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Didactics of Mathematics as a Scientific Discipline, 403-414.
© 1994 Dordrecht: Kluwer Academic Publishers. Printed in the Netherlands.
2. DEVELOPMENT OF COMPARATIVE EDUCATION
Early comparative studies of mathematics education offered researchers and
policymakers opportunities for an international exchange of ideas and ex-
periences at a system level. Studies such as projects coordinated by the
International Commission on Mathematical Instruction (ICMI) at the turn of
the century and in the 1950s used narrative reports prepared by participating
countries as data to compile summary descriptions about the organization of
mathematics content and instruction within an international context (e.g.,
United States Bureau of Education, 1911; Fehr, 1959; Freudenthal, 1959).
These early studies were descriptive in nature and were not designed to
compare student achievement internationally.
It was not until the first IEA study conducted in the early 1960s that com-
parative studies of achievement on a large collaborative scale emerged.

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DAVID ROBITAILLE & CYNTHIA NICOL
Many situations have occurred that have created an environment that may
have enhanced the development of such studies. One important considera-
tion is the nature of the political and economic context over the last 30
years. In particular, there has been a great deal of concern centered around
issues of excellence in education with regards to achievement and account-
ability. As well, there have been developments and adoptions of various re-
search methodologies that have made the conducting of comparative studies
feasible. Furthermore, the growth of intergovernmental organizations may
also have enhanced the environment for the emergence of comparative
studies.
Since the 1960s, there has been increased concern worldwide by public
and governments over the need to relate educational investments to educa-
tional accomplishments and outcomes. The suggestion that a nation’s well-
being, economic prosperity, and growth are dependent upon the develop-
ment and sustainment of an educated work force (Walberg, 1983) has strong
political and economic implications. As a consequence, over the years there
has been increased interest by nations for demonstrated relationships be-
tween achievement and educational variables such as curricula, instructional
methods, teacher characteristics, organizational processes, and societal or
contextual factors. Interest in international comparisons of these relation-
ships has emerged as countries seek to develop or maintain positions of
economic competitiveness in world markets. Thus interests of accountabil-
ity and excellence in education within and between countries have provided
a need for comparative studies of achievement.
The ongoing development and construction of research methods that
enable the identification and analysis of educational variables associated
with achievement have made it possible to seriously consider conducting
comparative studies of achievement. Without appropriate research methods,
it is difficult to conduct international comparative studies and to produce
valid and reliable data from which decisions can be made. Early compara-
tive studies of achievement often consisted of records from observations
made by researchers or government representatives while traveling abroad.
Spaulding (1989) notes that data from such studies focused on describing
educational institutions, systems, and programs, but that these studies lacked
the systematic and sophisticated methods that would enable appropriate
quantification and comparability between and within cultures. Over the last
30 years, researchers have borrowed research techniques from the social and
behavioral sciences and theoretical frameworks from the effective schools
literature. This has enabled the quantification and comparison of cross-cul-
tural differences in achievement and the identification of relationships be-
tween school variables and achievement. In addition, the development of
methodologies in comparative education has also benefited from the ad-
vances in technology making it possible to identify, measure, control, and
analyze numerous educational variables related to school achievement.
404

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Conducting such large-scale studies also requires the collaboration of
many researchers, educators, and government agencies and their sharing of
information internationally. Eckstein (1982) and Spaulding (1989) note that
the growth and development of various organizations such as the United
Nations Educational, Scientific, and Cultural Organization (UNESCO), the
Organization for Economic Development (OECD), and the World Bank has
strengthened the possibility of conducting comparative studies. Organiz-
ations such as these have provided valuable system-level statistics such as
enrollment rates at various educational levels, teacher-student ratios, and
per-student expenditures. The World Bank, in particular, has focused on
stressing the quantification of educational indicators so that it can assess the
impact of its investment in educational developments worldwide. The
growth of these organizations has provided a valuable infrastructure for the
sharing of information, providing nations with a surface-level view of what
is happening in other educational systems in comparison to their own.
COMPARATIVE INTERNATIONAL RESEARCH
405
3. IMPORTANCE OF COMPARATIVE STUDIES IN EDUCATION
There is a great deal of variation among different societies and education
systems. Different cultures have different beliefs and values concerning the
teaching and learning of mathematics. Some differences include degrees of
access to resources such as textbooks, centralized versus decentralized de-
cision-making, systems of comprehensive and/or selective schools, and
varying retention or enrollment rates through high school. However, there
are also similar issues in education that many countries share, for example,
the question of how to provide effective and efficient education is a com-
mon international concern (Spaulding, 1989). Comparative studies, there-
fore, provide opportunities for the discussion and debate of these important
issues in an international context. Researchers, educators, and policymakers
can be provided with opportunities to reflect on their own educational
situation, to gain further insight into possible alternatives to curricula and
instruction, and to challenge previous notions about what is possible to ex-
pect concerning what students can learn and what instructional activities
promote that learning.
Mathematics education has been a central area of comparative interna-
tional research. Mathematics has always held a privileged position in the
school system, in fact, it is one of the few subjects that is taught in most
school systems worldwide (Howson & Wilson, 1986). Although countries
differ in social, economic, and employment opportunities, there is still a
surprising degree of similarity in the mathematics curricula of countries in-
ternationally (Howson & Wilson, 1986). This universal status and impor-
tance of mathematics, the similarity of mathematics curricula worldwide,
and the supposed link between the study of mathematics or science and the
development of a nation’s economic strength (Walberg, 1983) make studies

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of international comparison in mathematics education of important interest
to researchers, educators, and policymakers.
However, comparative international studies in mathematics education are
not without their critics. Many critics state that such studies are expensive to
conduct, require a great deal of time and effort, and produce results that are
of questionable significance and difficult to compare. More specifically,
Freudenthal (1975), criticized the first IEA mathematics study for, among
other things, the failure to appropriately consider whether or not students
had been taught the content needed to respond correctly to the various test
items and for the failure to consider curriculum as a variable. As a result, the
construction of powerful concepts such as opportunity to learn has proved
valuable in accounting for between-country differences and in making ap-
propriate international comparisons. Criticisms such as these strongly influ-
ence the structure, design, and development of comparative studies. It is in
this way that such studies continue to define their importance and to im-
prove in their search for quality comparable data.
DAVID ROBITAILLE & CYNTHIA NICOL
406
4. DIRECTIONS AND TRENDS IN COMPARATIVE EDUCATION
One direction for cross-cultural research has been the consideration of the
importance of culture in teaching and learning. Some of the early cross-cul-
tural anthropological studies conducted in the 19th century focused on de-
scribing the nature of “primitive mentality” independent of cultural social
needs and conditions (Stigler & Baranes, 1988). Recently such cross-cul-
tural research has been called into question. New advances in cognitive sci-
ence suggest that the situated nature of learning (Brown, Collins, & Duguid,
1989; Harris, 1989; Saxe, 1988), that is, the cultural contexts in which
learning occurs, is an important consideration in understanding cross-
cultural differences from an international perspective. As a result, a great
deal of comparative education research is now placing more emphasis on
the role of social and cultural contexts and the contextualization of data for
the development of meaningful interpretations and comparisons.
The consideration of qualitative research methods is another direction in
which many researchers in the international comparative education
community are moving. Altbach (1991) notes that the consideration of new
research orientations and an emphasis on qualitative research methods
promise researchers a more comprehensive study of differences in not only
approaches to curriculum but also instructional approaches and the
relationship of these to student achievement. Similarly, Stigler and Baranes
(1988) suggest that the inclusions of qualitative research methods in
comparative studies of schooling provide opportunities for in-depth
investigations of the nature of schooling differences and the cultural
contexts of such differences.
Comparative studies in the IEA tradition have focused mainly on the use
of survey research methods to determine the influence of particular vari-

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COMPARATIVE INTERNATIONAL RESEARCH
ables on teaching and learning within an international context. Over the last
30 years, IEA studies have increased the number and nature of the variables
included for investigation and have made significant advances in the devel-
opment of instrumentation. For example, the Second International
Mathematics Study (SIMS) analyzed curricula internationally, investigated
teaching practices, included a longitudinal study to determine student
achievement growth patterns over the school year, and utilized the oppor-
tunity-to-learn construct as a method of accounting for achievement differ-
ences. Although “comparative studies done by IEA are among the best ex-
amples of comparative research” (Altbach, 1991, p. 491), researchers such
as Stigler and Baranes (1988) suggest that such studies need to be comple-
mented by work with a more in-depth qualitative analysis.
407
5. IEA SURVEYS
IEA, established in 1960, is a cooperative network of research centers
(Postlethwaite, 1971). The organization began with a group of researchers
from around the world who, notes Purves (1989), “were concerned with a
number of issues that could not be studied well within the confines of one
school system” (p. vii). Today, the membership of IEA consists of institu-
tions from more than 50 countries under the united goal of investigating the
potential influence of alternative curricula, teaching strategies, and adminis-
tration strategies on student achievement (Hayes, 1991). The first major IEA
study was conducted in 1964, and, although it was designed to be a general
study of the outcomes of schooling, the subject area of mathematics was
chosen as the vehicle through which national comparisons in education
would be made.
5.1 The First International Mathematics Study
This first IEA study was a very ambitious study measuring achievement in
various mathematics topics in 12 countries. Countries that agreed to partic-
ipate were mainly European industrialized countries: Australia, Belgium,
England, the Federal Republic of Germany, France, Finland, Israel, Japan,
the Netherlands, Scotland, Sweden, and the United States. The student
populations sampled for this study consisted of 13-years-old students and of
students in their last year of secondary school (for complete population def-
initions, see Husén, 1967).
Since IEA projects are a cooperative international effort, all participating
countries were involved in some way in the construction of the achievement
tests. Using a two-dimensional item-specification grid consisting of a con-
tent-by-cognitive behavior matrix, appropriate topics involving arithmetic,
algebra, geometry, and calculus were selected for each population level.
Students, teachers, school principals, and national experts were also asked
to complete a number of questionnaires. Students responded to attitude
scales providing information on their personal views of mathematics, their

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DAVID ROBITAILLE & CYNTHIA NICOL
school work, and career aspirations. Teachers were asked about their own
experience, education, and qualifications and how well they expected their
students to perform.
The major findings of the first IEA study have been summarized in many
volumes and articles over the years (Husén, 1967; Kilpatrick, 1971;
Postlethwaite, 1971; Robitaille & Travers, 1992). Therefore a selection of
some of the important findings related to student achievement and attitudes,
selectivity and retentivity, and opportunity to learn will be discussed here.
The results of the first IEA study indicate that all groups of students from
all participating countries found the tests difficult. For example, the majority
of mean achievement test scores for each population were below 50%
across all countries. It was found that 13-year-old students had a more posi-
tive view of mathematics as a process than did senior students. This may
indicate that student’s attitudes and interest in mathematics declines with
age and with the continued study of mathematics.
A major issue addressed by this study was to determine the situations that
enable the most talented students to perform and develop. Many of the