Is there a trend towards convergence in countries mathematics achievement?

• In Event: Secondary Analysis of International Large-Scale Assessment Data

Abstract

Purposes
The main purpose of this paper is to explore if there has been a harmonization of countries’ performances, resulting in a “world curriculum”. If countries tend to converge with respect to their response patterns to mathematics tests, this may be an indication of harmonization of their school systems and curricula. For example, if students in different countries show more similar response patterns over time this may be taken as an evidence for a global force, which, in literature has been related to, among others, the international studies.

Theoretical framework
The international comparative studies have been widely debated in media the last decade. Although these studies have provided valuable information, the studies have met a fair amount of criticism, from different angles and perspectives. One line of this criticism mainly concern the policy borrowing across countries that the international studies have been argued to contribute to: countries curricula tend to converge over time into a so called ‘world curriculum’ (Baker & LeTendre, 2005). Poor performing countries may focus to specific knowledge and skills to achieve high results in the international comparisons. This might hamper other competences such as innovativeness and creativity. Such competences have been argued to decline with increasing results in international comparisons (e.g., Zhao, 2012). However, the empirical evidence in this area is quite limited. Rutkowski and Rutkowski (2009) studied country-level item responses for a range of countries participating in TIMSS 95, 99, and 03. Although they identify similarities on regional level (e.g. East European), their find not global forces. However, the time span this study covers might be too limited to capture global trend that indicate convergence.

Analytical methods
We use latent profile analysis on aggregated country level data to identify different achievement profiles in mathematics. Countries are included in the dataset multiple times if they participated in different mathematics studies. For each country, achievement information on four content domain subscales is available. The latent profile analysis aims to identify a set of countries (latent classes) that are defined in terms of their score profile on the four content domain subscales. In a second step, we introduce time as an explanatory variable to test the hypothesis of convergence, that is, if fewer latent classes represent more countries. In other words, we investigate if countries become more similar over time.

Data sources
The current study employs data from several previous IEA studies on mathematics in secondary school: SIMS 1980, and TIMSS 1995, 1999, 2003, 2007, and 2011. More than 80 educational entities (countries or regions) participated in at least one study, and the assessment material covers 744 test items. We used the mathematics assessment framework from the latest TIMSS cycles to assign each test item to one of the four content areas Numbers, Algebra, Geometry, and Data & Chance. This step is necessary because the older studies used different labels (e.g., Arithmetic instead of Numbers). In a second step, we calculated proportion correct scores for four subscales. These scores serve as a basis for the latent profile analysis. To avoid that the latent classes are rather based on the overall performance on the subscales than on qualitative differences in the patterns, we standardized the raw proportion correct statistic within each country and this was done separately for each study. We used a set of dummies for each study as a measure of time.

Results and Conclusions
Preliminary findings show that it is possible to identify different latent clusters of countries with similar patterns in the four mathematic subdomains. The classes differ with respect to relatively high achievement on certain subdomains of mathematic and in terms of their size, i.e. the number of countries that are best described by the respective clusters’ pattern. However, introducing time as a covariate does not predict class membership. In other words, we did not observe that certain latent classes increase consistently over time.

The international studies may have large impact on the school debate and the policy discussions in different countries. The may also constitute a base for decisions and reforms. However, that unintended consequences such as convergence of curricula actually would lead to convergence of actual achievement is more difficult to prove. Even though countries strive to be equally good as the best performing, there is no evidence in this study that they conform in their response patterns over time.

Educational Significance
The study concerns an issue of great educational importance, which previously has been difficult to study empirically. Moreover, the methodological approach used is also of significant interest.

Authors

• Stefan Johansson, University of Gothenburg

• Rolf Strietholt, TU Dortmund