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 article presents different approaches to a problem, dubbed by the author as "the consecutive pages problem". The aim of this teaching-oriented article is to promote the teaching of abstract concepts in mathematics, by selecting a challenging amusement problem and then presenting various solutions in such a way that it can engage the attention…

We present a research report on addition and subtraction conducted with Down syndrome students between the ages of 12 and 31. We interviewed a group of students with Down syndrome who executed algorithms and solved problems using specific materials and paper and pencil. The results show that students with Down syndrome progress through the same…

This classroom note shows how Fibonacci numbers with negative subscripts emerge from a problem-solving context enhanced by the use of an electronic spreadsheet. It reflects the author's work with prospective K-12 teachers in a number of mathematics content courses. (Contains 4 figures.)

This note discusses a possible method for teaching an example of problem solving to intermediate grade students. Under the guidance of the instructor, students may see the links between the 'guess' method and the arithmetic operation 'strings'. This may help enhance their logical thinking ability as well as arithmetic operation skills. For…