teachers reluctance to participate due to time cons traints and pressures resulting from federal mandates. In addition, poor return and turn -around of parent c onsent forms impacted which students ultimately participated in the study. However, the overall availability of students during school hours was also a major related limitation. Students were in school for approximately seven hours a day. Within those seven hours, students were expected
103 to be present for classroom lessons, discus sions, practice activities, assessments, and other learning opportunities. Thus, students were available for only a limited time to participate in this study. These factors affect ed sample size and generalizability of data (i.e., survey, interview, and focus groups). Another limitation was acce ssibility of White students. A pool of White students from whom to select as part icipants was limited due to the decision to recruit students from Algebra I. After the study was broadene d to include students from all mathematics courses, there continued to be a limited numbe r of White students from whom to select. In turn, their voices were not equally represented in comp arison to African American students. This limitation impacted the resear chers ability to compare African American and White students experiences. The limitations that resulted in a lo w number of participants and limited accessibility of White students were limitations that impacted external validity, more so the transferability of the findings acro ss schools and mathematic classrooms and conclusion validity. Thus, the sample size limited statistical power and the researchers ability to make definitive and reasonable conclusions about relationships found in the data (conclusion validity) as well as generalizability. The participants pre-high school experience was also a limitation for transferability because students were not grouped or identified by the elementary or middle school attended prior to high school. Thus, in understanding their mathematical experience, their diverse pre-high school experiences shaped their attitude and perspectives and limited the researchers ability to generalize the stud ents experiences.
104 However, the intent of gathering data on students perspectives was achieved. As for internal validity or the credibil ity of data, the focus group approach limited anonymity within the group. The students within a particular group were pooled from the same mathematics classroom. So, to some degree, many of the students knew each other outside of the research study. Consequentl y, participants may have been less apt to disclose experiences that influenced their mathematics behavior or achievement due to concerns related to social pr essures as an outcome of par ticipation. This phenomenon is referred to as evaluation apprehension (Trichom, 2006). For example, a concern for a student may have been what his/her fellow group participant would share with others outside of the study or a concern with trying to look good for fellow participants or the researcher. Thus, internal validi ty may have been impacted. The organization of focus group by race a nd performance level could also be a possible limitation in the study. Students in this study were grouped by race and performance to provide an environment for st udents to share with peers who might have similar racial and achievement experiences. However, this grouping could have limited students recall of experiences or expression of various perspe ctives, thus, also impacting validity. Random or extraneous variances in the setting are also threats to conclusion validity. Random or extraneous variance in the studys setting included disturbances related to traffic outside of th e classroom and other disturban ces near the setting that may have impacted researchers or participants (Shadish, Cook, & Campbell, 2002; Trichom, 2009). The research for this study was collected in the schools media center or cafeteria.
105 Therefore, the disturbances consisted of stude nt and adult traffic. Although the study was conducted away from most of the traffic flow (i.e., corner in media center or cafeteria), the impact of the movement and noise could have affected students attentiveness or willingness to respond candidly. Despite these limitations, insight into students experiences was provided by the study. The results provided information relevant to understanding how students perceived their mathematical environment. In addition, the limitations presented will inform researchers of school realities su ch as the knowledge that, depending on the school or district, many White students have taken algebra I in middle school. Directions for Future Research In essence, this research allowed studen ts to voice their perspectives on factors that shaped their attitudes in mathematics and instructional pract ices that aided in contributing or hindering their success. Fr om this study, we learned that students attitudes seem to be shaped by their relations hips with teachers a nd the level of support they receive at home and in school. In this study, students discussed the need for learning activities and instructional practices that allow for hands-on experiences, use of cooperative groups for support from peers, and the use of supplementa l instruction that included more explicit teaching of concepts (i.e., breaking down steps or concepts). Some students also shared that positive teacher-stude nt interactions played a role in their mathematics success. Future research should answer the question: What is the impact of teachers attitudes and instructional prac tices on students mathematic performance? In Maslows
106 hierarchy of needs, after an individuals phys iological and safety needs are met, a sense of belonging and love is recommended to help the individual reach a healthy level of selfesteem and productivity (Ormrod, 2000). This basis must be embraced in all classrooms, elementary and secondary. In this study, a commonality across race and struggling students was the negative classroom experi ences related to how students perceived teachers attitude and willingness to expand on lessons to foster their understanding of mathematical concepts. Therefore, in observing the mathematics classroom setting, particularly, interactions betw een teacher and students, inst ructional practices, students outcomes related to the instructional practices, and teacher an d student attitudes, future investigations should examine how successful secondary mathematics teachers support struggling and excelling students. Observati ons within the classroom along with focus group or interview data would enhance the researchers ability to make accurate connections across data. Thus, a more ethnographic or field research qualitative approach might be taken. This approach would allow for the research er to use participant observation and/or direct observation data to understand what occurs in secondary mathematics settings, to observe the partic ipants interactions, to gain knowledge on various ways instruction is provided, and to connect practices and other teacher and student behaviors with students' outcomes. Students across race and performance groups reported that the level of support in learning mathematics changed from elementary school to secondary school. In fact, many students reported that the level of suppor t decreased over time. Based on students report, this perceived decrease in support im pacted how well they were able to master
107 mathematical concepts. Thus, future rese arch is needed to examine available and practical resources to assist secondary ma thematics teachers in designing mathematics interventions and progress monitoring tools to support the need s of students. In reflecting on this studys outcomes and limitations, there are a number of steps that could be taken to reduce limitations, in crease conclusion validity, and to support generalizability. As mentioned above, the researchers familiarity with the setting through direct and/or participant observation would be necessary in this effort. In addition, methods to increase student participa tion also would increase statistical power and increase generalizability. In this study, high school students appeared comfortable in sharing their experiences. However, to decrease evaluation apprehension, social desi rability pressures, and other factors that impact students response and credibi lity of the data, the use of groups comprised of students with similar profiles (e.g., race and pe rformance level) and from different schools would be another tact ic. In addition, to reduce the impact of extraneous variance in the experimental setting a wellthought out location within a school or neutral setting also would be helpfu l. Another would be to take into account prior schools attended and make groupings by elementary and middle schools the high school students attended, in addition to their race and performance le vel. This approach would allow for generalizations connected to specific educational settings. Lastly, defining excelling students with an exclusio nary factor would ensure a more accurate representation of excelling student s experiences. The exclusi onary factor would be that students identified as excelling must be enroll ed in advanced or targeted mathematics
108 courses for their specific grade level. In addition, an organization method altoge ther different from the aforementioned groupings would be to group students based on pe rformance level alone. After allowing students to share experiences and recall expe riences from others shared experiences, students would later be grouped by performan ce and race. This group organization may allow for more in-depth discussions relate d to supports and hindrances in the home or school environment. Working with high school students was necessary to get a historical perspective of students mathematical experiences. Collecti ng these historical perspectives through the use of a longitudinal study may have provide d more comprehensive accounts of students experiences. Overall, it was rewarding to wo rk with high school students as they were able to share their perspectives and how they were able to connect mathematics with their future goals in life. It is my hope that this research illust rates how valuable students voices are in studying what students believe works in ma thematic classrooms to promote student achievement. Students are vital in the proce ss of change, not only as the unit of change or study, but as the link to discovering what needs to be changed and as the source in which to measure change in education. In combination with other empirical research findings, we can learn from stude nts experiences how to prov ide what it is needed for their success.
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119 Appendix A Focus Groups and Interviewees Stude nt Demographics and Activities Focus Groups Student Demographics and Activities Group 1: White Struggling ( n=4) School A Student Gender Age Grade Number of math courses Course enrolled during study School clubs Favorite subjects WT Female 14 9 1 Algebra I Gear Up None TT Female ---Algebra I --LL Female 16 9 1 Algebra I JROTC, Drill team, Raider Team English, It used to be math CC Female 15 9 1 Algebra I Cosmetology Science Note JROTC = Junior Reserve Office Training Corps
120 Group 2: White Excelling (n=4) School B Student Gender Age Grade Number of math courses Course enrolled during study School clubs Favorite subjects RA Male 17 11 5 Advanced Placement Calculus AB FBLA, NTHS, Web design team, Robotics team Web design DM Male 15 10 2 Algebra II Honors Japanese club Japanese RXA Male 16 11 3 Advanced Placement Statistics Baseball Math WK Male 16 10 4 Algebra II Honors Air Force JROTC, AIAA Aerospace Note JROTC = Junior Reserve Office Training Corps, FBLA = Future Business Leaders of America; NTHS = National Technical Honor Soc iety; AIAA = American In stitute of Aeronautics and Astronaut; NTHS = National Technical Honor Society Group 3: African American Excelling (n=2) School A Student Gender Age Grade Number of math courses Course enrolled during study School clubs Favorite subjects BJ Female 14 9 2 Algebra I None Language Arts GZ Male 15 10 2 Algebra I Football team Math
121 Group 4: African American Excelling (n=5) School B Student Gender Age Grade Number of math courses Course enrolled during study School clubs Favorite subjects LR Male 17 11 4 Algebra I None Physical education and computers LA Female 14 9 1 Algebra I JV basketball, Varsity track, JV volleyball American government JL Male 14 9 1 Algebra I None Math and English HN Male 15 9 1 Algebra I Basketball Math JR Female 14 9 2 Algebra I -Math Note JV = Junior Varsity
122 Group 5: African American Excelling (n=4) School B Student Gender Age Grade Number of math courses Course enrolled during study School clubs Favorite subjects GD Male 19 12 4 Trigonometry Ladies and Gents Math BK Female 17 12 5 Trigonometry Dance team, drama, FBLA, Student government, JR Civitans English WS Female 17 12 5 Advanced Placement Statistics SWAT, DECA, NHS, Auxiliary Math BI Female 16 9 2 Intensive Math NHS Math Note FBLA = Future Business Leaders of America; SWAT = Students Working Against Tobacco; NHS = National Honor Society; DECA = Dis tributive Education Clubs of America Group 6: African American Struggling ( n=5) School A Student Gender Age Grade Number of math courses Course enrolled during study School clubs Favorite subjects BN Female 15 9 2 Algebra I Flag football, volleyball, karate Medical skills BS Female 15 9 1 Algebra I None Reading AC Male 15 9 1 Algebra I None Reading ED Male -10 2 Algebra I None English CS Male 17 9 1 Algebra I Computer Tech English
123 Group 7: African American Struggling ( n=4) School B Student Gender Age Grade Number of math courses Course enrolled during study School clubs Favorite subjects WX Male 15 9 2 Intensive Math None Science QE Female 15 9 2 Intensive Math None English and math WC Female 15 9 2 Intensive Math None American government BN Female 15 9 2 Intensive Math Gear Up English Group 8: African American Struggling ( n=2) School B Student Gender Age Grade Number of math courses Course enrolled during study School clubs Favorite subjects McCla Male 17 10 3 Algebra II Honors Band English and math McClo Female 16 10 2 Geometry Softball Science
124 Interviewees Student Demographics and Activities Interviewees: White Excelling ( n=2) School C Student Gender Age Grade Number of math courses Course enrolled during study School clubs Favorite subjects HT Female 15 9 2 Algebra I Honors HOSA, ASL, Veterinarian Math and ASL MJ Male 13 9 1 Algebra I Honors Skills USA and baseball Math Note HOSA = Health Occupation Student of America; ASL = Amer ican Sign Language; Skills USA = Industrial Student Organization
125 Appendix B Demographic Questionnaire ID#:_________________________ Age:____________________ Grade:_________________________ # of Parents in home_______ List your hobbies: ______________________________________________________________________________________ __________________________________________________________ List school clubs/activities: ______________________________________________________________________________________ __________________________________________________________ How do you spend your free time (a fter school, weekends, etc): ______________________________________________________________________________________ __________________________________________________________ When do you study (e.g., after school, weekends, never): ______________________________________________________________________________________ __________________________________________________________ Describe a typical school week (include at school and after school experience): ______________________________________________________________________________________ __________________________________________________________ ________________________________________________________________________ What is your favorite school subject: ______________________________________________________________________________________ __________________________________________________________ How many close friends do you have? ________________________________________________________________________ What kind of grades do you earn in mathematics: Circle the best answer Mostly As Mostly Bs Mostly Cs Mostly Ds Mostly Fs What kind of grades do you earn in English: Circle the best answer Mostly As Mostly Bs Mostly Cs Mostly Ds Mostly Fs What kind of grades do you earn in Science: Circle the best answer Mostly As Mostly Bs Mostly Cs Mostly Ds Mostly Fs What kind of grades do you earn in your elective courses: Circle the best answer Mostly As Mostly Bs Mostly Cs Mostly Ds Mostly Fs What kind of grades does your closest friend make in most subjects: Mostly As Mostly Bs Mostly Cs Mostly Ds Mostly Fs
126 Appendix C Focus Group and Interview Questions Factors: family/community factors, school fact ors, self factors, early math experiences, teaching practices, tracking and ability gr ouping, courses taken, motivation, value, and utility. Question #1: What kind of help did you receive from your parents in math? Probing questions: How would you describe the help parents gave you when you had a difficult time understanding how to solve a math problem? Was the help useful in helping you grasps the skill, did your parents seem impatient or usually willing to provide extra help? Do you believe other Black youth have a chance to achieve the American dream if they do well in school? Are there Black (White) people in your communi ty or family who seem to have a hard time making it (being succe ssful) in society? Question #2: How would you describe the help teachers gave you when you had a difficult time understanding how to solve a math problem? Was the help useful in helping you to grasp the skill, did teachers seem impatient or usually willing to provide extra help ? Probing questions: Describe your elementary school (i.e., were mi nority teachers and administrators present, were most of your classmates White or Black). In what subjects were you successful? In what activities were you successful (school, home, community)? In what subjects were challenging? In elementary (middle, high) school, what kind of help did you receive from your teachers in math (e.g., assistance during independent seatwork, after school help)? School: In elementary school, were you grouped for math instruction or work? What kind of work did your group complete in comparison to other gr oups in class (i.e., advance work or work same as other students, etc). How did you feel about being grouped in math? In elementary (middle, high), do you believe you were in the right math groups or classes? If so, why? If not, why? Do you believe what is taught in school is helpful to becoming a successful AA (White) adult?
127 Do you believe you were in the right math gr oups or classes in el ementary, middle, high school? If so, why? If not, why? Question #3: Who helped you select your math courses in middle (high) school? Probing questions: Were you advised as to what courses to ta ke based on your future goals, grades, test scores, or enjoyment of math? How many math courses have you taken? How many math courses do you plan to complete by graduation? Question #4: What are th e benefits of getting superior grades in math? Probing questions: What does success mean to you? If so, what will make you successful? Do your grades show how you feel about school? Do your test scores show how you feel about school? What are your plans when you graduate from high school? If you plan to attend college, what will be your major? What does the term American dream mean? What does it take to achieve the American dream? If you do well in school, do you believe you ha ve a chance to achieve the American dream? If not, what will prevent you from achieving the American dream? Question #5: How do you prefer to prac tice a new math skill (e.g., through group work, independent seatwork, discussion, pairs, etc.)? Probing questions: To whom do you turn when you need advice? To whom do you turn when you need help understanding school work? Did you fear asking for help in math? Do you enjoy doing math problems? Do you get nervous before going to ma th class or before math tests? Question #6: Were you encouraged by anyone to do well in math? Probing questions: What or who influenced your decision to take X# of math courses? Did a teacher, parent, friend, or someone influen ce your like or dislike for math? If so, in what ways?
128 Question #7: Do you believe math is important? Probing questions Why is math important? Question #8: In what ways can you use math outside of school? Probing questions: How often does an individual use math? What other areas will learning math help you
About the Author Sharondrea Rotreece King received a Bachelor s Degree in Elementary Education in 2000. While completing her undergraduate degree, she earned scholarships and other awards such as the University of South Fl orida Honor Recipient, Multicultural Scholars Award, Black Scholars Award, and the Florid a Fund for Minority Teachers Scholarship. During her junior year of undergraduate studies, she was accepted into the McNair Scholars Program. The McNair Scholars Pr ogram prepared her fo r graduate school and provided her with research opportunities. Ms. King was accepted to the School Psychology program at the University of South Florida in 2000. She later earned her Masters Degree in Curriculum and Instruction in 2001 and her Educational Specialists Degree in School Psychology in 2005. She currently works as a school psyc hologist in the state of Florida.