International Comparative Studies in Mathematics

The main focus of International Comparative Studies in Mathematics is to examine how students learn not only between various schools, but how they perform in mathematics around the globe. As pointed out in the introduction, Postlethwaite (1988) identified four objectives of comparative studies:

• Identifying what is happening in different countries that might help improve education systems and outcomes;
• Describing similarities and differences in educational phenomena between systems of education and interpreting why these exist;
• Estimating the relative effects of variables that are thought to be determinants of educational outcomes (both within and between systems of education); and
• Identifying general principles concerning educational effects.

Through these international perspectives, teachers gain a broader view of how to effectively teach students and are able to exchange ideas. The focus of this ICME-13 Topical Survey is to have an open discussion on the effective ways international comparative studies can be used to enhance student’s learning. The Organization for Economic Co-operation and Development (OECD), the group that administers the Programme for International Student Assessment (PISA), presents results on where countries stand and tries to motivate policymakers to identify any shortcomings and room for improvements but also give approvals. This survey talks about four of the many considerations we can take away from these studies:

1. Understanding students’ thinking,
2. Examining the dispositions and experiences of mathematically literate students,
3. Changing classroom instruction, and
4. Making global assessment research locally meaningful.

The first two items focus on the students’ mathematical thinking and achievement, the third considers classroom instruction, and the last talks about policy in the local context. Throughout the book, both large- and small-scale international comparative studies are considered.

The book starts on the State-of-the-Art with section 2.1, “Lesson 1: Understanding Students’ Thinking.” Here, the Pizza and Ratio problem is presented, in which there are 7 girls sharing 2 pizzas equally and 3 boys share 1 pizza equally. This problem asks students to decide and justify whether each girl gets the same amount of pizza as each boy. If not, who will get more? A figure presents the eight arguments (presented by Cai, 2000) used by both Chinese and United States students. Most of the Chinese students used fractions for their answers whereas the U.S. students did not.

As presented in section 2.2.3, there have always been discrepancies among the genders in mathematics. In particular, there have been differences in confidence between males and females. As pointed out on page 16, PISA 2012 (OECD 2013b) found that the gender difference was not observed in the formal mathematics tasks that match likely classroom content, such as solving linear equations. There were large gender differences, however, in the applied tasks. Across OECD countries, 75% of girls reported being confident or very confident when calculating a 30% discount on a TV, compared to 84% of boys. These differences were even greater when the context was stereotypically male. Across OECD countries, 67% of boys but only 44% of girls reported feeling confident about calculating the petrol consumption rate of a car.

This self-efficiency index explains more than 30% of the variance in proficiency for about a third of the PISA participating countries (OECD 2013b). These gender gaps in the self-efficacy for mathematical problems are most likely having an impact on gender when it comes down to achievement and future career endeavors.

Section 2.4, “Lesson 4: Making Global Research Locally Meaningful: TIMSS in South Africa,” discusses the apartheid social engineering project in South Africa and how it withheld mathematics as a school subject from the African population. South Africa had participated in TIMSS in 1995, 1999, 2002, 2011, and 2015 and also participated in the African Consortium for Monitoring Educational Quality (SACMEQ) in 2000, 2007, and 2015. On pages 27–28, Table 2 provides a summary of the findings from analysis of the TIMSS data along with Table 3 on page 29, which provides the trends in mathematics achievement for TIMSS for 1995, 1999, 2002, and 2011. When seeing these two pieces of data, it is clear that the lack of change in scores from 1995 to 2002 may have been due to the structural and educational changes as Africa moved from apartheid to a democratic state. Nevertheless, this shows how important a global perspective should be when thinking about the international comparative studies in mathematics education. In the end, our students’ future is of paramount importance.

Peter Olszewski is a Mathematics Lecturer at Penn State Behrend, an editor for Larson Texts, Inc. in Erie, PA, and is the 362^nd Pennsylvania Alpha Beta Chapter Advisor of Pi Mu Epsilon. He is interested in mathematics education, Cayley Color Graphs, Markov Chains, and mathematical textbooks. He can be reached at pto2@psu.edu. Outside of teaching and textbook editing, he enjoys playing golf, playing guitar and bass, reading, gardening, traveling, and painting landscapes.