Introduction
What causes schools' mathematics curricula and teaching
methodologies to change over time? To what extent do
they change in a rational response to external objective
considerations; to what extent subjectively in accordance
with beliefs and social pressures? What does success
mean in relation to change? Often enough, the effect of
change (planned or otherwise) is to metamorphose
antecedent success criteria to validate the change, at
least in the short term. In the world 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 Scottish context,
see Macnab (1999a).
In Fullan's words, the essence of the difficulty 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 results in a system that is
more likely to retain the status quo than to
change. When change is attempted under such
circumstances it results in defensiveness,
superficiality, or at best short-lived pockets of
success." (Fullan, 1993, p. 3).
All those involved in promoting and implementing change
do so from a sense of moral purpose to improve education.
In a study of educational innovation in science
mathematics and technology education in 13 countries
(Black & Atkin, 1996), the authors conclude that "things
are much more complicated than they seem.... Comparisons
[between different countries] illustrate 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 complexity of change.
Fashionable opposites, such as top-down v. bottom-up, or
teacher-active v. teacher-passive, are not helpful. In
the real world action and change take place in more
complex ways and at intermediate points along these
bi-polar axes. There is another reason why change is
complex. When it succeeds, it often does so for
unforeseen causes. Those who think they control it
sometimes find that unpredictable inner imperatives have
passed control to others. Planned hierarchies of people
collapse. Students may be better motivated but learn
less. Teachers may be enthusiastic but students
resistant, or vice-versa." (Black & Atkin, 1996, pp. 1-2).
Black and Atkin devote a chapter of their book to the
question "What drives reform?" They comment that "every
country that participated 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 country seems to be more
or less unhappy with what it has today.... At any moment,
however, 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
pressures and influences that promote change in science,
mathematics, and technology education in schools keep
re-appearing as we move from one country to another. None
appears 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 problems 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 & Atkin, 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
enthusiasm 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
conclude a further set of questions commenting that, "the
questions, it seems are endless.... [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 which they began.
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 is
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 Science Study
(TIMSS), the largest international survey of attainment
in mathematics and science ever attempted, took place in
1994/5 in over 40 countries, (Martin et al., 1996, 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
secondary school, was tested.
A summary of the average scores of the various nations
is presented 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) | 546 | 530 | 522
| | (AUSTRIA) | 559 | 539 | 518
| | BELGIUM-FLEMISH | | 565* |
| | (BELGIUM-FRENCH) | 526 | |
| | (BULGARIA) | 540 | |
| | CANADA | 532 | 527 | 519
| | (COLOMBIA) | 385 | |
| | CYPRUS | 502 | 474 | 446
| | CZECH REPUBLIC | 567 | 564 | 466
| | (DENMARK) | | 502 | 547
| | (FRANCE) | | 538 | 523
| | ENGLAND | 513+* | 506+* |
| | (GERMANY) | | 509+* | 495
| | GREECE | 492 | 464 |
| | HONG KONG | 587 | 588 |
| | (HUNGARY) | 548 | 537 | 483
| | ICELAND | 474 | 487 | 534
| | IRAN, ISLAMIC REP. | 429 | 428 |
| | IRELAND | 550 | 527 |
| | (ISRAEL) | 531 | 522+ |
| | (ITALY) | | | 476
| | JAPAN | 597 | 605 |
| | KOREA | 611 | 607 |
| | (KUWAIT) | 400 | 392 |
| | (LATVIA) | 525 | 493* |
| | (LITHUANIA) | | 477+ | 469
| | (NETHERLANDS) | 577 | 541 | 560
| | NEW ZEALAND | 499 | 508 | 522
| | NORWAY | 502 | 503 | 528
| | PORTUGAL | 475 | 454 |
| | (ROMANIA) | 482 | |
| | (RUSSIAN FEDERATION) | | 535 | 471
| | SCOTLAND | 520* | 498 |
| | SINGAPORE | 625 | 643 |
| | SLOVAK REPUBLIC | | 547 |
| | (SLOVENIA) | 552 | 541 | 512
| | (SOUTH AFRICA) | | 354 | 356
| | SPAIN | | 487 |
| | SWEDEN | | 519 | 552
| | SWITZERLAND | | 545* | 540
| | (THAILAND) | 490 | 522 |
| | UNITED STATES | 545 | 500* | 461
|
Mathematics International Average = 529 for Pop. 1
Mathematics International Average = 513 for Pop. 2
Mathematics 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 was excluded from testing are shown
with a +. (In Latvia, only Latvian 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 refusals were substituted are shown with a *.
Sources:
- Mullis, I.V.S. et al. (1997) Mathematics Achievement in the Primary
School Years. Table 1.1. Boston College: Chestnut, MA.
- Beaton, A. et al. (1996) Mathematics achievement in the middle school years.
Table 1.1. Boston College. Chesnut Hill, MA.
- Mullis, I.V.S. et al. (1997) Mathematics and Science Achievement in the Final
Year of Secondary School. Table 2.1. Boston College: Chestnut, MA.
|
TIMSS
caused or was partly responsible for the initiation of
curricular change in mathematics and science education in
a number of the 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, from
TIMSS country reports, and from official documents and
related sources.
The 23 countries for which
information was available were as follows:
| Argentina | Belgium(Flemish) | Belgium(French)
| | Canada | Cyprus | Czech
Republic
| | Denmark | England | France
| | Germany | Hong Kong | Iran
| | Ireland | Israel | Japan
| | New Zealand | Norway | Scotland
| | Singapore | Spain | Sweden
| | Switzerland | USA |
|
The range of possible effects of
TIMSS was structured under the following headings:
- Nature of official response to TIMSS.
- Degree of publicity given to TIMSS.
- Changes to mathematics curricula as a result of
TIMSS.
- 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
national response to TIMSS, namely:
|
Belgium(Flemish) | Cyprus | Denmark
| | England | France | Germany
| | Iran | Japan | New Zealand
| | Norway | Scotland | Singapore
| | Sweden | USA |
|
The nature of the response varied from country to country
as shown below.
|
Type of Response | Countries |
PUBLICATION OF AN
OFFICIAL REPORT |
Belgium(Flemish)
Canada(*)
Denmark
France
HongKong(*)
Iran
Japan
New Zealand
Norway(*)
Scotland
Singapore
Spain
Sweden
USA
* Issued by the national TIMSS team.
|
|
NATIONAL/REGIONAL CONFERENCES | Belgium(Flemish)
England
Iran
Japan
Scotland |
FORMATION OF NATIONAL/REGIONAL
POLICY GROUPS TO
PROMOTE CHANGE | Cyprus
England
Germany
Iran
Norway
Scotland
USA |
PLANNING IMPLEMENTATION OF
POLICY INITIATIVES | Cyprus
Germany |
INITIATION OF DEVELOPMENTAL
PROJECTS |
Belgium(Flemish)
Norway
USA |
Publicity Given to TIMSS
|
Type of publicity | Countries
| | WIDESPREAD THROUGH MEDIA |
Belgium(French)(*)
Cyprus
England
Germany
Norway
Scotland
Sweden
Singapore
Switzerland
USA
* For Science only.
| | MINOR ITEM IN NEWS MEDIA |
Hong Kong
Iran
Ireland
Israel
Czech Republic
Japan
Spain
| | WITHIN EDUCATIONAL COMMUNITY |
Belgium(Flemish)
Canada
Denmark
New Zealand
| LIMITED TO THOSE IN SENIOR
EDUCATIONAL POSITIONS | France
| | NO PUBLICITY OUTSIDE RESEARCH TEAM |
Argentina
|
Changes to Mathematics Curricula and Teaching Methodology
as a Result of TIMSS
England, Cyprus, Denmark, France, Japan, Norway,
Scotland, and Sweden all indicated a variety of changes
in curricular emphasis, while England, Denmark, France,
Japan, and Scotland also indicated changes to teaching
methodology, mainly in the direction of increasing active
pupil participation in the learning process
Individual Country Effects
We now look at the effect of TIMSS, country by country.
Essentially direct quotations from questionnaires or
official documents are given in quotation marks.
- ARGENTINA
Results not included in official TIMSS report. 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
achievement which TIMSS had not considered.
- BELGIUM(FRENCH)
Only Population 2 tested, performing moderately well.
Main emphasis on Science results, with little publicity
given to mathematics.
- CANADA
In Canada there is no Federal Ministry of Education.
Educational decision-making rests with individual
provinces. For details, see Robitaille (1997a). The
Canada TIMSS team have published two detailed reports,
(Robitaille, 1996b, 1997b). Individual Canadian
provinces—for, example British Columbia and Ontario—have
revised their mathematics curricula in the wake of
the TIMSS survey.
- CYPRUS
Cypriot students performed relatively poorly in both
Populations. Mathematics curriculum is under scrutiny.
Some topics to be deleted from the curriculum.
- CZECH REPUBLIC
In both Populations 1 and 2 Czech performance was good.
"The Czech ministry of Education used the results to
argue against innovation. Critics of Czech mathematics
education based their arguments for change on TIMSS
background variables—attitude to the subject , for
instance."
- DENMARK
Only population 2 tested. "Ministry of Education has
focused on gender differences. Greater emphasis to be
given to participation of girls in mathematics and
science. Comparisons are being made between TIMSS
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 reaction 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 numeracy strategy
for England is developed. The essence of the strategy is
contained in the following set of practices recommended
to Primary school teachers (Reynolds, 1998b, p. 16):
- teaching all pupils a daily 45 to 60 mathematics
lesson;
- teaching mathematics to all pupils within a class at
the same time, with a high proportion of lessons
concentrating on the development of numeracy skills;
- teaching mathematics to the whole class or to groups
for a high proportion of the time, promoting
participation from, and co-operation between, pupils;
- including oral and mental work within each daily
mathematics lesson;
- providing regular mathematical activities and exercises
that pupils can do at home.
The complementary National Numeracy Project (NNP) with
its detailed Framework for Teaching Mathematics:
Reception to Year 6 (Department for Education and
Employment, 1999) emphasises the enhanced importance
given to numeracy in the primary mathematics curriculum.
A first evaluation of NNP is available from The National
Foundation for Educational Research in England and Wales,
(Minnis et al., 1999))
- FRANCE
France participated in Population 2 only, performing
moderately well somewhat ahead of England and Scotland.
A national government report was published but there do
not appear to be direct links 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 report an interstate five year
program was installed with 15 of the 16 states (Laender)
taking part. Under the co-ordination of the Institute
for Science education (IPN) in Kiel, an intervention
program was instigated in 180 schools to optimize science
and mathematics instruction."
- HONG KONG
Hong Kong students performed well. No government
response. Minor item on news media. The Hong Kong TIMSS
team have published two reports (TIMSS Hong Kong,
1996,1997).
- IRAN
Iranian students performed comparatively very poorly in
both Populations. "A group of educational experts has
been formed to identify the reasons for students' low
performance. During the last two years (i.e. 1997/8)
many steps have been taken by the group and the national
research co-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 educational 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 similar to that
of England and Scotland. "Reports analysing national
standing relative to other countries were published (in
Hebrew) in the maths teachers journal for each of the
TIMSS Populations. Very few take the results seriously.
Many look for excuses and find ways to ignore TIMSS
results."
- JAPAN
Japanese students performed very well in both
populations. "TIMSS revealed that Japanese children
didn't like (mathematics). Therefore spontaneous
activities were emphasised. In order to find time for
this, topics 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 real- life contexts, in the
process of acquisition of basic knowledge and skills
in number, quantity, and geometrical figure;
- "some reduction in curriculum content, in particular
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
school 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 was established
because of reported difficulties of classroom teachers
(especially primary teachers) in implementing the new
curricula for mathematics and science and in the light of
the reported results of the Third International
Mathematics 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;
- "Under achievement amongst Maori and Pacific island
students;
- "Professional skills and knowledge of teachers;
- "Material resources for teachers;
- "Professional development."
In particular, the report places considerable stress on
the availability of effective material resources, stating
that its recommendations are made in a spirit of
pragmatism and "are based on the realities if the current
situation in schools, and not on idealistic notions of
teachers' ability to invent rich activities by themselves
and teach them with the pedagogical knowledge of an
experienced researcher in (mathematics)education."
- NORWAY
Norwegian children performed similarly to those 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 training 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 Achievement Project (AAP)—which
has reported a continuing decline in standards of
mathematics attainment since 1983, (Macnab et al., 1988;
Robertson et al., 1993,1996; Scottish Office Education
and Industry Department, 1998). The evidence of these
reports has been largely ignored by the educational
community for reasons explored in Macnab (1999a).
However, publication of the TIMSS results has led to an
official government report, Improving Mathematics 5-
14 (Scottish Office Education and Industry
Department 1997b), which put forward a series of
recommendations for improving the situation, based at
least partly on the perceptions of HM Inspectorate of
Schools (Scotland) regarding characteristics of teaching
in high performing TIMSS countries mainly in the Far
East, and including:
- Moving from mixed ability to some form of setting by
ability;
- Moving from individualised approaches to learning to
more teacher-led whole class activity;
- Reducing dependence on the calculator;
- Increasing pupils facility in mental arithmetic.
Roughly contemporaneously with the publication of the
report three regional conferences were organised to which
both teachers and education administrators were invited.
The effects of the report and the conferences 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 TIMSS tests. A
national report has been published on the TIMSS website:
http://TIMSS.bc.edu. This report listed 7 possible
reasons for this success.
- THE HOMOGENEITY AND COHERENCE OF THE EDUCATION
SYSTEM.
- CHANGES TO THE CURRICULUM - placing greater emphasis
on the development of mathematical concepts and the
ability to apply them to solve mathematical problems.
- THE WORKING ETHOS OF TEACHERS.
- TRAINING AND PROFESSIONAL DEVELOPMENT.
- HOME ENVIRONMENT - the virtue of hard work and the
need to strive for excellence is ingrained in students
in Singapore from an early age.
- PEER INFLUENCE - while students in Singapore feel
that doing well in schools is important, what is
perhaps more important is that they also perceive
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.
- SPAIN
Spain participated in Population 2 only. No official
government response. "There is no tradition of
evaluation in Spain and up to now there are no channels
created by the administration to spread and give
relevance and impact on possible consequences to the
outcomes of evaluations in which we take part, no matter
whether they are national or international evaluations."
A report in Spanish has been published by INCE, the
Instituto Nacional de Calidad y Evaluacion, in Madrid.
- SWEDEN
Sweden participated in Population 2 only, performing
slightly better than England and Scotland. National
government reports have been published in Swedish .
Curriculum change is underway but not because of TIMMS as
such.
- SWITZERLAND
Switzerland participated in Population 2 only, performing
moderately well. No government report has been published
and no program of curricular change initiated.
- USA
The United States did not come out well from the test
results, although at both age levels it was placed above
the UK countries. A national curriculum development
program, Attaining Excellence, has been prepared
involving a set of video-taped lessons from classrooms in
the US, Germany, and Japan, together with an action
strategy for improving achievement in 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 discuss in detail their
consequences for US mathematics education. These
publications reveal considerable soul-searching regarding
the causes of the poor performance of the US. Three of
the main conclusions reached are that US schools
mathematics curricula are:
- Too fragmented and lack coherence;
- Cover too many topics and lack depth;
- Concentrate too much on skills and too little on
problem-solving.
Discussion
The most obvious outcome of the study is the difference
in the degree of attention individual responding
countries gave to the TIMSS results and in their
reactions to them, varying from the extensive
documentation emerging from the USA, and to a lesser
extent the UK and New Zealand, to the almost nil.
reaction in Argentina. In a number of countries - France
and Sweden, for example - curricular change in
mathematics education is in progress but not directly
because of TIMSS.
The case of Scotland is interesting. The main
recommendations for change contained in Improving
Mathematics Education 5-14 concerned matters such as
increased emphasis on whole-class teaching, inter-active
teaching, and mental arithmetic, rather on the
mathematics curriculum as a whole, its content and
coherence. These recommendations were, moreover, agreed
and accepted with virtually no dissent at the February
1998 Conferences (McKaig, 1998). There was not felt
either by teachers or by the schools inspectorate - who
in Scotland have 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 mathematics curriculum and
standards of attainment in the Primary and early
Secondary years; indeed, the curriculum development
emphasis from 1998 has been on Environmental Education.
This being so, it is a valid question to ask why the near
unanimity on the way forward occurred. If teachers were
indeed so persuaded of the rightness of the
recommendations, why did they not implement them sooner?
If not, why the sudden apparent enthusiasm to implement
them now? It is still too early to judge in what measure
implementation will actually take place, but an early
survey (Macnab, 1999b) suggests that those at the
conferences have moved to put at least some of the
recommended changes into place and that school pupils
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 classroom organisation,
but includes also a breakdown of lesson structure with
time guides for the various elements. Detailed guidance
on Oral Work, on Teaching Input and associated Pupil
Activities, and on Lesson Conclusions is given. By far
the greater part 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 general character:
"Pupils should (be able to):
-
Respond rapidly to oral questions phrased in a variety 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 sentence
using + and - signs."
There are thus quite considerable differences 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 and so of the scale of reform
required. Time alone will tell which of the two will be
the more effective in implementation and in the effect on
pupils' standards of attainment, although official
figures (Summer 1999) have been published to show that
standards in England 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 Assessment of Achievement Survey scheduled
for Year 2000.
In the US different states have a freedom to 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
students are capable of learning rigorous mathematics
and learning it well, and all are capable of learning
more than is currently expected. Proficiency in
mathematics is not an innate characteristic; it is
achieved through persistence, effort and practice in
the part of students and rigorous and effective
instruction on the part of teachers.....The standards
emphasise computational and procedural skills,
conceptual understanding, and problem-solving. These
three components of mathematical instruction and
learning are not separate from each other; instead
they are intertwined and mutually 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 to
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 service in that
they give participating countries the opportunity in
mathematics (and science) education to "see oorselves as
ithers see us", to quote from Scotland's national poet
Robert Burns. The survey reported here demonstrates that
not all the countries made use of this opportunity; of
those that did, not all were prepared to accept what was
revealed; and that among those who did accept the verdict
of TIMSS, there was not agreement 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 TIMSS will indeed make a
difference.
References
Adams, 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
Strategy Research-based? British Journal of
Educational Studies, 46, 362-385.
California State Board of Education (1999). The
Mathematics Content Standards for California Public
Schools, Kindergarten Through Grade Twelve. Sacramento
CA: Calfornia State Board of Education.
Department for Employment and Education (1999). The
National Numeracy Strategy: Framework for Teaching
Mathematics from Reception to Year 6. London: DfEE.
Fullan, M. (1993). Change Forces: Probing the Depths
of Educational Reform. 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 Primary 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 Secondary Level in Hong Kong.
Hong Kong: University of Hong Kong.
Law, N, (Ed.), (1997). Science and Mathematics
Achievements at the Mid-Primary Level in Hong Kong.
Hong Kong: University of Hong Kong.
McKaig, G. (1998). Improving Mathematics Education 5-
14: Conference Report. Glasgow: St. Andrew's College.
Macnab, D.S.; Page, J. & Kennedy, M. (1989).
Assessment of Achievement Programme Second Round
Mathematics l988. Aberdeen: Northern College.
Macnab, D.S. (1999a). Mathematics Education in Scottish
Schools: An Uncertain Vision? Scottish Educational
Review, 31, 10-20.
Macnab, D.S. (1999b). Implementing Change in
Mathematics Education: A Paper Presented to the 1999
Annual Conference of the Scottish Educational Research
Association. Aberdeen: Northern College.
Macnab, D.S. (1999c). Improving Standards in
Mathematics Education: Values, 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.
Martin, M.O. et al. (1997). Mathematics Achievement
in the Primary School Years. 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 Strategy: 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) Fourth 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 Study 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 Systems 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 of 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 (TIMSS). 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.
About the Author
Donald S. Macnab
Senior Research Fellow
Northern College
Aberdeen Campus
Hilton Place
Aberdeen AB24 4FA
UK
Phone: +44 1224 283552
Fax: +44 1224 283900
Email:
d.s.macnab@norcol.ac.uk
Donald Macnab is Senior Research Fellow and Professor of Mathematics
Education at Northern College, a teacher education institution affiliated
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
attainments of Scottish Primary and Secondary schoolchildren - the
Assessment of Achievement 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.
|
times since February 28, 2000