In this paper, we analyse a grade 8 (age 13-14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in…

Efficient collaborative learning relies on productive interaction among learners. Previous studies have suggested that group gender composition might affect the group dynamics. While previous studies have generally focused on the learning performance of different gender groups, relatively little effort has been devoted to scrutinising the learning…

Mathematical Communication Skills (MCS) refer to the students' ability to (1) arrange and link their mathematical thinking through communication; (2) communicate their logical and clear mathematical thinking to their friends, teachers, and others; (3) analyze and assess mathematical thinking and strategies used by others; and (4) use mathematical…

This study compared students' learning in troubleshooting and problem solving activities. The troubleshooting activities provided students with solutions to conceptual problems in the form of refutation texts; namely, solutions that portray common misconceptions, refute them, and then present the accepted scientific ideas. They required students…

I examined the impact of a self-diagnosis activity on students' conceptual understanding and achievements in physics. This activity requires students to self-diagnose their solutions to problems that they have solved on their own--namely, to identify and explain their errors--and self-score them--that is, assign scores to their solutions--aided by…

Students often voice computations during group discussions of mathematics problems. Yet, this type of private speech has received little attention from mathematics educators or researchers. In this article, we use excerpts from middle school students' group mathematical discussions to illustrate and describe "computational private…

In this study, 100 Italian eighth graders were divided into two groups to compare the effects of two instructional interventions--the first based on problem-solving through discussion, the second on individual problem-solving--on students' learning of two historical topics (World War I and the economic boom), interest and self-perception of…