In recent decades, mathematics education scholarship has promoted a shift from traditional teaching and learning approaches to novel approaches that privilege peer-to-peer collaboration. To mobilize researchers towards advancing scholarship on collaborative learning, scholars need to understand the methodologies available to them for examining…

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…

Current international curriculum frameworks and research advocate for K-12 mathematics to emphasize proof and argumentation. This review synthesizes literature related to conceptions, content, and supportive actions for proof and argumentation across four grade-level bands: K-2, 3-5, 6-8, and 9-12. Our systematic search and subsequent screening…

This research is a secondary analysis with Korean students' data collected in the TIMSS 2015 to describe the moderation effects of instructional practices on the relationships between students' emotional dispositions toward mathematics and mathematics achievement. From the TIMSS 2015 database, we collected mathematics achievement scores, a…

This paper compares sections on functions and linear functions from two Korean textbooks and an American standards-based textbook (University of Chicago School Mathematics Project [UCSMP] Algebra) to understand differences and similarities among these textbooks through horizontal and vertical analyses. We found that these textbooks provide…

The common teaching practice habit of connecting mathematics classroom activities with reality is still substantially delegated to wor(l)d problems. A growing body of empirical research suggests that the practice of word problem solving in school mathematics does not match this idea of mathematical modeling. Presents some classroom activities that…

Three approaches to the same geometrical problem are presented to demonstrate the role of intuition in mathematics and to clarify the concept of insight. (MP)

Suggests six characteristics of mathematical play. Analyzes the problem-solving process for the Six Circles and observations of students solving calculator and integration problems in relation to theories of play and cognitive gain. Discusses some difficulties of implementing a 'play' approach in the classroom and proposes further research…

The concept of school curriculum in science and mathematics is discussed and related to the structures of the disciplines and theory developments. Recent epistemological studies on theory dynamics (Kuhn, Sneed) are put into context with the understanding of learning processes. (Author/MK)

The potentials of computer systems designed to help students in learning mathematics are explored, and some barriers to implementation are discussed. (MP)

In this paper, prepared for a European conference on mathematics education in the 1980's, the author discusses the relationships among the mathematician, the teacher, and society. He also addresses the problems of language in mathematics teaching and the appropriate use of physical models in the classroom. (SD)

The behavioristic approach to education is appropriate only to areas of skill development. To design mathematics curricula from the point of view of behaviorism is to miss the essence of mathematics as a discipline. Mathematics curricula should include strong emphasis on problem solving. (SD)

The aims of the article are: (1) to outline the general tenets of the "back to basics" movements; (2) to indicate how these tenets go counter to emerging research on hemispheric specialization; and (3) to suggest methods which are brain-compatible and likely to produce competent creative problem solvers. (Author/TG)