Mathematics Teaching and Learning: An International Perspective

• In Event: Comparison of 67 Countries in Achievement and Noncognitive Factors: Highlights of PISA (Programme for International Student Assessment) 2012

Abstract

Objective
The goal of this paper is to identify aspects of mathematics teaching and learning in secondary school that are universally relevant for students, teachers, and schools worldwide and thus explain differences in students learning outcomes both within school systems and across.
Theoretical background
Educational researchers have described classroom teaching and learning processes from different perspectives and with different levels of depth. First, observable practices can be described and classified into patterns such as teacher-directed instruction, student-centered teaching, or inquiry-based learning (cf. Vieluf, Kaplan, Klieme & Bayer, 2011). Second, the subject matter that is covered, and the kind of tasks and problems that are assigned to students may be judged in terms of content coverage and focus. This “opportunity-to-learn” approach is well-established in international studies (Schmidt & Maier, 2009). Third, student-teacher interactions may be judged either by observers or by students and teachers themselves to assess basic dimensions of classroom quality such as structure (efficient classroom management), support (positive classroom climate), and challenge (high cognitive activation; see Klieme, Pauli & Reusser, 2009). In accordance with models of educational psychology such as self determination theory (Deci & Ryan, 2002) and constructivist approaches (Tobias & Duffy, 2009) all three approaches have been shown to explain both cognitive and non-cognitive (e.g., motivational) outcomes of student learning.
One problem with these concepts is low comparability of measures, samples, and observed outcomes across studies. Also, there is some debate on the culture-specificity vs universality of teaching and learning (Stigler & Hiebert, 2001; Baker & LeTendre, 2006). So there are at least three caveats of research: a) international comparability of aspects of classroom quality and teaching practices, b) patterns of relations between quality and practices, and c) universal or differential relations between classroom quality and practices on the one hand and student outcomes on the other hand.
Method and sample
The paper will analyze data of the international study PISA 2012. Relevant data is available for more than 140,000 students in 68 countries worldwide. Data preparation has been finalized and data currently awaits release later this year. The paper refers to mathematic literacy scores and the international index of students’ interest in mathematics, linking these outcome measures to student reports on quality ratings (teacher support, classroom management, and cognitive activation) as well as frequencies of teaching practices in the classrooms. Steps of analyses will include an international comparison of classroom quality aspects, international comparison of patterns of teaching practices and their relations to measures of classroom quality, and finally a study of effectiveness of such patterns for student outcomes in three cultures (US, Germany, and Japan). The paper will apply multilevel modeling of regression and factor analyses techniques.
Results and conclusions
Preliminary analyses point to different clusters of teaching practices that are related to aspects of classroom quality ratings. Classroom quality and teaching practices display shared and individual relations to cognitive and non-cognitive student outcomes. The discussion will focus on possible improvements in mathematics teaching and learning and lessons learnt from an international perspective.

Authors

• Susanne Kuger, German Institute for International Educational Research

• Eckhard J. Klieme, German Institute for International Educational Research