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PAGE 1 Congruence Among Mathematics Skills Used On The Job By Practical Nurses vs. The Prerequisite Skills Required For Admission Into The Practical Nursing Program by G.H. CLARY A thesis submitted in partial fulfillment of the requirements for the degree of Educational Specialist Department of Adult, Career and Higher Education College of Education University of South Florida Major Professor: William E. Blank, Ph.D. Dr. Jeffrey Kromrey Dr. Janet Scaglione Date of Approval: October 27, 2003 Keywords: Practical Nursing, Mathematics Skills, Postsecondary Vocational Education, TABE Copyright 2003, G.H. Clary PAGE 2 Table Of Contents List of Tables iv List of Figures v Abstract vi Chapter 1: Introduction 1 Statement of the Problem 3 The Practical Nursing Program 5 The Trend Toward Relevant Mathematics 6 Purpose of the Study 8 Research Questions 9 Educational Implications 10 Definition of Terms 11 Assumptions 12 Limitations 12 Organization of the Study 12 Chapter 2: Review of Related Literature 14 Mathematics in America 14 Practical Nursing 18 The TABE 22 Approaches in Determining Occupational Math Requirements 23 PAGE 3 The OMRA Instrument 25 Other Studies: Predictors of Student Success 26 Summary 28 Chapter 3: Methods 30 Research Design 30 The Setting 31 The OMRA Instrument 32 Job Related Materials 34 The TABE 34 The Analysis Teams 35 Procedures 36 Pilot 38 Compiling of Data 39 Chapter 4: Findings 41 Job Related Math Operations 41 TABE Math Operations 46 Congurence Among the Sets 47 Correlation Between TABE and Job Sample Rankings 50 Chapter 5: Discussion, Conclusions, Implications and Reccomdations 54 Summary of Study Procedures 55 Discussion of Findings 56 Conclusions 57 ii PAGE 4 Implications 58 Recommendations for Practice 58 Suggestions for Future Research 59 References 61 Appendix A: Modual Analysis of Learning Difficulties (MALD) of TABE forms 5&6, Level A, Mathematics 64 Appendix B OMRA Instrument 67 Appendix C: OMRA Coordinator Manual 76 Appendix D: Pilot OMRA Application Calculation Sample 87 Appendix E: Job Related Math Applications for Practical Nursing 91 Appendix F: Assortment of Job Related Math Samples Collected 94 iii PAGE 5 List of Tables Table 1: Practical Nursing Occupational Math Operations (Ordered by Frequency Ratings Across Teams) 45 Table 2: Prioritized Math Operations of the TABE 47 Table 3: OMRA Instrument Math Operations Used in Work Related Samples, and the TABE 48 Table 4: Correlation Across the TABE and the Practical Nursing Job Samples 51 iv PAGE 6 List of Figures Figure 1. Practical Nursing Programs in the United States 20 Figure 2. Scatter Plot of Spearman Rank Correlation across Practical Nursing Mathematics Job Requirements and the TABE 52 : v PAGE 7 Congruence Among Mathematics Skills Used On The Job By Practical Nurses vs. The Prerequisite Skills Required For Admission Into The Practical Nursing Program G.H. Clary ABSTRACT The standard for evaluating a students mathematic ability (grade level) for admission to many vocationaltechnical programs is through the administration of the Tests of Adult Basic Education (TABE). There has come forth a concern from vocational educators, that students entering programs may not be prepared for the mathematics required by the curriculum, even though the student has met the criteria for entry as established by the state curriculum frameworks as evidenced by their scores on a TABE which had recently been administered. Furthermore, questions raised among instructional, administrative and guidance personnel about the congruence of math skills required on the TABE vs. those used by practical nurses on the job supported the need for a study to determine the congruence of these sets of mathematics skills. Using the OMRA inventory developed by David Pucel, the mathematic operations required for job related math applications are indicated by samples collected from active nursing practitioners. Three analysis teams consisting of practical nurses and math experts were established and determined the math operations required for solving the job related math samples collected. The math skills tested by the TABE were then compared to the job related math samples. With the math operations of the variables ranked, the Spearman Rank Correlation was used to evaluate the correlation across the TABE and the mathematic job requirements of practical nursing. Based on 19 math operations identified from the Practical Nursing job math vi PAGE 8 requirements, the results showed that there was little correlation among these two variables (r=. 4974). Keywords: Practical Nursing, Mathematics Skills, Postsecondary Vocational Education, TABE. vii PAGE 9 Chapter 1: Introduction Mathematics is viewed as a basic skill required by all citizens in society. Yet many employed adults and those preparing for employment do not have the minimal basic mathematics skills needed to function successfully in the workplace (U.S. Department of Labor, 1991). The Educational Testing Service reported that only 25 out of 100 young adults can use a bus schedule to select the appropriate bus for a given departure or arrival, and only ten percent can select the least costly product from a list of grocery items on the basis of unitpricing information (1989). These tasks are hardly complex, yet only a fraction of young people aged twentyone through twentyfive can perform them. In todays workforce, the need for employees to think analytically and have the basic skills to do so is ever increasing. American businesses are estimated to lose $60 billion in productivity each year due to employees lack of basic skills (Ivy, 2002). When we hired a production worker in the old days, we used to say crudely that we hired his hands and not his head. Very frankly, what we are finding out is that there is an awful lot in his head (John Foley, Xerox Corporation, [n.d.]). Motorola Corporation found out that it had a serious problem with the skills of its frontline workers only when it was well into its program of restructuring for Total 1 PAGE 10 Quality Management. If you take one of our mainline factories in Chicago . we have about 7,500 people, roughly 3,200 or 3,300 are . production workers. One thousand of those individuals lack basic math skills adding, subtraction, multiplication, division . (Bill Wiggenhorn, VP, 1987). The NAEP 2000 results show that roughly onethird of U.S. students fail to meet basic levels of competence, about onethird demonstrate basic levels, and about onethird are proficient or advanced in all of the tested areas. The average score of twelfthgraders increased between 1990 and 1996, but then declined between 1996 and 2000. Despite this recent downturn in performance, the twelfthgrade average score in 2000 was higher than that in 1990 (NAEP, 2000). While the jobs in most occupations will grow on average by only 20 percent between 1990 and 2005, the U.S. Department of Labor, Bureau of Labor Statistics, predicts that employment in major technical fields such as health and other scienceand mathrelated areas will increase on average by 33 percent from 1990 to 2005 from 3.7 million jobs to 5.1 million jobs (May, 1992). Health services which accounted for 7% of total wage and salary worker employment in 1975 and 8% in 1990, will approach 9% of total employment in 2005 (Workforce 21, 2001). Technical education in secondary and twoyear postsecondary schools has made significant efforts in the last 10 years to become more relevant to the needs of industry. Technical educators are assisting industry associations in the creation of national voluntary skill standards administered through grants by the Education and Labor Departments. They were also the leading proponents behind the drive for industry2 PAGE 11 recognized standards for occupational education, implemented in all states in September 1992 (NACFAM, 1992) In vocationaltechnical education curriculum frameworks, the state of Florida recommends a minimum grade level of mathematics skill required for entry into any specific occupational training program area. Detailed student performance standards have been established that dictate the mathematic functions which the student must master in order to satisfy the program requirements for completion. Beyond this, it is at the discretion of each individual school, program or instructor to include additional math competencies to be mastered in order to meet more stringent conditions for program completion. One such program is Practical Nursing. As in many technical areas, individuals facing the rigorous challenges of the medical profession need a knowledge of mathematics. Theirs is an occupational area in which a mathematical error in the calculation of the quantity or mixture of medication can be critical to a patients survival. This occupation requires a demanding daily routine in which the use of mathematics is significant, from measuring medications, to taking temperatures, to timing intravenous feedings; they must be consistent in their ability to complete these tasks with accuracy. Statement of the Problem The standard for evaluating a students mathematic ability (grade level) for admission to many vocationaltechnical programs is through the administration of the Tests of Adult Basic Education (TABE). These are normreferenced tests designed to 3 PAGE 12 measure achievement in reading, mathematics, and language. Because the tests combine the most useful characteristics of normreferenced and criterionreferenced tests, they provide information about the relative ranking of examinees against a norm group as well as specific information about the instructional needs of examinees. The tests enable teachers and administrators to diagnose, evaluate, and successfully place examinees in adult education programs. TABE tests are designed to measure the understanding and application of conventions and principles, and are not intended to measure specific knowledge or recall of facts. There has come forth a concern from vocational educators, that students entering programs are not prepared for the mathematics required by the curriculum, even though the student has met the criteria for entry established by the state curriculum frameworks as evidenced by their scores on a TABE which had recently been administered. For example, a student may demonstrate an ability to score at the appropriate level on the TABE to be admitted to the program, but still fail to complete the program based on an inability to satisfactorily perform the required mathematic operations. Further, there is concern among vocational educators that the math skills required for program entry and the math skills needed to complete the training program may be out of synch with the math skills ultimately used by the graduate on the job. There is an uncertainty of knowing just what the specific math skills are that are needed on the job versus the specific math skills taught in the curriculum versus the math skills tested on the TABE. The problem may be the possible lack of validity of math on the TABE and curriculum as compared to actual math required on the job. 4 PAGE 13 Questions raised among instructional, administrative and guidance personnel supported the need for a study comparing the mathematics skills tested on the TABE to the math skills needed by entrylevel workers on the job. The problem addressed by this study was the uncertainty regarding the congruence among the level of mathematics required for admission into the Practical Nursing program, the math addressed in the TABE, and the level of math required by practical nurses as they go about their duties. The Practical Nursing Program One area in which particular concern has been expressed about mathematics requirements is in the Practical Nursing program. The program is designed to prepare students for employment as licensed practical nurses or to provide supplemental training for a person previously or currently employed in this occupation. The Florida State Board of Nursing must approve the program so the graduate may take the examination to practice as a Licensed Practical Nurse. The content includes, but is not limited to, theoretical instruction and clinical experience in medical, surgical, obstetric, pediatric, and geriatric nursing; theoretical instruction and clinical experience in both acute and long term care situations; theoretical instruction and clinical application of vocational role and function; personal, family and community health concepts; nutrition; human growth and development over the life span; body structure and function; interpersonal relationship skills, mental health concepts; pharmacology and administration of medications; legal aspects of practice; America 5 PAGE 14 Heart Association Basic Life Support (BLS) course C or equivalent and current issues in nursing. Clinical experience should make up 50% of the total program. The Health Careers Core must be taken by all students (secondary, postsecondary adult and postsecondary vocational) planning to complete any Health Occupations program (Florida DOE, 2003). This core consists of the first eleven intended outcomes of the program, as outlined in the curriculum framework (Appendix A), and introduces the student to health careers, personal responsibilities, medical terminology, computation and math, computers, employability skills, anatomy, basic procedures, nutrition, infection control, safety, and holistic care. Completion of the core allows the student ease of transferability among health care programs. This study was concerned with the computation and math standards of this program. Nursing Program instructors have expressed concern where students fail to master the math skills required, even though they have scored at the established level on the TABE for entry into the program. The Trend Toward Relevant Mathematics In his research, David Pucel (1992) cited a number of supporting opinions for the need for mathematics to be relevant to the occupation for which one is being trained. Mathematics is viewed as a basic skill required by all citizens in society. Yet many employed adults and those preparing for employment do not have the minimal basic mathematics skills needed to function successfully in the workplace (U.S. Department of labor, 1991). This has led to a reexamination of how mathematics is taught in 6 PAGE 15 elementary and secondary education programs and in programs designed to prepare people for employment (National Research Council, 1989). Pucel points out that a central theme of the movement to revise mathematics education is the Teaching for understanding is in; learning rote skills is out (Burns, 1994, p.471). The challenge is to adopt new approaches that have the potential for allowing adults to be more successful. Those approaches must allow people not only to learn mathematics but to be able to apply it in the workplace (Pucel, 1995, p.52). Math courses are often ineffective because students view many of the mathematics skills that are taught as irrelevant. Such perceived irrelevance often causes adults to drop out of such programs and forsake their occupational preparation (Shelby & Johnson, 1988). It is becoming a popular conception that more is not necessarily better. It is becoming clear that it is not possible to teach all people all of the mathematics skills that could be taught, especially during our current era of increased knowledge in all fields, especially mathematics. It has been suggested that we not call on the schools to cover more and more (mathematics) material, but instead recommend a set of learning goals that will allow them to concentrate on teaching less and doing it better (Blackwell & Henkin, 1989, p.ix). Too much of school reform has focused on morea longer day, a longer year, more courses, higher standards, more teaching and more testing. What we need is not more, but differenta different mission, a different philosophy, different content, a different structure, different methods and a different view of testing (Blank, 1996). Pucel (1995) points out that there are a couple of major groupings of approaches to teaching mathematics. 7 PAGE 16 1. Applied academics, in the context of preparing people for work, refer to teaching academic content around work related applications. The emphasis is on teaching the academic content. Integrated academic and vocational education programs are designed to emphasize both academic and vocational content and to teach them together as complimentary. 2. Related academics shift the emphasis from academic to vocational education. The process starts with examining the type of vocational education content to be taught and then determining the academic content that is needed to support that occupational content. Differences exist in perceptions of whether the mathematics skills for specific occupations are substantially different, or whether occupational mathematics skills are essentially the same for all occupations prepared for through vocational education (Pucel, 1995). If the TABE test accurately measures a students ability to perform the mathematics requirements required by the student performance standards of the Practical Nursing program, do those student performance standards reflect the actual occupational mathematics skills needed on the job by a Licensed Practical Nurse? Purpose of the Study The purpose of this study was to (1) determine the specific math skills required on the job for entry level Licensed Practical Nurses, (2) identify the math skills tested by the TABE, and (3) to determine the congruence among these two sets of math skills. This 8 PAGE 17 study utilized the Occupational Mathematics Requirements Assessment (OMRA) instrument developed by David Pucel of the University of Minnesota in 1992 as a tool with which to accomplish this task (Appendix B). This study did not involve the collection of individual student data. The Occupational Math Requirements Assessment (OMRA) was designed to determine the mathematics operations (skills) required for success in an occupation. The results of OMRA can be used as a basis for curriculum development and/or for judging an individuals occupational math preparation (Pucel, 1992, p.C1). The intent of this study was not to question the validity or reliability of the TABE test in evaluating an individuals basic skills level, but rather to determine its suitability in being the sole determining factor of a students eligibility for entry into a specific occupational program area. For example, a quick scan of the mathematics portion of the TABE test (Form 5, Level A) revealed that there are no questions relating to the metric system, while in reality, the medical occupations deal almost entirely with metric measurement in all of its applications. Research Questions This project investigated the following research questions. 1. What are the specific mathematics operations used routinely on the job by entry level Licensed Practical Nurses? 2. What are the specific mathematics operations tested by the mathematical subtests of the TABE? 9 PAGE 18 3. To what extent are the specific mathematical operations identified for each of the above consistent? Educational Implications State of Florida curriculum frameworks dictate the minimum grade level ability in basic skills to enter occupational programs. The minimum basic skills grade level required for mathematics for the Practical Nursing program when offered at the postsecondary adult vocational level is grade eleven (rule 6A10.040 FAC). This grade level number corresponds to a grade equivalent score obtained on a state designated basic skills examination (TABE). When students are admitted to a program such as Practical Nursing, based on a test score measuring their abilities and meeting state requirements for admission, they are expected to be successful. Nursing instructors have observed that when students do not meet the realistic mathematic achievement levels required by the curriculum or by the occupation, the end result is that they often fail to complete their occupational program. Learning more about the degree of noncongruence among the skills required for admission and those required in the curriculum with those required on the job can assist in the development of a more effective curriculum, a better admissions test, and more appropriate entrance criteria. 10 PAGE 19 Definition of Terms For the purposes of this study, and to promote a common basis for understanding, the following definitions are used: 1. TABE: Tests of Adult Basic Education. Norm referenced tests designed to measure achievement in reading, mathematics, language, and spelling. (TABE Examiners Manual) 2. OMRA: The Occupational Mathematics Requirements Assessment is designed to determine the mathematics operations (skills) required for success in an occupation. (OMRA Coordinator Manual) 3. Curriculum Frameworks: Outline of State Department of Education requirements, intended outcomes and student performance standards for programs and areas of study in which the student will be involved. 4. Student Performance Standards: Specific occupational tasks which the student is expected to master in order to receive a certificate of completion. (Curriculum Framework, Florida Department of Education) 5. Job Related Materials: Written materials specifically containing math applications routinely used by workers in an occupation. (OMRA Coordinators Manual). 5. Math Category: A major division of math such as integers, fractions, decimals, percents, algebra, or geometry. (OMRA Coordinators Manual). 11 PAGE 20 7. Math Expert: A person formally trained in mathematics that has command of the structure and skills of mathematics, such as a math instructor. (OMRA Coordinators Manual). 8. Occupational Expert: A person who has mastered the skills of the occupation to be analyzed, such as an occupational instructor. (OMRA Coordinators Manual). Assumptions The only assumption that is being made in conducting this study is that the math skills evident, or implied, by work samples collected are generally representative of the math skills required on the job. Limitations (1) This study is limited to the Practical Nursing instructional program and the Practical Nursing occupation. (2) The results of this study cannot be generalized beyond the limited geographical setting in which the study was conducted. Organization of the Study Chapter 2 contains a review of literature related to practical nursing as a career, the TABE test, occupational mathematics, the use of standardized tests as predictors of student success, and the OMRA instrument. Chapter 3 identifies the methods and 12 PAGE 21 procedures to be used in completing this study. Chapter 4 includes the findings of the study and an interpretation of the results, and Chapter 5 presents a summary of the study, its conclusions, and recommendations for continuing research. 13 PAGE 22 Chapter 2: Review of Related Literature This chapter presents a review of the status of mathematics skills of the American student, Practical Nursing as a career, the TABE test, OMRA instrument, and other studies conducted relevant to predicting student success in Nursing programs. Mathematics in America The April, 1983 U.S. government publication A Nation At Risk reported to the American people . that while we can take justifiable pride in what our schools and colleges have historically accomplished and contributed to the United States and the wellbeing of its people, the educational foundations of our society are presently being eroded by a rising tide of mediocrity that threatens our very future as a Nation and a people. This report points out that between 1975 and 1980, remedial mathematics courses in public 4year colleges increased by 72 percent and now constitute onequarter of all mathematics courses taught in those institutions. The average graduate of our schools and colleges today is not as well educated as the average graduate of 25 or 35 years ago, when a much smaller proportion of our population completed high school and college. Business and military leaders complain that they are required to spend millions of dollars on costly remedial education and training programs in such basic skills as reading, writing, spelling, and computation. These deficiencies come at a time when the 14 PAGE 23 demand for highly skilled workers in new fields is accelerating rapidly (p.3). Although a million and a half new workers enter the economy each year from our schools and colleges, the adults working today will still make up about 75 percent of the workforce in the year 2000. Another government education research report Meeting Goal 3: How Well Are We Doing? (1992), examined the achievement of todays 17 year olds and 9 year olds in math, reading, and science. The data in the report are from the National Assessment of Educational Progress (NAEP) report Trends in Academic Progress (1991). It provides information on student achievement patterns across time at ages 9, 13, and 17 in math, reading, and science. The results show that many of the nations 17 year olds are failing to acquire the skills they need, but also that todays 9 year olds, who leave high school at the turn of the century, are not performing better than 9 year olds in the past. As measured by the NAEP data, the nations 17 year olds do not appear to be well prepared for todays workforce or further education. Only 56 percent of 17 year olds can compute with decimals, fractions, and percents; recognize geometric figures; solve simple equations; and use moderately complex mathematical reasoning. Only seven percent can solve problems that involve fractions and percents, solve twostep problems involving variables, identify equivalent algebraic expressions, and solve linear equations and inequalities. Nearly one out of every five (18 percent) nine year olds in 1990 could not add and subtract two digit numbers or recognize relationships among coins. It is clear from these results that students are not leaving high school with the skills they need. It is difficult to understand why so many people must struggle with concepts that are actually simpler than most of the ideas they deal with every day. It is far easier to 15 PAGE 24 calculate a percentage than it is to drive a car (Dewdney, 1993, .1). Innumeracy is more socially acceptable and tolerated than illiteracy (Dewdney, 1993). Numeracy involves the functional, social, and cultural dimensions of mathematics. Numeracy is the type of math skills needed to function in everyday life, in the home, workplace, and community (Withnall, 1995). Low levels of numeracy limit access to education, training, and jobs; on the job, it can hinder performance and productivity. Numeracy is not just about numbers, but rather is a socially based activity that requires the ability to integrate math and communication skills (Withnall, 1995). Words can have everyday meanings as well as math meaning: for example, and is a conjunction, but in math it can also mean plus. Some words are math specific: numerator, multiplicand, and divisor. Interpretation of these words can cause confusion for people with low literacy levels. Despite the myth that mathematical principles are fixed for all time, new discoveries and theories about math continue to emerge. The uses of math in the world evolve as societal needs change. For example, computers are changing the need for some kinds of math skills and creating the need for others (Bishop et al., 1993). Numeracy has an uncertain place in adult basic education. Instructors are not always prepared to teach math and may even share some of their students anxieties about it. Adult math instruction often focuses on preparation for the General Educational Development Test, which is based on high school math and perhaps cannot serve as a complete road map for what adult numeracy provision should encompass (Gal 1992, p.22). 16 PAGE 25 Major curriculum reform is not new in the field of school mathematics. The last such reform was the new math of the late 1950s and 1960s which emphasized the unifying mathematical concepts of logic and set theory. For a variety of reasons the new math did not receive widespread acceptance. It did not pay close attention to how students learn and what they are capable of learning at different ages. The new math was followed by the back to basics movement, which emphasized rote memorization of arithmetic facts and the learning of paper and pencil algorithms. The current reform movement grew out of the inability of the back to basics movement to address key issues, including: Neglect of higher order thinking and problem solving skills Disquieting findings about American students in recent international studies on mathematics achievement. Changing mathematical skills needed in the work force. (U.S. Department Of Education, 1994) The need for a workforce equipped with more and different mathematical concepts is transforming the mathematics curriculum. Routine problems rarely involve ideas from just one part of mathematics. Thus the curriculum at all grade levels needs to include geometry and measurement, probability and statistics, pre algebra or algebra, patterns, relations, functions, and discrete mathematics (Lacampagne, 1993). Curricular and pedagogical changes in mathematics must transform how students are assessed. As mathematics curricula and pedagogy are changed, the instruments for measuring student achievement must also be changed. It is not fair to students, teachers, or school districts to be measured by outdated standards. The majority of standardized 17 PAGE 26 tests our children take are still overly reliant on multiplechoice items that measure predominantly lowlevel mathematics skills. Although they are beginning to reflect the changes in mathematics teaching and learning, these tests include few types of questions that require higher order problemsolving skills (Lacampagne, 1993). Practical Nursing As defined by the Occupational Outlook Handbook (U.S. Department of Labor, 1996) licensed practical nurses (LPNs) care for the sick, injured, convalescing, and handicapped, under the direction of physicians and registered nurses. Most LPNs provide basic bedside care. They take vital signs such as temperature, blood pressure, pulse, and respiration. They treat bedsores, prepare and give injections and enemas, apply dressings, give alcohol rubs and massages, apply ice packs and hot water bottles, and insert catheters. LPNs observe patients and report adverse reactions to medications or treatments. They may collect samples from patients for testing and perform routine laboratory tests. They help patients with bathing, dressing, and personal hygiene, feed them and record food and liquid intake and output, keep them comfortable, and care for their emotional needs. In states where the law allows, they may administer prescribed medicines or start intravenous fluids. Some LPNs help deliver, care for, and feed infants. Some LPNs supervise nursing assistants and aides. In doctors offices and clinics they may also make appointments, keep records, and perform other clerical duties. 18 PAGE 27 Most licensed practical nurses in hospitals and nursing homes work a 40hour week, often including nights, weekends and holidays. They often stand for long periods of time and help patients move in bed, stand, or walk. They also face the stress of working with sick patients and their families. LPNs may face hazards from caustic chemicals, radiation, and infectious diseases. LPNs also are subject to back injuries when moving patients and shock from electrical equipment. They often face heavy workloads. Licensed practical nurses held about 702,000 jobs in 1994, working in hospitals, nursing homes, doctors offices, clinics, temporary help agencies, home health care services, or government agencies. All States require LPNs to pass a licensing examination after completing a State approved practical nursing program. In 1993, approximately 1,098 State approved programs provided practical nursing training. Almost 6 out of 10 students were enrolled in technical or vocational schools, while 3 out of 10 were in community and junior colleges, with the balance in high schools, hospitals, and colleges and universities (Figure 1). Most practical nursing programs last about one year and include both classroom study and supervised clinical practice. LPNs should have a caring, sympathetic nature, and should be emotionally stable because work with the sick and injured can be stressful. As part of a health care team, they must be able to follow orders and work under close supervision. 19 PAGE 28 Figure 1 Practical Nursing Programs in the United States V ocational Technical Schools60%Community Colleges30%Other10% 20 PAGE 29 The Curriculum Framework in the state of Florida (rule 6A10.040 FAC) requires a minimum basics skills grade level of 11.0 in mathematics for Practical Nursing programs when offered at the postsecondary adult vocational level. This grade level number corresponds to a grade equivalent score obtained on a state designated basic skills examination. In the state of Florida, the TABE test is such a basic skills examination. The TABE Form 5, level A mathematics test is designed to measure the following computation abilities (Appendix A): Addition of decimals and fractions. Subtraction of decimals and fractions. Multiplication of whole numbers, decimals and fractions. Division of whole numbers, decimals and fractions. Integers and percents Exponents and algebraic expressions Additionally, the TABE Form 5, level A mathematics test is designed to measure concepts and applications in the following categories: Numeration. Number sentences. Number theory. Problem solving Measurement Geometry 21 PAGE 30 The TABE The Tests of Adult Basic Education, Forms 5 and 6 (TABE 5 and 6) are normreferenced tests designed to measure achievement in reading, mathematics, language, and spelling the subject areas commonly found in adult basic education curricula. TABE 5 and 6 focus on basic skills that are required to function in society. Because the tests combine the most useful characteristics of normreferenced and criterionreferenced tests, they provide information about the relative ranking of examinees against a norm group as well as specific information about the instructional needs of examinees. The tests enable teachers and administrators to diagnose, evaluate, and successfully place examinees in adult education programs. The TABE test items reflect language and content that is appropriate for adults and measure the understanding and application of conventions and principles; they are not intended to measure specific knowledge or recall of facts. TABE can be used to provide preinstructional information about an examinees level of achievement in basic skills, to identify areas of weakness in these skills, to measure growth in the skills after instruction, to involve the examinee in appraisal of his or her learning difficulties, and to assist in preparing an instructional program to meet the examinees individual needs (TABE Examiners Manual, 1987). The mathematics portion of the TABE test consists of two sections. First (Test 3) is mathematics computation, 48 items that measure the operations of addition, subtraction, multiplication and division. Depending on the level of the test, content includes whole numbers, decimals, fractions, integers, algebraic expressions, exponents, 22 PAGE 31 and percents. Second (Test 4) are mathematics concepts and applications, 40 items that measure understanding of mathematics concepts. Specific skills include numeration, number sentences, number theory, problem solving, measurement, and geometry. Throughout the development of the TABE test, careful considerations were made to control for content bias, where questions of ethnic background, age and gender were concerned. The item selection process involved a threeparameter statistical model that took into account item discrimination, difficulty and guessing. The math operations included in the TABE test are summarized through the Modular Analysis of Learning Difficulties (MALD) developed by the Florida Department of Education, Division of Vocational, Adult, and Community Education in 1989 (Appendix B). The Department of Technical & Vocational Studies through the University of West Florida, Pensacola produced this evaluation tool for the SAIL project. The SAIL project is concerned with remedial training of vocational students in order to elevate their basic skills to an acceptable level, and utilizes student scores on the TABE test as an indicator of their ability level. This Modular Analysis of Learning Difficulty (MALD) is a summary sheet of the results of student scores on the TABE, forms 5 and 6, level A, for tests 3 and 4. In this study, form 5, Level A will be used for analysis. Approaches in Determining Occupational Math Requirements In his review of the literature, Pucel (1992) points out that there are two general approaches for determining occupationrelated math requirements. The two general approaches are (a) occupational analysis of job or training requirements and the math 23 PAGE 32 associated with fulfilling those requirements, and (b) standardized testing and establishing norms for occupations. The occupational analysis approach is primarily used by educators interested in determining the basic skills needed by a person on the job as a basis for the development of a training program, with the goal being to determine the requirements of a job and to prepare people to meet those requirements. The states student performance standards are a good example of the result of this approach. The main problem with this is in the oftenused group consensus method in which the occupational and related mathematics skills are identified through expert judgment, group opinion and formal analysis, and the taxonomy of math skills used as a basis for analyzing the math requirements. Through this process, various groups of experts often generate disparate lists of math skills. Each group creates its list around a math classification system uniquely agreed upon by the members of that particular group. The justification or the lack of reliability seems to be based on the assumption that the list will only be used in relation to the particular training program being developed (Greenan, 1984). The standardized testing approach is generally used to determine the global math requirements of a job as a basis for assessing the extent to which individuals have met those requirements. This approach often yields a grade level score or cutoff scores on test subscales. It is often used to screen people in terms of their ability to succeed in training or on the job with little or no concern for providing training to meet the psychological requirements of the job. There are two basic types of standardized tests related to math: (a) those tests which have been developed to measure student potential or aptitude and (b) basic skills achievement tests. These tests rarely provide sufficient 24 PAGE 33 information to direct curriculum development for specific math skills used in a particular occupation ( Pucel, 1992). The OMRA Instrument In an article published in the Journal Of Industrial Teacher Education (1995), Pucel describes the development of the performance based Occupational Mathematics Requirements Assessment (OMRA) instrument, the primary purpose of which is to assist in determining if the types of mathematics skills and the applications of those skills differ substantially among occupations prepared for through vocational education (Appendix B). The problem was stated that if there are substantial differences in the mathematics skill requirements of different occupations, and/or if the same skills are applied differently in different occupations, it might be more appropriate to tailor mathematics instruction to each occupation. The range of mathematics operations included in the OMRA inventory was developed for occupations requiring less than a baccalaureate degree those typically taught through vocational and technical education. The technique provides a vehicle for recording the number of occupational applications that require mathematics skills and the specific mathematics operations required for the completion of those applications. The OMRA instrument includes 63 specific mathematic operations, but as with the TABE, does not address the metric system. 25 PAGE 34 Pucels initial study in 1992 included the occupations of (1) secretary and (2) electronics technician, representing two different types of occupations that might require different types of mathematics skills. The study concluded that mathematics instruction for adults preparing for employment should not be taught again using traditional techniques used in elementary and secondary schools. The results clearly indicated that there are major differences in not only the mathematics skills required in different occupations but in the ways mathematics is applied in different occupations, and that these differences have curricular implications. The application of mathematics in one occupation may have little relevance for people in other occupations. Other Studies: Predictors of Student Success A 1988 study was conducted to evaluate the effectiveness of the Tests of Adult Basic Education in predicting success or lack of success in selected postsecondary health occupations programs, including Practical Nursing. The total population for the research was 1,485 students enrolled in postsecondary health occupations programs in the state of Kentucky. The predictor variables used were the TABE reading and mathematics grade equivalent scores and the number of times each section of the TABE was taken. Criterion variables were (1) successful completion of a health program or withdrawal and (2) scores from the Kentucky Vocational Achievement Test (KVAT). Pearson product moment correlation coefficients and true stepwise multiple regression analysis were used to test the correlation using .05 level of significance. The conclusion was that the TABE 26 PAGE 35 reading and mathematics grade equivalent scores and number of attempts were not good predictors of program completion or withdrawal. Discriminant analysis failed to classify completion or withdrawal correctly from any of the health programs (Author /KC). At the University of South Florida, the purpose of a 1992 dissertation was to examine the predictive capabilities of the Tests of Adult Basic Education for Adult Vocational/Technical programs of Licensed Practical Nursing and Business Education. Each of the three sections of the TABE was examined to determine which contributed to the prediction of success in the two programs, and for those sections that did contribute to the prediction of success, a linear equation was developed to help counselors determine what combinations of scores best predict success. The variables sex and race were examined to establish if either added significantly to the prediction equation. The sample consisted of 100 students from each of the two programs. Discriminant analysis was used to ascertain the predictive capabilities of the variables as well as provide a means to assign group membership to the criterion variable. The TABE and the variables Sex and Race were found significant predictors of success in the LPN program. The three sections of the TABE together classified students better than the other combinations of variables. Reading alone classified students almost as well as the three sections of the TABE. Recommendations included (1) removing an existing cutoff grade level and examining the predictive capabilities again for possible changes, and (2) examining other variables for their predictive capabilities in conjunction with the TABE (Kittner, 1982). Another ED.D dissertation study conducted at Florida Atlantic University, although not directly relating to the TABE, used predictive discriminant analysis to determine the existence of variable subsets that predicted success in practical nursing 27 PAGE 36 programs. Chisquare analysis was used to test the significance of differences between program completion rates of remediated and nonremediated groups of practical nursing students. Of the 362 practical nursing students who entered this particular program approximately sixty percent completed. Analysis revealed that a number of crossvalidated models, or predictor sets, were significantly better at predicting success than both maximum and proportional chance criterion. The model that was the best predictor of dropouts contained the variables age, reading subtest score and math subtest score. Significant differences (p<.05) between the program completion rates of Licensed Practical Nursing students requiring remediation before program entry and those not requiring remediation were found for all subtests except reading (Booth, 1992). Summary The review of the literature demonstrates that there is indeed a concern in the value of the Tests of Adult Basic Education as a predictor of student success in Nursing and other vocational program areas. The TABE Examiners Manual admits that the test is not designed to measure specific knowledge. Pucel concludes that the application of mathematics in one occupation may have little relevance for people in other occupations, thus substantiating the question of whether the TABE can measure student ability levels pertaining to all occupations with the same criteria. The concern over the status of American education in the global environment, and the need for a work force equipped with more and different mathematical concepts, dictates that there be a transformation of our current mathematics curriculum. As this 28 PAGE 37 transformation has begun to occur over recent years, has there also become a need to change the instruments for measuring student achievement, and if so, does the TABE reflect these changes? As Lacampagne (1993) points out, the majority of standardized tests are still overly reliant on multiplechoice items that measure predominantly lowlevel mathematics skills. Does this also hold true for the TABE? Does the TABE in fact measure lower level skills where higherlevel skills are required for successful completion of the Practical Nursing program? Finally, the review of the literature demonstrates that the additional studies cited are contradictory to one another and inconclusive. 29 PAGE 38 Chapter 3: Methods This chapter describes the procedures followed for this investigation, which were consistent with the procedures outlined by Pucel in the coordinator manual for the Occupational Math Requirements Assessment (OMRA) instrument (Appendix C), which has been adjusted to meet the needs of this study, an analysis comparing the mathematics skills measured by the TABE vs. the mathematics requirements of the Practical Nursing program vs. what is indicated to be the math used on the job. Research Design This is a validation study of the TABE and the practical math operations required in the real world of the Practical Nursing occupation. The variables studied were (1) Math skills identified in job related application samples and (2) the math skills tested on the TABE. The congruence of these two sets of math skills was determined by using the OMRA inventory and the Spearman Rank Correlation. Using the OMRA inventory, the job related mathematic skills as indicated by the samples collected from active nursing practitioners were evaluated by three review teams, each consisting of an occupational expert and a math expert, and prioritized in regard to the frequency of use as an indicator of relative importance in the workplace. 30 PAGE 39 A listing of the specific mathematic operations tested by the mathematical subtest of the TABE was published by the State of Florida Department of Education, Division of Vocational, Adult, and Community Education in 1989 in the form referred to as the Modular Analysis of Learning Difficulties(MALD). This document was produced by the Department of Technical & Vocational Studies SAIL project at the University of West Florida. Following the analysis of each of these sets of mathematic skills, a comparison was made in order to determine whether the math skills tested on the TABE are consistent with the job related math skills identified by the samples collected from nursing practitioners. The correlations across the Practical Nursing mathematics job requirements and the TABE were determined using the Spearman Rank Correlation. The Setting The concern of students passing the math section of the TABE and subsequently not succeeding in the Practical Nursing program was expressed by the nursing program staff at the Sarasota County Technical Institute in Sarasota Florida. Most of the support, data collection and evaluation involved these people. Data was collected through a survey of program advisory committee members, local hospitals, medical offices and practicing nursing professionals. Teams of occupational and math experts were solicited from this same institution. The nursing occupation experts were nursing program instructors, and the math experts included instructional, administrative, and classified staff from the same school. 31 PAGE 40 The OMRA Instrument The Occupational Math Requirements Assessment (OMRA) is designed to determine the mathematics operations (skills) required for success in an occupation. The results of OMRA can be used as a basis for curriculum development and/or for judging an individuals occupational math preparation. OMRA was designed for use with occupations requiring less than baccalaureate degree preparation; therefore, the range of mathematics operations presented includes skills typically used in such occupations. It was also designed as a tool for local curriculum and training program development. Consequently, results are not necessarily generalizable beyond a local setting (Pucel, 1992). The OMRA Coordinator Manual points out that the OMRA can be used to determine the math operations required in an occupation, or as a basis for curriculum development in determining job applications which require math operations. This study was concerned with the math operations used in the Practical Nursing occupation. The resources required for using the OMRA include (1) a project coordinator, (2) occupational practitioners from whom samples of onthejob materials which contain applications requiring math can be obtained, (3) occupational experts, (4) math experts and (5) sample jobrelated materials which include applications requiring math. In order to conduct the analysis, the occupation which will be the focus of the analysis must be clearly defined. An occupational title which clearly communicates the 32 PAGE 41 occupation to be analyzed (in this case Practical Nursing) and a description of the occupation is required. One or more review teams, each of which includes an occupational expert proficient in the occupation to be analyzed and a math expert who has had experience with students preparing for the occupation, should be assembled. The more teams that are involved, the more valid the analysis will be. Three teams are recommended. Each of the occupational experts should be asked to recommend two or more people who have direct contact with jobrelated materials used by people in the occupation. People selected should include those individuals who actually engage in or supervise an occupation and who can furnish samples of on the job math requirements. OMRA is designed for use with samples of jobrelated materials, which include job applications requiring math. Job related math materials include any materials that contain references to the use of math and which are used by a worker on the job. They include, but are not limited to, materials containing charts, manuals, job aids, and tables used on the job. They can also include verbal references to job activities requiring math. The examples may contain actual math calculations, or they may verbally call for a job application, which requires math. The accuracy of the math assessment generated by the OMRA is enhanced when the jobrelated math materials are uptodate and when the accurately represent the entire range of occupational skills. Pucel suggests that the materials can be gathered entirely by mail or through a combination of mail and interviews. 33 PAGE 42 Job Related Materials Job related mathematic work samples (Appendix E) were obtained through sources supplied by nursing instructors and their advisory committee members and other practicing health care providers and facilities in a three county area. These sources included hospitals, assisted living facilities, pharmacies, doctors offices, governmental agencies, home health care providers, Nursing textbooks and other printed references. Some sources offered mathematic solutions to specific tasks, while others simply listed tasks without examples (Appendix F). The nature of the data requested was to supply examples of job related math materials used by practical nurses in their particular work environment while performing on the job. The information received demonstrated a range of mathematics applications associated with the occupation, including taking vital signs (temperature, blood pressure, respiration), collecting samples for testing and performing routine lab tests, and measure and administer pharmaceuticals. The TABE The Tests of Adult Basic Education (TABE) was examined since it must be taken by Practical Nursing students for entry into the program. TABE 3, form 5 was used. A related document produced by the Department of Technical & Vocational Studies (SAIL project) at the University of West Florida for the Florida Department of Education was published in 1989. This Modular Analysis of Learning Difficulties (MALD) itemized the math operations tested by the TABE, and prioritized the operations listed (Appendix A). 34 PAGE 43 This existing document was used as being representative of the math operations included in the TABE. The Analysis Teams Three analysis teams, each of which included an occupational expert proficient in the occupation to be analyzed and a math expert who has had experience with students preparing for the occupation, were assembled. It is not reasonable to assume that an occupational expert has the necessary knowledge of math, nor that a math expert has the knowledge of the occupation needed to analyze the math requirements of an occupation. Therefore, teams consisting of an occupational expert and a math expert reviewed the materials to identify the math skills involved. Three pairs of occupational and mathematics experts were identified. The occupational experts were vocational nursing instructors at the technical institute where the study took place. The instructors recommended math experts to be invited to work with them. The math experts included a high school math teacher, a testing center statistician and pharmacologist. Each team was charged with the task of evaluating both the mathematics functions included in the student performance standards of the program and the samples of mathematics applications provided from the workplace. 35 PAGE 44 Procedures The following procedures were adapted from David Pucels OMRA Coordinator Manual (1992). The process for coordinating the assessment followed the steps outlined below. A. Determine the specific mathematic operations used routinely on the job by entry level Licensed Practical Nurses. 1. The researcher identified three pairs of occupational and math experts to fulfill the need of analysis teams for the purpose of this study. 2. Occupational practitioners were identified through the recommendations of the members of the analysis teams, nursing experts, program nursing instructors and the Practical Nursing program advisory committee. 3. Samples were obtained from occupational practitioners of job related materials that include applications requiring math. These materials were later compiled and became the job related material source used by occupational experts and math experts when completing their part of OMRA. (Appendix E) 4. A pilot sample application was administered to the analysis teams to review and to confirm their comprehension of the procedures required of the OMRA instrument. (Appendix D) 5. The teams of occupational and math experts were provided with Team Member Evaluation Packets (sets of materials collected pertaining to 36 PAGE 45 this study) including job related materials, the OMRA Inventory, OMRA Applications Supplement, and directions. (Appendix B) These materials were reviewed with each team for understanding. Using the OMRA inventory, each team evaluated the mathematics operations required to complete each of the workplace mathematics applications as supplied in the workplace samples package. For each workplace sample, team members would record the question number in the OMRA inventory box beside the math operations required to solve that sample. Upon completing this process for each sample math application, each team submitted their results to the researcher for compilation 6. After receiving the results for each of the analysis teams, the math operations noted in the OMRA inventory boxes were prioritized, and a list of math operations for the occupation was developed. B. Determine the specific math operations tested by the mathematical subtests of the TABE. 1. The math operations tested by the TABE are identified and prioritized by the published MALD for Test 3, Form 5. (Appendix A) C. Determine to what extent the specific mathematical operations identified for each of the variables were congruent. 37 PAGE 46 1. The prioritized lists of job related math operations and the math operations tested by the TABE were compared using the Spearman rank correlation. 2. The job related math applications were compared to the math applications tested on the TABE by a side by side comparison of related math operations. Pilot Prior to commencing the study of occupational math requirements for the Practical Nursing program, a pilot was conducted to test each teams understanding of the procedures to be followed, and also to check for internal reliability. The following example was used: The perimeter of a shape is 275 feet. Four of its six sides add up to 195 feet. The remaining to sides are equal. What is the length of each remaining side? 275 195 = 80 / 2 = 40 The mathematic operations involved in this calculation include subtraction of whole numbers and division of whole numbers. These operations would be recorded for this question on the OMRA inventory in the appropriate blocks for Integers, sections 14 and 16 as noted in Appendix D. 38 PAGE 47 Compiling of Data The specific mathematic operations used routinely on the job by Practical Nurses was determined through the collection of samples of job related math applications acquired through a variety of practicing nursing professionals. Using the OMRA inventory, these applications were then broken down into specific math operations as itemized by the OMRA instrument, by each team. The team results were compiled and compared item by item to examine the intergroup consistency. Operations identified by only one team were reviewed to determine if there appeared to be any systematic bias. This was done by reviewing the actual jobrelated materials and to verify that math was required. A list containing only those operations which were selected by more than one team (or were selected by one group and verified by the other analysis teams) was developed. A prioritized list of these math operations was created, determined by the frequency of use of an operation. This was done by adding the frequencies of use for all math operations indicated in the cells in the tally block for that operation on the OMRA instrument. Once the total frequency of usage had been calculated for each operation for each team, an average frequency across all three teams was calculated. The prioritized list was created, based first on the number of teams indicating the operation was required, then on the average frequency of use calculated across the teams. The specific mathematic operations tested by the TABE were published by the Florida Department of Education in the form on a Modular Analysis of Learning 39 PAGE 48 Difficulties (MALD) for the test (Appendix A). This form was used for the prioritizing of the math operations tested by the TABE. 40 PAGE 49 Chapter 4: Findings This project investigated the following research questions. 1. What are the specific mathematics operations used routinely on the job by entry level Licensed Practical Nurses? 2. What are the specific mathematics operations tested by the mathematical subtests of the TABE? 3. To what extent are the specific mathematical operations identified for each of the above consistent? The findings of this study are presented for each specific research question relating to mathematics and the Practical Nursing occupation. Job Related Math Operations To address research question number one, it was necessary to determine what specific mathematic applications are routinely involved on the job for entry level Licensed Practical Nurses as evidenced by work samples. This was accomplished through the solicitation of a variety of nursing practitioners, including hospitals, assisted living facilities, medical offices, program instructors and advisory committee members. The practitioners were asked for samples of job related materials which include job applications requiring the use of math. These job related math materials could include 41 PAGE 50 any materials that contain references to the use of math and which are used by practical nurses on the job They could include, but were not limited to materials containing charts, manuals, job aids, and tables used on the job. They could also include verbal references to job activities requiring math. The materials received in response to the request included textbook examples, hospital patient medication records, physicians order sheets, classroom learning modules, hospital employment test, lists of job tasks involving math (applications), some sample math problems with solutions, and blood bank procedural examples where math calculations or skills would be required. Three pairs of occupational and mathematics experts were identified for the purpose of evaluating the materials collected. Occupational experts were vocational nursing instructors at the technical institute where the study took place. The instructors recommended math experts to be invited to work with them. The math experts included two math teachers and a statistician. The teams of occupational and math experts were provided with Team Member Evaluation Packets which included the job related math work sample problems and documents collected by the practitioners, and through consensus agreed on the math applications which were required by the profession to be calculated. The applications ranged from calculating medicinal dosages to intravenous drip flow rates to household conversions. From all of the examples submitted by all of the contributors, duplications and redundancies were eliminated, condensed or combined to a representative total of fifteen math applications (sample problems) to be broken down into specific math operations (Appendix E). Although the list of summarized math 42 PAGE 51 applications is not extensive, it was deemed to be representative of the math needs of the Practical Nursing profession and suitable for the research purposes. Using the OMRA inventory, each team determined the mathematics operations (multiplication, division, addition, etc.) required to complete each of the workplace mathematics applications as indicated on the workplace samples package solicited from the practical nurses. For example, the math application of converting temperatures from Centigrade to Fahrenheit would involve the two math operations of multiplying decimals and adding whole numbers. Upon completing their evaluations using the materials supplied to them, each team submitted their results to the researcher for compilation. The job related math applications required for the Practical Nursing profession consisted of a total of 19 of the 63 mathematics operations contained on the OMRA Inventory (Table 1). Based on the analyses of the work samples provided by the nursing practitioners conducted by the evaluation teams, it appears as if the nurses surveyed used approximately 30% of the 63 math operations listed on the OMRA. Each math operation was identified as being a part of the work samples by at least one of the three teams. Those skills identified by only one team were verified by all analysis teams as being an acceptable method to perform the applications based on the job materials review, or to be an acceptable alternative method of calculation. Six math operations were identified by all three groups, six by two groups, and seven by only one group. The frequency of these operations were determined by the members of the analysis teams with math experts ranging from a math teacher on team #1, a pharmacist on team #2, and a statistician on team #3 and do not necessarily reflect the preferred methods of mathematic calculations that would be used by any or all individual nurses. For example, 43 PAGE 52 where one might prefer to multiply fractions, another might use decimal equivalents. Where one might prefer to use algebraic equations, another may not. This might explain the dramatically varying frequency of some math operations while all teams looked at the same materials. The frequency of each operation was recorded for each team and then averaged. The operations used were then ranked by priority based on the average number of times it was identified (Table 1). In examining the correlation between the teams preference in math operations used, using the frequency of each math operation as ranked by each team, the Spearman Rank Correlation was used. With n=19, and a significance at the a 1 =.05 level, the critical value for rejecting the null hypothesis p=0 is .338. The results are as follow. Correlation of Team #1 and Team #2: r = .9 Correlation of Team #1 and Team #3: r = .64211 Correlation of Team #2 and Team #3: r = .5535 The variety of the teams opinions on the priority of math preferences is evidenced by the rejection of the null hypothesis this for each of the correlations among the teams. 44 PAGE 53 Table 1 Practical Nursing Occupational Math Operations (Ordered by Frequency Ratings Across Teams) Cell OMRA Operation Identified in Work Samples Team 1 Team 2 Team 3 Avg. f Priority Three Teams Selected the Operation 15 Multiply Whole Numbers 5 20 16 13.7 1 16 Divide Whole Numbers 2 14 11 9 2 24 Multiply Fractions 3 8 8 6.33 3 52 Solve the Proportion 4 5 9 6 4 14 Subtract Whole Numbers 3 4 3 3.3 5 31 Add Decimals 1 2 2 1.7 6 Two Teams Selected the Operation 25 Divide Fractions 0 7 4 3.7 7 53 Conversion of Units 0 3 7 3.3 8 66 Solve Equations for x 0 41 4 2.7 9 67 Solve Equations for fractions for x 0 5 1 2 10 35 Multiply Decimals by Decimals 0 2 3 1.7 11 13 Add Whole Numbers 0 1 2 1 12 One Team Selected the Operation 17 Round Off 0 0 6 2 13 27 Reduce Fractions 0 0 4 1.3 14 46 Determine the Percent 0 0 2 0.7 15 28 Write as a Mixed Number 0 0 1 0.3 16 213 Fraction of a Whole Number 0 0 1 0.3 17 32 Subtract Decimals 0 0 1 0.3 18 65 Transpose Formulas 1 0 0 0.3 19 45 PAGE 54 TABE Math Operations To answer research question number two, the published Modular Analysis of Learning Difficulties (MALD) for TABE 3, Form 5 was used since the math operations itemized for this test are already listed and prioritized, not necessarily by the number of times used on the exam, but in their assumed relative importance (Appendix A). Not all of the math operations used in the practical nursing job samples were listed in the MALD, thereby increasing the number of outliers encountered in the analysis. The top 19 prioritized math operations listed by the MALD are listed in Table 2. When compared to the ranked 19 job related math operations on Table 4, a difference in priorities can be observed. 46 PAGE 55 Table 2 Top Prioritized Math Operations TABE Priority TABE 1 Expanded Notation 2 Multiply Whole Numbers 3 Divide Whole Numbers 4 Add Fractions 5 Subtract Fractions 6 Multiply Fractions 7 Divide Fractions 8 Add Decimals 9 Subtract Decimals 10 Multiply Decimals 11 Divide Decimals 12 Recognize Numbers 13 Place Value 14 Numeration Comparisons 15 Rounding 16 Estimating 17 Number Lines 18 Exponential Notation 19 Scientific Notation Congruence Among the Sets The third research question was to determine to what extent the specific mathematical operations identified from each of the two sources were congruent. The unranked math operations listed on the OMRA instrument are listed in the column on the left in Table 3, and those operations identified in the job related samples and on the TABE MALD are listed in the appropriate column to the right. An X in the cells indicates if that math operation was used in the work related math samples and/or on the 47 PAGE 56 TABE. With 19 math operations identified from the work related samples, and 31 from the TABE MALD, a mismatch between the two variables is initially evident. Table 3 OMRA Instrument Math Operations Used in Work Related Samples, and the TABE OMRA Operation Work Related Samples TABE MALD INTEGERS Words to Arabic Numbers Add Whole Numbers X X Subtract Whole numbers X Multiply Whole Numbers X X Divide Whole Numbers X X Round Off X X Add Signed Numbers Subtract Signed Numbers Multiply Signed Numbers Divide Signed Numbers FRACTIONS Order Fractions Add Fractions X Subtract Fractions X Multiply fractions X X Divide Fractions X X Least Common Denominator Reduce Fractions X Write as a Mixed Number X Add Mixed Numbers X Subtract Mixed Numbers X Multiply Mixed Numbers X Divide Mixed Numbers X Fraction of a Whole Number X X DECIMALS Add Decimals X X Subtract Decimals X X Decimal to a Fraction Fraction to a Decimal Multiply a Decimal by a Decimal X X Divide a Decimal by a Decimal X 48 PAGE 57 OMRA Operation Work Related Samples TABE MALD PERCENTS Convert Percents to Fractions Convert Percents to Decimals Convert Fractions to Percents X Take the Percent X Determine the Percent X X RATIOS Ratio in Lowest Terms X Solve the Proportion X X Conversion of Units X ALGEBRA Add Monomials Subtract Monomials Divide Monomials Transpose Formulas X Solve Equations for x X X Solve Equations with Fractions for x X X Solve Equations: Graphically Solve Equations: Algebraically Find the Root X Factor Quadratic Equation Quadratic Equation Complete the Square Quadratic Equation Use Quadratic Formula GEOMETRY Identify Two Dimensional Figures Identify Three Dimensional Figures Estimate Angles X Name Angles Name Combination of Angles Perimeter X Circumference or Diameter of a Circle Area of a Square or Rectangle X Area of a Triangle or Circle X Volume of a Rectangular Solid X Volume of a Cylinder or Sphere X Total Math Skills 19 31 49 PAGE 58 Correlation Between TABE and Job Sample Rankings. With the job related math operations and the TABE math operations being prioritized, or ranked, the Spearman rank correlation was used to determine the correlation between the TABE test and the practical nursing mathematics job samples. The mathematic operations in the left column of table 4 are listed according to the ranked list of the job related math requirements (x). The TABE MALD rankings of those same operations are listed in the next column (y). Where the math operation of multiplying whole numbers was ranked number 1 in the job related math skills listing from Table 1, the TABE MALD rated that same operation as number 2. The same was done for each of the 19 job related math operations identified from the work samples. In some cases the TABE MALD did not include a ranked job related math operation at all. These are reflected as the highest rankings in the TABE column. The differences were subtracted and squared, thus preparing for the calculation of the value of r. 50 PAGE 59 Table 4 Correlation of Math Skill Priorities between the TABE and the Practical Nursing Job Samples. Prioritized Description of Operation Job Related Math (x) Ranking TABE (y) Ranking D D 2 Multiply Whole Numbers 1 1 0 0 Divide Whole Numbers 2 2 0 0 Multiply Fractions 3 3 0 0 Solve the Proportion 4 15 11 122 Subtract Whole Numbers 5 17 12 144 Add Decimals 6 5 1 1 Divide Fractions 7 4 3 9 Conversion of Units 8 10 2 4 Solve Equations for x 9 14 5 25 Solve Equations for fractions of x 10 9 1 1 Multiply Decimals by Decimals 11 7 4 16 Add Whole Numbers 12 18 6 36 Round Off 13 8 5 25 Reduce Fractions 14 12 2 4 Determine the Percent 15 13 2 4 Write as a Mixed Number 16 11 5 25 Fraction of a Whole Number 17 19 2 4 Subtract Decimals 18 6 12 144 Transpose Formulas 19 16 3 9 D 2 = 573 Calculated value of r = 1 6D2 = 1 6(573 ) =1 3438 = 1 .5026 =.4974 n(n 2 1) 19(3611) 6840 With a significance at the a 1 = .05 level when n=19, the critical value for rejecting the null hypothesis p=0 is 0.338 (Glass & Hopkins, Table K, 1984). With an r of .4974, the null hypothesis will be rejected, demonstrating little correlation among the Practical Nursing job requirements math and that tested by the TABE. 51 PAGE 60 A visual reference to the correlation between the Practical Nursing mathematics job requirements (X) and the TABE test (Y) is demonstrated by the following scatter plot (Figure 2). Figure 2 Scatter Plot of Spearman Rank Correlation across Practical Nursing Mathematics Job Requirements and the TABE 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 TABE Ranking (Y) 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Job Related Samples Ranking (X) It can be observed that there exists little correlation among the Practical Nursing job related math skill priorities and priorities of the math skills tested by the TABE. Although some operations such as subtracting whole numbers may seem to be inclusive 52 PAGE 61 in math operations in daily life, they were not specifically included in the TABE MALD and as such were given the highest of the TABE rankings. 53 PAGE 62 Chapter 5: Discussion, Conclusions, Implications and Recommendations This preliminary study was based on a concern expressed by Practical Nursing staff at a technical institute. The concern was that students who had scored acceptably on the Tests of Adult Basic Education (TABE) for program entry very often were unable to succeed in the actual math requirements of the program. They were not prepared for the mathematics required by the curriculum of the program as outlined by the Florida Department of Education Curriculum Frameworks. In accordance with rule 6A10.040 FAC, as stated in the curriculum frameworks, the minimum skills grade required for the program when offered at the postsecondary adult vocational level 11.0 for mathematics. This grade level number corresponds to a grade equivalent score obtained on a state designated basic skills examination (the TABE). Instructors were concerned that the TABE, while testing general math skills, did not reliably test the specific math skills necessary for successful completion of the Practical Nursing program. The intent of this study was to compare job related math requirements of the Practical Nursing occupation as evidenced from work samples collected, and then determine how congruent these math skills were with those measured by the TABE math sections. The Occupational Math Requirements Assessment (OMRA), developed by David Pucel in 1992, was chosen as the instrument to be used for this purpose. The procedures for this study were based on those suggested by the instrument. 54 PAGE 63 Summary of Study Procedures Three occupational experts were selected nursing instructors from a Practical Nursing program. These three occupational experts selected three math experts with which to form teams for the purpose of assessing the scope of math in question. Additional participants also suggested by the nursing instructors included nursing program advisory committee members representing a sampling of local hospitals, assisted living facilities, medical offices, blood banks and other current practitioners. These sources were instrumental in the collection of samples of job related work mathematics required for the profession. Following the selection of participants and the forming of the teams of experts as outlined by the OMRA instrument, samples of job related mathematics requirements were collected from a variety of sources. Using the OMRA instrument, each of the three teams evaluated the job math applications, and determined the specific mathematics operations required to complete these applications. The mathematics portion of the TABE (Form 5, Level A) was used as the sample test, as this version of the TABE was in effect at the time of the initiation of this study for admission standards required by the Practical Nursing and other occupational program areas. The mathematic operations determined by the teams to be required for job related math applications were compared to the operations stated on the TABE MALD. The job related operations were prioritized by the average usage of each as determined by the 55 PAGE 64 teams, and ranked accordingly. The TABE math operations were ranked as stated by the MALD. The Spearman rank correlation was used to evaluate the correlation between the TABE and the Practical Nursing program mathematic job requirement rankings. Discussion of Findings A summary of the findings of this study are as follow: Based on a collection of work related math samples submitted by local practitioners, it was determined that the Practical Nursing occupation requires 15 math applications which utilize 19 math operations to solve. It appears that the Practical Nursing practice uses only a moderate amount of math on the job, as evidenced by utilizing only 19 of the 63 math operations contained on the OMRA inventory. The TABE does measure to some extent the mathematics required by the Practical Nurses. This was determined by the use of the Spearman rank correlation between the top ranked TABE math operations and those determined by the OMRA instrument from the job related math applications. With an r of .2202, the correlation was near the critical value of 0.338. 56 PAGE 65 Conclusions It may be concluded from this study that assumptions that are often made by educators and policy makers regarding the level of mathematics needed for entry into and for success in the completion of a vocational education program may not be consistent with the level of math skills that workers in that occupation need to perform their job related duties. Through the collection of job related math samples (applications) supplied by Practical Nursing practitioners, the actual mathematic operations required to calculate those applications were determined through the use of the OMRA instrument. When compared to the TABE mathematic operations identified on the TABE MALD, it was determined that the TABE is not a very adequate tool for measuring a students basic understanding of math, although it is far from perfect for measuring the requirements of the Practical Nursing program with an r =. 4974. One major problem found with the math skills evaluated on the TABE in relation to the Practical Nursing program is that reference to the metric system in the TABE math sections is not evident. The medical field, including Practical Nursing, is primarily driven by the metric system. Although the same math operations (add, subtract, multiply, divide, etc.) are required to work a problem whether in metric or standard measures, the possible lack of understanding of metrics could be detrimental to a students success in the program, whether scoring high on the TABE or not. This may not be related to the math operations involved, but rather in the terminology. 57 PAGE 66 Implications Where there is a low correlation with the job related math operations and the math operations tested by the TABE, it may hold that although a students score reflects their grade level ability in basic math operations, it may not accurately reflect a students ability to successfully complete the Practical Nursing program. The TABE may be considered to be a valid instrument for school or program entry, but should not be relied on as a predictor of student success. The question is raised as to whether the curriculum is also part of the problem. Are teachers of the program teaching the wrong math? Are they teaching more and different math than is required by the occupation? Recommendations For Practice A recommendation for increasing the correlation between the TABE and job related math operations, might be to add the job math operations not included into the TABE. The Practical Nursing program could develop and administer its own mathematics exam utilizing those applications and operations as discovered in this study, or as determined by conducting their own research in soliciting data from their own advisory committees and local practitioners. 58 PAGE 67 The Practical Nursing program staff appears to be aware of the problem, which initiated this study, and should be prepared to put more emphasis on teaching their students the required math. Each TABE form comes with several different levels. The TABE Form 5, Level A was used for this study. If TABE Form 5, Level E or M were used, then different math operations such as adding and subtracting whole numbers would have been included. A review of all forms and the levels included in those forms should result in a relatively appropriate instrument. In addition, the TABE is also offered in a Health Form for Health Occupations. This should deserve some investigation. Suggestions for Future Research Future research on this topic might be implemented in other geographical areas to determine if the math skills important to the Practical Nursing occupation are the same wherever it is found. A different mathematics assessment instrument other than the OMRA might be used to compare the differences in real world job related math operations required and those tested by the TABE. Investigate the correlation between TABE and other technical programs to see how accurately it predicts student success in those areas. 59 Utilize each available version of the TABE in order to determine which would be most appropriate for a specific program area. PAGE 68 Use the OMRA instrument to assess the math operations of the TABE, rather than utilizing the existing MALD. Utilize a different mathematics instrument other than the TABE to measure a students ability to succeed in the program. 60 PAGE 69 REFERENCES Blackwell, D., & Henkin, L. (1989). A Project 2061 Report: Mathematics. American Association for the Advancement of Science, Washington DC. Blank, William E. (1996). Lets Rethink Increasing Higher Level Math Requirements for All Students. A presentation at the National Academic and Vocational Education Integration Conference. Beaver Creek, Co Booth, Ernest G.(1992). Predicting Success In Practical Nursing Programs. Dissertation Abstracts International, 5303(B), 1274. Burns, M. (1994). Arithmetic: The Last Holdout. Phi Delta Kappan. 75(6), 471476. Dewdney, A.K. (1993). 200% Of Nothing. Wiley, New York. Gal, I. (1993). Issues and Challenges in Adult Numeracy. National Center on Adult Literacy, Philadelphia, PA. Gall, M.D., Borg, W.R. & Gall, J.P. (1996). Educational Research: An Introduction. Longman Publishers USA, White Plains, N.Y., Greenan, J.P. (1984). The Development and Validation of Generalizable Mathematics Skills Assessment Instruments. Journal of Vocational Education Research, 9(3), 1430. K.C. (1988). Health Program Entrants Math/Reading/Success Review. ED302655, 36. Kittner, Marcy L. (1982). Validating The Use of the Tests of Adult Basic Education for Predicting Success in Selected Vocational/Technical Programs. Dissertation Abstracts International, 4312(A), 3799. Lacampagne, Carole B. (1993). Transforming Ideas for Teaching and Learning Mathematics. U.S Department of Education, Washington, DC National Coalition For Advanced Manufacturing (1992). Preparing Technical Workers For The New Industrial Era, A Position Paper. 61 PAGE 70 Mosbys Comprehensive Review of Practical Nursing (1990). C.W. Mosby Company, St. Louis. United States Department of Labor (2002). Occupational Outlook Handbook, McGraw Hill, New York. Payne, David A. (1992). Measuring and Evaluating Educational Outcomes. Macmillan Publishing Company, New York. Pucel, David J. (1995). Occupationally Specific Mathematics Requirements and Application Contexts. Journal of Industrial Teacher Education 32 (2), 5175. Pucel, D.J., Feickert, J.D. & Lewis, M. (1992). Performancebased occupational mathematics requirements assessment (OMRA): Implementation and Supporting Research. National Center for Research in Vocational Education, University of California at Berkeley, Berkeley, CA.. Pucel, D.J. & Knaak, W.C. (1975). Individualizing Vocational and Technical Instruction. Charles E. Merrill Publishing Company, Columbus, Ohio. Pucel, David J. (1989 ). Performance based instructional design McGrawHill Publishing Company, New York. Shelby, S., & Johnson, J. (1988). Tying It All Together. Vocational Education Journal, 63(2), 2729. State of Florida, Department of State (1989). Department of Education, Division of Vocational, Adult and Community Education. Modular Analysis of Learning Difficulties (MALD) Produced by Department of Technical & Vocational Studies (SAIL Project). The University of West Florida, Pensacola. TABE Tests of Adult Basic Education (Forms 5 and 6),(1990). Norms Book, CTB/McgrawHill, Monterey, CA. TABE Tests of Adult Basic Education (Forms 5 and 6), (1987). Examiners Manual, CTB/McgrawHill, Monterey, CA.. TABE Tests of Adult Basic Education (Form 5, Level A), (1987). Complete Battery, CTB/McgrawHill, Monterey, CA. TABE Tests of Adult Basic Education (Level D), (1987). Survey Form, CTB/McgrawHill, Monterey, CA. 62 PAGE 71 R. Marshall & M. Tucker (1992). Thinking For A Living HarperCollins Publishers, New York, New York. U.S. Department of Education (1983). A Nation At Risk. U.S. Government Printing Office, Washington DC. U.S. Department of Education (1987). What Works: Research About Teaching and Learning. Second Edition. Washington DC. U.S. Department of Education (1991). Trends in Academic Progress, Report No. 21T01. Washington DC. U.S. Department of Labor (1991). What work requires of schools: A SCANS report for AMERICA 2000 U.S. Government Printing Office, Washington, DC. U.S. Department of Labor, Bureau of Labor Statistics (May, 1992). Outlook 19902005, Bulletin 2402, Monthly Labor Review, U.S. Government Printing Office, Washington, D.C. Withnall, A. (1995). Older Adults Needs and Usage of Numerical Skills in Everyday Life. Rutgers University Press, New Brunswick, NJ. 63 PAGE 72 Appendix A Modular Analysis Of Learning Difficulties (MALD) TABE Test Forms 5 and 6, Level A Mathematics 64 PAGE 73 65 PAGE 74 66 Appendix A (Continued) PAGE 75 Appendix B OMRA Instrument 67 PAGE 76 68 PAGE 77 69 Appendix B (Continued) PAGE 78 70 Appendix B (Continued) PAGE 79 71 Appendix B (Continued) PAGE 80 72 Appendix B (Continued) PAGE 81 73 Appendix B (Continued) PAGE 82 74 Appendix B (Continued) PAGE 83 75 Appendix B (Continued) PAGE 84 Appendix C OMRA Coordinator Manuel 76 PAGE 85 77 PAGE 86 78 Appendix C (Continued) PAGE 87 79 Appendix C (Continued) PAGE 88 80 Appendix C (Continued) PAGE 89 81 Appendix C (Continued) PAGE 90 82 Appendix C (Continued) PAGE 91 83 Appendix C (Continued) PAGE 92 84 Appendix C (Continued) PAGE 93 Appendix C (Continued) 85 PAGE 94 86 Appendix C (Continued) PAGE 95 Appendix D Pilot OMRA Application Calculation 87 PAGE 96 88 PAGE 97 Appendix D (Continued) 89 PAGE 98 90 Appendix D (Continued) PAGE 99 Appendix E Job Related Math Applications for Practical Nursing 91 PAGE 100 Conversions 1 Household 3 tsp = _______gtt teaspoons : drops :: teaspoons : drops 1 : 60 :: 3 : x x = 180 gtt = 3 tsp 2 Apothecary 3 oz = ____dr ounces : drams :: teaspoons : drops 1 : 8 :: 3 : x x = 24dr = 3 oz 3 Metric 250 mg = ____ g milligram : gram :: milligram : gram 1000 : 1 :: 250 : x 1000x = 250 x = 0.25 g = 250 mg 4 Conversion Between Systems Gr 1/6 = ______mg grains : milligrams :: grains : milligrams 1 : 60 :: 1/6 : x lx = 60 x 1/6 x = 10 mg = gr 1/6 5 Centigrade to Fahrenheit 20 o C x 1.8 + 32 o = 68 o F 6 Fahrenheit to Centigrade 68 o F 32 o x .5556 = 20 o C 92 Appendix E (Continued PAGE 101 Dosage Calculations 7 Give 500 mg of tetracycline using capsules containing 250 mg. 500 mg 250 mg x 1 capsule = 2 capsules 8 Physician orders Demerol 35 mg. IM. You have on hand 50 mg/cc. How much do you give? 35 50 x 1 = .7 cc IV Drip Calculations 9 Administer 1000 ml of dextrose 5% in water over 8 hr using an infusion set that delivers 10 gtt per minute. 1000ml 8 hr = 125 ml/hr 125 ml/hr 60 min/hr = 2.1 ml/min 2.1 ml/min x 10 gtt/ml = 21 gtt/min 10 Physician has ordered 2500 ml to be delivered in 24 hours. After 12 hours, 1500 ml have been delivered. The solution must run at _____ ml/hr to deliver the remaining solution. 2500 ml 1500 ml = 1000 ml remaining solution to be delivered 24 hrs 12 hrs = 12 hrs remaining time to complete delivery 1000 ml 12 hr = 83 ml/hr 11 Using 10 gtt tubing, give 125 ml/hr. Flow rate in gtts/min = ____ 125 ml x 10 gtts/ml = 1250 = 21 gtts 1 hr x 60 min/hr 60 min Appendix E (Continued) 93 PAGE 102 Calculate Infection Control Statistics 12 If there are 1534 patient days for the month of August If there were 17 nosocomial urine infections The % rate for total nosocomial urine infections for the month is __ (17 1534) x 100 = 1.10821 Blood 13 Determine the percent RBC recovery. mls RBC post x 100 = % RBC recover mls RBC pre 14 Calculate Platelets/Unit and record results. Raw Count x 10 3 x volume = Plt/Unit x 10 10 15 Calculate the amount of blood to draw from a donor who weighs 90 pounds. 450 x (donor weight / 110) = ml to draw 450 x (90 / 110) = 450 x o.81 = 365 ml 94 PAGE 103 Appendix F Assortment of Job Related Mathematics Samples Collected 95 PAGE 104 Appendix F (Continued) 96 PAGE 105 Appendix F (Continued) 97 PAGE 106 Appendix F (Continued) Appendix F (Continued) 98 PAGE 107 99 Appendix F (Continued) PAGE 108 Appendix F (Continued) 100 PAGE 109 Appendix F (Continued) 101 PAGE 110 Appendix F (Continued) 102 PAGE 111 Appendix F (Continued) 103 PAGE 112 Appendix F (Continued) 104 PAGE 113 105 xml version 1.0 encoding UTF8 standalone no record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd leader nam Ka controlfield tag 001 001447448 003 fts 006 med 007 cr mnuuuuuu 008 040114s2003 flua sbm s0000 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0000189 035 (OCoLC)54702536 9 AJN3892 b SE SFE0000189 040 FHM c FHM 090 LC1043 1 100 Clary, G. H. 0 245 Congurence among mathematics skills used on the job by practical nurses vs. the prerequisite skills required for admission into the practical nursing program h [electronic resource] / by G. H. Clary. 260 [Tampa, Fla.] : University of South Florida, 2003. 502 Thesis (Ed.S.)University of South Florida, 2003. 504 Includes bibliographical references. 516 Text (Electronic thesis) in PDF format. 538 System requirements: World Wide Web browser and PDF reader. Mode of access: World Wide Web. 500 Title from PDF of title page. Document formatted into pages; contains 113 pages. 520 ABSTRACT: The standard for evaluating a student's mathematic ability (grade level) for admission to many vocationaltechnical programs is through the administration of the Tests of Adult Basic Education (TABE). There has come forth a concern from vocational educators, that students entering programs may not be prepared for the mathematics required by the curriculum, even though the student has met the criteria for entry as established by the state curriculum frameworks as evidenced by their scores on a TABE which had recently been administered. Furthermore, questions raised among instructional, administrative and guidance personnel about the congruence of math skills required on the TABE vs. those used by practical nurses on the job supported the need for a study to determine the congruence of these sets of mathematics skills. Using the OMRA inventory developed by David Pucel, the mathematic operations required for job related math applications are indicated by samples collected from active nursing practitioners. Three analysis teams consisting of practical nurses and math experts were established and determined the math operations required for solving the job related math samples collected. The math skills tested by the TABE were then compared to the job related math samples. With the math operations of the variables ranked, the Spearman Rank Correlation was used to evaluate the correlation across the TABE and the mathematic job requirements of practical nursing. Based on 19 math operations identified from the Practical Nursing job math requirements, the results showed that there was little correlation among these two variables (r=. 4974). Keywords: Practical Nursing, Mathematics Skills, Postsecondary Vocational Education, TABE. 590 Adviser: Blank, William E. 653 tabe. postsecondary vocational education. math skills. practical nursing. 690 Dissertations, Academic z USF x Vocational Education Specialist. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.189 