This study investigates the characteristics of Japanese primary school mathematics lessons that adopt a problem-solving approach. We argue that these characteristics are reflected in three key aspects: collective teaching and learning, the lesson as a "drama" (i.e., its structured flow), and the focus on mathematical knowledge. In this…

The competency-based approach conceives mathematics as a necessary tool for dealing with daily-life tasks. Many studies have focused on examining the low math competency people show when solving problems in real-life contexts, but rarely characterize the type of mathematics needed in these contexts and how people use this mathematics. The current…

We propose to assess conceptual knowledge of mathematical notions by having recourse to isomorphic word problems. We assumed that failing to solve isomorphic problems is an indicator of lack of conceptual knowledge. To reach these conclusions, two experiments were conducted among 4th and 5th grade students. In experiment 1, each student had to…

Algebra has been explicit in many school curriculum programs from the early years but there are competing views on what content and approaches are appropriate for different levels of schooling. This study investigated 12-13-year-old Australian students' algebraic thinking in a hybrid environment of functional and equation-based approaches to…

It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle,…

This study investigated mathematics teachers' professional knowledge among elementary school teachers exposed to a professional training program that either supported self-regulated learning (SRL) or offered no SRL support (no-SRL). The SRL support was based on the IMPROVE metacognitive self-questioning method that directs students' attention to…

This paper describes the problem-solving behaviors of 12 mathematicians as they completed four mathematical tasks. The emergent problem-solving framework draws on the large body of research, as grounded by and modified in response to our close observations of these mathematicians. The resulting "Multidimensional Problem-Solving Framework" has four…

Investigates proficiencies when students work on mathematics problems and the extent captured by knowledge categories. Explores competency that goes beyond knowledge to include mathematical 'dispositions' and 'practices' in which students engage. Considers ways in which research knowledge is conceived and developed, reflecting upon the role of…