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Educational policy analysis archives.
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c February 28, 2000
Forces for change in mathematics education : the case of TIMSS / Donald S. Macnab.
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1 of 18 Education Policy Analysis Archives Volume 8 Number 15February 28, 2000ISSN 1068-2341 A peer-reviewed scholarly electronic journal Editor: Gene V Glass, College of Education Arizona State University Copyright 2000, the EDUCATION POLICY ANALYSIS ARCHIVES. Permission is hereby granted to copy any article if EPAA is credited and copies are not sold. Articles appearing in EPAA are abstracted in the Current Index to Journals in Education by the ERIC Clearinghouse on Assessment and Evaluation and are permanently archived in Resources in Education Forces for Change in Mathematics Education: The Case of TIMSS Donald S. Macnab Northern College Aberdeen, ScotlandAbstractThe results of the Third International Study in Mat hematics and Science Education (TIMSS) were published in 1996/7. Since t hat time the participating countries have reacted in a variety o f ways to the comparative performance of their students. This art icle investigates the diverse effects these reactions have had on mathema tics curricula and teaching methodologies in a selection of these coun tries, within the context of a wider analysis of the motivations whic h determine change in education.Introduction What causes schools' mathematics curricula and teaching methodologies to change over time? To what extent do they change in a ratio nal response to external objective considerations; to what extent subjectively in acco rdance with beliefs and social pressures? What does success mean in relation to ch ange? Often enough, the effect of change (planned or otherwise) is to metamorphose an tecedent success criteria to validate


2 of 18the change, at least in the short term. In the worl d of politics this is a commonly recognised practice; in education, less so. Fullan (1993) documents many such instances in education from the 1960s onwards. Reviewing the last 30 years, he concluded that "we have been fighting an uphill battle.... We need a different formulation to get at the heart of the problem, a different hill, so to speak We need, in short, a new mindset about educational change."(p 3). For an analysis in a Sco ttish context, see Macnab (1999a). In Fullan's words, the essence of the diffi culty is that "we have an educational system that is fundamentally conservative. The way that teachers are trained, the way that schools are organised, the way the educational hierarchy operates, and the way that education is treated by political decision-makers r esults in a system that is more likely to retain the status quo than to change. When change is attempted under suc h circumstances it results in defensiveness, superfic iality, or at best short-lived pockets of success." (Fullan, 1993, p. 3). All those involved in promoting and impleme nting change do so from a sense of moral purpose to improve education. In a study of e ducational innovation in science mathematics and technology education in 13 countrie s (Black & Atkin, 1996), the authors conclude that "things are much more complic ated than they seem.... Comparisons [between different countries] illustrat e how the historical perspective and the cultural embedding—of educational thinking, of conceptions of change, and of the nature of the particular subjects involved—all have a profound effect on any process of change. [These comparisons] also illustrate the com plexity of change. Fashionable opposites, such as top-down v. bottom-up, or teache r-active v. teacher-passive, are not helpful. In the real world action and change take p lace in more complex ways and at intermediate points along these bi-polar axes. Ther e is another reason why change is complex. When it succeeds, it often does so for unf oreseen causes. Those who think they control it sometimes find that unpredictable inner imperatives have passed control to others. Planned hierarchies of people collapse. Stu dents may be better motivated but learn less. Teachers may be enthusiastic but studen ts resistant, or vice-versa." (Black & Atkin, 1996, pp. 1-2). Black and Atkin devote a chapter of their b ook to the question "What drives reform?" They comment that "every country that part icipated in our international study is dissatisfied with that education of its students in science, mathematics, or technology. Every country is trying to make changes.... Every c ountry seems to be more or less unhappy with what it has today.... At any moment, h owever, each country will be preoccupied about different perceived ills.... Each country is fighting its own demons. But there is a paradox. All the most important pres sures and influences that promote change in science, mathematics, and technology educ ation in schools keep re-appearing as we move from one country to another. None appear s only in a single country, and in that sense little is unique. Yet the countries are different and distinct, because each attributes a different weight to particular problem s and to how they combine and interact. No country is ever exactly in phase with any other because each is a creature of its own unique history and evolution." (Black & Atk in, 1996, pp. 12-13). In an earlier study, (Adams & Chen, 1981), the authors ask "Why then is the history of innovation such a doleful one? Why, according to the literature, is failure its companion so frequently? Why, given the burning ent husiasm of the advocates of reform, do teachers remain unimpressed, even glum, and administrators shudder?" (p. 1). In the final two paragraphs of their book they conc lude a further set of questions commenting that, "the questions, it seems are endle ss.... [T]o finish the book on such a note of uncertainty is distressingly unimaginative. (p. 282). They do not, however, provide clear-cut answers to the questions with whi ch they began.


3 of 18 The evidence from these studies and others is that the central imperative and dilemma underlying the change process in education is a sense of dissatisfaction with the status quo giving rise to the feeling that change i s necessary, combined with confusion about its purpose, and uncertainty about the nature and value of its outcomes, with potential resulting disappointment and frustration for planners and teachers alike.TIMSS and Change The Third International Mathematics and Sci ence Study (TIMSS), the largest international survey of attainment in mathematics a nd science ever attempted, took place in 1994/5 in over 40 countries, (Martin et al., 199 6, 1997). Details of the underlying research questions and project design are contained in Robitaille, (1996a). For detailed technical reports see Martin and Kelly (1996, 1997) Two main groups of children were tested: Population 1, 8/9 years old, and Population 2, 13/14 years old. In addition, a third population, students in their "final year" of secon dary school, was tested. A summary of the average scores of the various nations is presen ted in Table 1.Table 1 TIMSS 1996/97 National Average Scores: Mathematics Pop. 1(8/9 yrs) Pop. 2 (13/14 yrs) Pop. 3 "Final Year" (AUSTRALIA)546530522(AUSTRIA)559539518BELGIUM-FLEMISH 565* (BELGIUM-FRENCH) 526 (BULGARIA)540 CANADA532527519(COLOMBIA)385 CYPRUS502474446CZECH REPUBLIC567564466(DENMARK) 502547(FRANCE) 538523ENGLAND513+*506+* (GERMANY) 509+*495GREECE492464 HONG KONG587588 (HUNGARY)548537483ICELAND474487534IRAN, ISLAMIC REP. 429428 IRELAND550527 (ISRAEL)531522+ (ITALY) 476


4 of 18 JAPAN597605 KOREA611607 (KUWAIT)400392 (LATVIA)525493* (LITHUANIA) 477+469(NETHERLANDS)577541560NEW ZEALAND499508522NORWAY502503528PORTUGAL475454 (ROMANIA)482 (RUSSIAN FEDERATION) 535471SCOTLAND520*498 SINGAPORE625643 SLOVAK REPUBLIC 547 (SLOVENIA)552541512(SOUTH AFRICA) 354356SPAIN 487 SWEDEN 519552SWITZERLAND 545* 540(THAILAND)490522 UNITED STATES545500*461Mathematics International Average = 529 for Pop. 1 Mathematics International Average = 513 for Pop. 2Mathematics General Knowledge International Average = 500 for Pop. 3 Nations not meeting international sampling or other guidelines are shown in parentheses.Nations in which more than 10% of the population wa s excluded from testing are shown with a +. (In Latvia, only Latvia n speaking students were tested, which represents less than 65% of the population.) Nations in which a participation rate of 75% of the schools and students combined was achieved only after replacement for re fusals were substituted are shown with a *. Sources:Mullis, I.V.S. et al. (1997) Mathematics Achievemen t in the Primary School Years. Table 1.1. Boston College: Ch estnut, MA. Beaton, A. et al. (1996) Mathematics achievement in the middle school years. Table 1.1. Boston College. Chesnut Hi ll, MA. Mullis, I.V.S. et al. (1997) Mathematics and Scienc e Achievement in the Final Year of Secondary School. Table 2.1. B oston College: Chestnut, MA.


5 of 18 TIMSS caused or was partly responsible for t he initiation of curricular change in mathematics and science education in a number of th e participating countries—mostly, but not entirely, the poorer performing countries. What follows is a survey of what happened in 23 of these countries. Information was obtained from a questionnaire sent to TIMSS representatives in participating countries, f rom TIMSS country reports, and from official documents and related sources. The 23 countries for which information was a vailable were as follows: ArgentinaBelgium(Flemish)Belgium(French)CanadaCyprusCzech RepublicDenmarkEnglandFranceGermany Hong KongIranIrelandIsraelJapanNew Zealand NorwayScotlandSingapore SpainSwedenSwitzerland USA The range of possible effects of TIMSS was s tructured under the following headings: Nature of official response to TIMSS. Degree of publicity given to TIMSS. Changes to mathematics curricula as a result of TIM SS. Changes to teaching methodology in mathematics as a result of TIMSS. General comments on the effect of TIMSS. Nature of Official Response to TIMSS In 14 of the 23 countries there was a nation al response to TIMSS, namely: Belgium(Flemish) CyprusDenmarkEnglandFranceGermanyIranJapanNew ZealandNorwayScotland SingaporeSweden USA The nature of the response varied from country to c ountry as shown below. Type of Response CountriesPUBLICATION OF AN OFFICIAL REPORT Belgium(Flemish)Canada(*)DenmarkFranceHongKong(*)IranJapanNew ZealandNorway(*)


6 of 18 ScotlandSingaporeSpainSwedenUSA* Issued by the national TIMSSteam. NATIONAL/REGIONAL CONFERENCES Belgium(Flemish)EnglandIranJapanScotland FORMATION OF NATIONAL/REGIONALPOLICY GROUPS TO PROMOTE CHANGE CyprusEnglandGermanyIranNorwayScotlandUSA PLANNING IMPLEMENTATION OFPOLICY INITIATIVES CyprusGermany INITIATION OF DEVELOPMENTAL PROJECTS Belgium(Flemish)NorwayUSAPublicity Given to TIMSS Type of publicityCountriesWIDESPREAD THROUGH MEDIA Belgium(French)(*)CyprusEnglandGermanyNorwayScotlandSwedenSingaporeSwitzerlandUSA* For Science only. MINOR ITEM IN NEWS MEDIA Hong KongIranIrelandIsraelCzech RepublicJapanSpain


7 of 18 WITHIN EDUCATIONAL COMMUNITY Belgium(Flemish)CanadaDenmarkNew Zealand LIMITED TO THOSE IN SENIOREDUCATIONAL POSITIONS France NO PUBLICITY OUTSIDE RESEARCH TEAMArgentinaChanges to Mathematics Curricula and Teaching Metho dology as a Result of TIMSS England, Cyprus, Denmark, France, Japan, No rway, Scotland, and Sweden all indicated a variety of changes in curricular emphas is, while England, Denmark, France, Japan, and Scotland also indicated changes to teach ing methodology, mainly in the direction of increasing active pupil participation in the learning processIndividual Country Effects We now look at the effect of TIMSS, country by country. Essentially direct quotations from questionnaires or official document s are given in quotation marks. ARGENTINA Results not included in official TIMSS repo rt. Little governmental interest in the outcomes. BELGIUM(FLEMISH) Only Population 2 (13/14 years old) tested. No curricular action taken due (a) to the relatively high position in the comparative tables, and (b) to a perception that there were variables affecting student achieve ment which TIMSS had not considered. BELGIUM(FRENCH) Only Population 2 tested, performing modera tely well. Main emphasis on Science results, with little publicity given to mat hematics. CANADA In Canada there is no Federal Ministry of E ducation. Educational decision-making rests with individual provinces. Fo r details, see Robitaille (1997a). The Canada TIMSS team have published two d etailed reports, (Robitaille, 1996b, 1997b). Individual Canadian pro vinces—for, example British Columbia and Ontario—have revised their mathematics curricula in the wake of the TIMSS survey. CYPRUS Cypriot students performed relatively poorl y in both Populations. Mathematics curriculum is under scrutiny. Some topi cs to be deleted from the curriculum. CZECH REPUBLIC In both Populations 1 and 2 Czech performan ce was good. "The Czech ministry of Education used the results to argue aga inst innovation. Critics of Czech mathematics education based their arguments f or change on TIMSS background variables—attitude to the subject for instance."


8 of 18DENMARK Only population 2 tested. "Ministry of Educ ation has focused on gender differences. Greater emphasis to be given to partic ipation of girls in mathematics and science. Comparisons are being made between TIM SS results and national tests." ENGLAND England performed relatively poorly in the TIMSS tests. Detailed results will be found in Keys et al. (1996,1997). The main react ion was the setting up of a Numeracy Task Force which produced two Reports— Numeracy Matters and The Implementation of the National Numeracy Strategy —(Reynolds, 1998a,b), in which, as the second title indicates, a national nu meracy strategy for England is developed. The essence of the strategy is contained in the following set of practices recommended to Primary school teachers (R eynolds, 1998b, p. 16): teaching all pupils a daily 45 to 60 mathematics le sson; teaching mathematics to all pupils within a class a t the same time, with a high proportion of lessons concentrating on the dev elopment of numeracy skills; teaching mathematics to the whole class or to group s for a high proportion of the time, promoting participation from, and co-o peration between, pupils; including oral and mental work within each daily ma thematics lesson; providing regular mathematical activities and exerc ises that pupils can do at home. The complementary National Numeracy Project (NNP) with its detailed Framework for Teaching Mathematics: Reception to Ye ar 6 (Department for Education and Employment, 1999) emphasises the enha nced importance given to numeracy in the primary mathematics curriculum. A f irst evaluation of NNP is available from The National Foundation for Educatio nal Research in England and Wales, (Minnis et al., 1999)) FRANCE France participated in Population 2 only, p erforming moderately well somewhat ahead of England and Scotland. A national government report was published but there do not appear to be direct link s between the TIMSS results and curricular change in mathematics. GERMANY Germany participated in Population 2 only, performing similarly overall to England and Scotland. "The Federal State Commission for Education Policy and Promotion of Research installed a group of experts to examine deficits in Science and Mathematics education and make suggestions for change. Their report was in published November 1997. As a consequence of this r eport an interstate five year program was installed with 15 of the 16 states (Lae nder) taking part. Under the co-ordination of the Institute for Science educatio n (IPN) in Kiel, an intervention program was instigated in 180 schools to optimize s cience and mathematics instruction." HONG KONG Hong Kong students performed well. No gover nment response. Minor item on news media. The Hong Kong TIMSS team have publis hed two reports (TIMSS Hong Kong, 1996,1997). IRAN Iranian students performed comparatively ve ry poorly in both Populations. "A group of educational experts has been formed to identify the reasons for


9 of 18students' low performance. During the last two year s (i.e. 1997/8) many steps have been taken by the group and the national research c o-ordinator in order to create positive attitudes to the outcomes of the project ( for curricular change)and as a result tangible changes have been observed among ed ucational policy makers as well as senior education experts. More emphasis to given to topics of proportion, data analysis, and measurement."IRELAND No direct publicity or government interest. Irish students performed somewhat better than those in England and Scotland but not markedly so. ISRAEL Israeli students overall performance was si milar to that of England and Scotland. "Reports analysing national standing rela tive to other countries were published (in Hebrew) in the maths teachers journal for each of the TIMSS Populations. Very few take the results seriously. M any look for excuses and find ways to ignore TIMSS results." JAPAN Japanese students performed very well in bo th populations. "TIMSS revealed that Japanese children didn't like (mathematics). T herefore spontaneous activities were emphasised. In order to find time for this, to pics were deleted from the curriculum. Greater emphasis was placed on children 's' mathematical activities." A report of the Japan National Curriculum Council ( 1988) included the following recommendations: "greater emphasis on practical and problem-solving activities, and on reallife contexts, in the process of acquisition of bas ic knowledge and skills in number, quantity, and geometrical figure; "some reduction in curriculum content, in particula r complicated computation and the use of complicated geometrical figures; "use of repetitious learning as a help in mastering computation skills; "establishing a new subject in upper secondary scho ol incorporating mathematical history and statistical processing of daily events, this subject to be a required elective." NEW ZEALAND The performance of New Zealand students was very similar overall to England and Scotland. A full report is contained in Garden, (1996,1997) The New Zealand Government set up a Mathematics and Science Taskforce which reported in December 1997 (NZ Ministry of Education, 1997). Quoting from the initial Background Section of the report, "The Taskforce wa s established because of reported difficulties of classroom teachers (especi ally primary teachers) in implementing the new curricula for mathematics and science and in the light of the reported results of the Third International Mat hematics and Science Study." In Section 2 of the report, entitled Overriding Issues five concerns are identified and analysed. These are: "The need to raise expectations; 1. "Under achievement amongst Maori and Pacific island students; 2. "Professional skills and knowledge of teachers; 3. "Material resources for teachers; 4. "Professional development." 5. In particular, the report places considerab le stress on the availability of effective material resources, stating that its reco mmendations are made in a spirit of pragmatism and "are based on the realities if th e current situation in schools,


10 of 18and not on idealistic notions of teachers' ability to invent rich activities by themselves and teach them with the pedagogical know ledge of an experienced researcher in (mathematics)education."NORWAY Norwegian children performed similarly to t hose in England and Scotland in Population 2, but rather less well in Population 1. The main effect of TIMSS has been an increased emphasis on mathematics in the tr aining of primary teachers. "Statistics to be given lesser emphasis." SCOTLAND Scottish children performed disappointingly in both Populations 1 and 2 (Scottish Office Education and Industry Department, 1996, 1997a). The reasons for this are not fully understood and a variety of explanations have been put forward. For one analysis and overview see Macnab ( 1999). Scotland has also an internal standards survey—the Assessment of Achieve ment Project (AAP)—which has reported a continuing decline in st andards of mathematics attainment since 1983, (Macnab et al., 1988; Robert son et al., 1993,1996; Scottish Office Education and Industry Department, 1998). Th e evidence of these reports has been largely ignored by the educational communi ty for reasons explored in Macnab (1999a). However, publication of the TIMSS r esults has led to an official government report, Improving Mathematics 514 (Scottish Office Education and Industry Department 1997b), which put forward a ser ies of recommendations for improving the situation, based at least partly on t he perceptions of HM Inspectorate of Schools (Scotland) regarding charac teristics of teaching in high performing TIMSS countries mainly in the Far East, and including: Moving from mixed ability to some form of setting b y ability; Moving from individualised approaches to learning t o more teacher-led whole class activity; Reducing dependence on the calculator; Increasing pupils facility in mental arithmetic. Roughly contemporaneously with the publicat ion of the report three regional conferences were organised to which both teachers a nd education administrators were invited. The effects of the report and the con ferences on the teaching and learning of mathematics in Scottish schools will be the subject of a separate article, (Macnab, 1999b). They are outlined briefly in the section on Discussion of Survey Outcomes. SINGAPORE Singapore students performed well in the TI MSS tests. A national report has been published on the TIMSS website: http://TIMSS.b This report listed 7 possible reasons for this success. THE HOMOGENEITY AND COHERENCE OF THE EDUCATIONSYSTEM. 1. CHANGES TO THE CURRICULUM placing greater emphasi s on the development of mathematical concepts and the abilit y to apply them to solve mathematical problems. 2. THE WORKING ETHOS OF TEACHERS. 3. TRAINING AND PROFESSIONAL DEVELOPMENT. 4. HOME ENVIRONMENT the virtue of hard work and the need to strive for excellence is ingrained in students in Singapor e from an early age. 5. PEER INFLUENCE while students in Singapore feel t hat doing well in schools is important, what is perhaps more importan t is that they also 6.


11 of 18perceive their friends to place a similar emphasis on academic achievement. FOSTERING OF INTEREST IN MATHEMATICS AND SCIENCE the climate of opinion in Singapore is conducive to the learning of mathematics and science. 7. SPAIN Spain participated in Population 2 only. No official government response. "There is no tradition of evaluation in Spain and u p to now there are no channels created by the administration to spread and give re levance and impact on possible consequences to the outcomes of evaluations in whic h we take part, no matter whether they are national or international evaluati ons." A report in Spanish has been published by INCE, the Instituto Nacional de C alidad y Evaluacion, in Madrid. SWEDEN Sweden participated in Population 2 only, p erforming slightly better than England and Scotland. National government reports h ave been published in Swedish Curriculum change is underway but not bec ause of TIMMS as such. SWITZERLAND Switzerland participated in Population 2 on ly, performing moderately well. No government report has been published and no prog ram of curricular change initiated. USA The United States did not come out well fro m the test results, although at both age levels it was placed above the UK countrie s. A national curriculum development program, Attaining Excellence, has been prepared involving a set of video-taped lessons from classrooms in the US, Germ any, and Japan, together with an action strategy for improving achievement i n mathematics and science. Two books have been published— A Splintered Vision (ASV) (Schmidt et al., 1997b) and Facing the Consequences (FC) (Schmidt et al., 1998)—which analyse the US results in their international setting and d iscuss in detail their consequences for US mathematics education. These publications re veal considerable soul-searching regarding the causes of the poor per formance of the US. Three of the main conclusions reached are that US schools ma thematics curricula are: Too fragmented and lack coherence; Cover too many topics and lack depth; Concentrate too much on skills and too little on pr oblem-solving. Discussion The most obvious outcome of the study is th e difference in the degree of attention individual responding countries gave to the TIMSS r esults and in their reactions to them, varying from the extensive documentation emerging f rom the USA, and to a lesser extent the UK and New Zealand, to the almost nil. r eaction in Argentina. In a number of countries France and Sweden, for example curric ular change in mathematics education is in progress but not directly because o f TIMSS. The case of Scotland is interesting. The ma in recommendations for change contained in Improving Mathematics Education 5-14 concerned matters such as increased emphasis on whole-class teaching, inter-a ctive teaching, and mental arithmetic, rather on the mathematics curriculum as a whole, its content and coherence. These recommendations were, moreover, agreed and ac cepted with virtually no dissent at the February 1998 Conferences (McKaig, 1998). Th ere was not felt either by teachers


12 of 18or by the schools inspectorate who in Scotland ha ve a curriculum development role to be any need to revise the 1992 curriculum document National Guidelines: Mathematics 5-14 which sets out official guidance on the mathemati cs curriculum and standards of attainment in the Primary and early Secondary years ; indeed, the curriculum development emphasis from 1998 has been on Environm ental Education. This being so, it is a valid question to as k why the near unanimity on the way forward occurred. If teachers were indeed so persua ded of the rightness of the recommendations, why did they not implement them so oner? If not, why the sudden apparent enthusiasm to implement them now? It is st ill too early to judge in what measure implementation will actually take place, bu t an early survey (Macnab, 1999b) suggests that those at the conferences have moved t o put at least some of the recommended changes into place and that school pupi ls perceive that change has occurred. In England Wales, on the other hand, a much greater degree of prescription has been applied, with the publication of The National Numeracy Strategy: Framework for Teaching Mathematics from Reception to Year 6 This bulky loose-leaf format document, with a Foreword by the Secretary of State for Education and Employment in England and Wales, has been implemented in Session 1999/2000. It sets out not only macro aspects of teaching such as methodology and c lassroom organisation, but includes also a breakdown of lesson structure with time guid es for the various elements. Detailed guidance on Oral Work, on Teaching Input and associ ated Pupil Activities, and on Lesson Conclusions is given. By far the greater par t of the document, however, is devoted to a description of pupil learning outcomes relating to numerical work, of which the following example from Year 1 conveys the gener al character: "Pupils should (be able to): Respond rapidly to oral questions phrased in a vari ety of ways such as: 4 take away 2. Take 2 from 7. 7 subtract 3,. Subtract 2 from 11, 8 less than 9,. What number must I take from 14 to leave 10? What is the difference between 14 and 12? How many more than 3 is 9? How many less than 6 is 4? 6 taken from a number leaves 3. What is the number? Find pairs of numbers with a difference of 2. I think of a number. I take away 3. My answer is 7. What is my number? Record simple mental subtractions in number sentenc e using + and signs." There are thus quite considerable differenc es between the two areas of the UK—England and Wales, and Scotland—in the degree of detailed guidance provided, and in the degree of consequential apparent leeway available., reflecting to some extent differing perceptions of the scale of the problem a nd so of the scale of reform required. Time alone will tell which of the two will be the m ore effective in implementation and in the effect on pupils' standards of attainment, a lthough official figures (Summer 1999) have been published to show that standards in Engla nd and Wales are improving, in advance of the across-the board introduction of the Strategy. In Scotland we may have to wait for the results of the next round of the Asses sment of Achievement Survey


13 of 18scheduled for Year 2000. In the US different states have a freedom t o devise their own mathematics curricula. California, for example, has prepared a set of mathematics standards (California, 1999) of which the Introduction says: These standards are based on the premise that all s tudents are capable of learning rigorous mathematics and learning it well, and all are capable of learning more than is currently expected. Proficien cy in mathematics is not an innate characteristic; it is achieved through pe rsistence, effort and practice in the part of students and rigorous and e ffective instruction on the part of teachers.....The standards emphasise comput ational and procedural skills, conceptual understanding, and problem-solvi ng. These three components of mathematical instruction and learning are not separate from each other; instead they are intertwined and mutual ly reinforcing. We can see from these examples and from the generality of the survey evidence that a perception of the need for curricular reform in mathematics education is widespread, but that there is no overall consensus on the nature of the change required. I have argued elsewhere (Macnab, 1999c) that what may be missing in at least some of the poorer performing countries is the necessary will t o ensure success in mathematics, by administrators, by teachers, by pupils and students a will admirably expressed in the California Standards document quoted from above. Surveys such as TIMSS perform a valuable se rvice in that they give participating countries the opportunity in mathematics (and scien ce) education to "see oorselves as ithers see us", to quote from Scotland's national p oet Robert Burns. The survey reported here demonstrates that not all the countries made u se of this opportunity; of those that did, not all were prepared to accept what was revea led; and that among those who did accept the verdict of TIMSS, there was not agreemen t as to the nature and depth of the changes required. Mathematics has a long history of being badly taught and worse understood. It would be pleasant that this time TIM SS will indeed make a difference.ReferencesAdams, R.S. & Chen, C. (1981). The Process of Educational Innovation: An International Perspective. London: Kogan Page. Askew, M. & Wiliam, D. (1995). Recent Research in Mathematics Education 5-16. London: HMSO.Black, P. & Atkin, J., M. (Eds.) (1996). Changing the Subject: Innovations in Mathematics and Science Education. London: Routledge. Brown, M. (1996). FIMS and SIMS: the first two IEA International Mathematics Surveys. Assessment in Education, 3 193-212. Brown, M. (1998). The Tyranny of the International Horse Race, in Slee, R., Weiner, G., with Tomlinson, S. School Effectiveness for Whom? London: Falmer Press. Brown, M. et al. (1998). Is the National Numeracy S trategy Research-based? British Journal of Educational Studies, 46, 362-385.


14 of 18California State Board of Education (1999). The Mathematics Content Standards for California Public Schools, Kindergarten Through Gra de Twelve. Sacramento CA: Calfornia State Board of Education.Department for Employment and Education (1999). The National Numeracy Strategy: Framework for Teaching Mathematics from Reception t o Year 6. London: DfEE. Fullan, M. (1993). Change Forces: Probing the Depths of Educational R eform. London: Falmer Press.Garden, R.A. (1996). Mathematics Performance of New Zealand: Form 2 and Form 3 Students. Wellington NZ: Ministry of Education. Garden, R.A. (1997). Mathematics and Science Performance in Middle Prim ary School. Wellington NZ: Ministry of Education.Keys, W., Harris, S., Fernandes, C. (1996). Third International Mathematics and Science Study First National Report Part 1. London: NFER. Keys, W.; Harris, S. & Fernandes, C. (1997). Third International Mathematics and Science Study First National Report Part 2. London: NFER. Law, N, (Ed.), (1996). Science and Mathematics Achievements at Junior Sec ondary Level in Hong Kong. Hong Kong: University of Hong Kong. Law, N, (Ed.), (1997). Science and Mathematics Achievements at the Mid-Pr imary Level in Hong Kong. Hong Kong: University of Hong Kong. McKaig, G. (1998). Improving Mathematics Education 514: Conference Report. Glasgow: St. Andrew's College.Macnab, D.S.; Page, J. & Kennedy, M. (1989). Assess ment of Achievement Programme Second Round Mathematics l988. Aberdeen: Northern C ollege. Macnab, D.S. (1999a). Mathematics Education in Scot tish Schools: An Uncertain Vision? Scottish Educational Review, 31, 10-20. Macnab, D.S. (1999b). Implementing Change in Mathematics Education: A Pa per Presented to the 1999 Annual Conference of the Scot tish Educational Research Association. Aberdeen: Northern College. Macnab, D.S. (1999c). Improving Standards in Mathematics Education: Valu es, Vision, and TIMSS. Aberdeen: Northern College. Martin, M.O. & Kelly, D. L. (1996). TIMSS Technical Report Volume 1:Design and Development. Boston: Boston College. Martin, M.O. & Kelly, D. L. (1996). TIMSS Technical Report Volume 2: Implementation and Analysis. Boston: Boston College. Martin, M.O. et al. (1996). Mathematics Achievement in the Middle School Years Boston: Boston College.


15 of 18Martin, M.O. et al. (1997). Mathematics Achievement in the Primary School Year s. Boston: Boston College.Minnis, M. et al. (1998). National Numeracy project Technical. Report Slough: NFER. New Zealand Ministry of Education (1997). Report of the Mathematics and Science Taskforce. Wellington NZ: Ministry of Education. Reynolds, D. et al. (1998a). Numeracy Matters. London: DfEE. Reynolds, D. et al. (1998b). The Implementation of the National Numeracy Strate gy: Then Final Report of the Numeracy Task Force. London: DfEE. Robertson, I.J. & Meechan, R. C. (1992). Assessment of Achievement Programme (Scotland) Mathematics Third Round 1991. Glasgow: Jordanhill College. Robertson, I.J. et al. (1996). Assessment of Achievement Programme (Scotland) Fou rth Survey of Mathematics 1994. Glasgow: University of Strathclyde. Robitaille, D.F. et al. (1993). TIMSS Monograph No. 1: Curriculum Frameworks for Mathematics and Science. Vancouver: Pacific Educational Press. Robitaille, D.F. et al. (1996a). TIMSS Monograph No. 2: Research Questions and Stud y Design. Vancouver Pacific Educational Press. Robitaille, D.F. et al. (1996b). TIMSS-Canada Report Volume 1: Grade 8. Vancouver: University of British Columbia.Robitaille, D.F. (Ed.) (1997a). National Contexts for Mathematics and Science Education: An Encyclopaedia of the Education System s Participating in TIMSS. Vancouver: Pacific Educational Press.Robitaille, D.F. et al. (1997b). TIMSS-Canada Report Volume 2: Grade 4. Vancouver: University of British Columbia.Schmidt, W. H. et al. (1996). Characterising Pedagogical Flow An Investigation o f Mathematics and Science Teaching in Six Countries. Dordrecht: Kluwer. Scottish Office Education Department (1991). Curriculum and Assessment in Scotland, National Guidelines Mathematics 5-14. Edinburgh: SOED. Scottish Office Education and Industry Department ( 1996). Achievements of Secondary 1 and Secondary 2 Pupils in Mathematics and Science (TIMSS). Edinburgh: SOEID. Scottish Office Education and Industry Department ( 1997a). Achievements of Primary 4 and Primary 5 Pupils in Mathematics and Science (TI MSS). Edinburgh: SOEID. Scottish Office Education and Industry Department ( 1997b). Improving Mathematics Education 5-14. Edinburgh: SOEID. Scottish Office Education and Industry Department ( 1997). Assessment of Achievement Programme: Fifth Round Survey of Mathematics. Edinburgh: SOEID.


16 of 18 About the AuthorDonald S. MacnabSenior Research Fellow Northern CollegeAberdeen CampusHilton PlaceAberdeen AB24 4FAUKPhone: +44 1224 283552Fax: +44 1224 283900 Email: Donald Macnab is Senior Research Fellow and Profess or of Mathematics Education at Northern College, a teacher education institution a ffiliated with the UK Open University. He has published two books and a number of papers, and led a Scottish Education Department study into the mathematical at tainments of Scottish Primary and Secondary schoolchildren the Assessment of Achiev ement Programme. He is currently undertaking an extensive investigation into factors and processes with underly and influence curriculum development and change, with a particular reference to mathematics.Copyright 2000 by the Education Policy Analysis ArchivesThe World Wide Web address for the Education Policy Analysis Archives is General questions about appropriateness of topics o r particular articles may be addressed to the Editor, Gene V Glass, or reach him at College of Education, Arizona State University, Tempe, AZ 8 5287-0211. (602-965-9644). The Commentary Editor is Casey D. C obb: .EPAA Editorial Board Michael W. Apple University of Wisconsin Greg Camilli Rutgers University John Covaleskie Northern Michigan University Alan Davis University of Colorado, Denver Sherman Dorn University of South Florida Mark E. Fetler California Commission on Teacher Credentialing Richard Garlikov Thomas F. Green Syracuse University Alison I. Griffith York University Arlen Gullickson Western Michigan University


17 of 18 Ernest R. House University of Colorado Aimee Howley Ohio University Craig B. Howley Appalachia Educational Laboratory William Hunter University of Calgary Daniel Kalls Ume University Benjamin Levin University of Manitoba Thomas Mauhs-Pugh Green Mountain College Dewayne Matthews Western Interstate Commission for HigherEducation William McInerney Purdue University Mary McKeown-Moak MGT of America (Austin, TX) Les McLean University of Toronto Susan Bobbitt Nolen University of Washington Anne L. Pemberton Hugh G. Petrie SUNY Buffalo Richard C. Richardson New York University Anthony G. Rud Jr. Purdue University Dennis Sayers Ann Leavenworth Centerfor Accelerated Learning Jay D. Scribner University of Texas at Austin Michael Scriven Robert E. Stake University of Illinois—UC Robert Stonehill U.S. Department of Education David D. Williams Brigham Young UniversityEPAA Spanish Language Editorial BoardAssociate Editor for Spanish Language Roberto Rodrguez Gmez Universidad Nacional Autnoma de Mxico Adrin Acosta (Mxico) Universidad de J. Flix Angulo Rasco (Spain) Universidad de Teresa Bracho (Mxico) Centro de Investigacin y DocenciaEconmica-CIDEbracho Alejandro Canales (Mxico) Universidad Nacional Autnoma Ursula Casanova (U.S.A.) Arizona State Jos Contreras Domingo Universitat de Barcelona Erwin Epstein (U.S.A.) Loyola University of Josu Gonzlez (U.S.A.) Arizona State


18 of 18 Rollin Kent (Mxico)Departamento de InvestigacinEducativa-DIE/ Mara Beatriz Luce (Brazil)Universidad Federal de Rio Grande do Sul-UFRGSlucemb@orion.ufrgs.brJavier Mendoza Rojas (Mxico)Universidad Nacional Autnoma deMxicojaviermr@servidor.unam.mxMarcela Mollis (Argentina)Universidad de Buenos Humberto Muoz Garca (Mxico) Universidad Nacional Autnoma deMxicohumberto@servidor.unam.mxAngel Ignacio Prez Gmez (Spain)Universidad de Daniel Schugurensky (Argentina-Canad)OISE/UT, Simon Schwartzman (Brazil)Fundao Instituto Brasileiro e Geografiae Estatstica Jurjo Torres Santom (Spain)Universidad de A Carlos Alberto Torres (U.S.A.)University of California, Los

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