In this article, we address a call by Thompson and Carlson to directly contribute to defining the variation of students' reasoning about varying quantities. We show that students as young as in sixth grade can engage in complex forms of reasoning about multiple quantities in contexts that involve exploring science phenomena using interactive…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

One of the aspects of programming that novices often struggle with is the understanding of abstract concepts, such as variables, loops, expressions, and especially Boolean operations. This paper aims to explore the effects of programming tools with different degrees of embodiment on learning Boolean operations in elementary school. To this end, 67…

Research in undergraduate physics and in K-12 science education has demonstrated challenges and successes in facilitating student engagement with reasoning practices associated with professional physicists. Here we focus on one important dimension of physics reasoning, using evidence to revise models. While this topic has been explored at the…

Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning…

Learning progressions (LPs) are novel models for the development of assessments in science education, that often use a scale to categorize students' levels of reasoning. Pictorial representations are important in chemistry teaching and learning, and also in LPs, but the differences between pictorial and verbal items in chemistry LPs is unclear. In…

In this paper, we discuss the process of identifying and validating students' abilities to think proportionally. More specifically, we describe the methodology we used to identify these proportional reasoning attributes, beginning with the selection and review of relevant literature on proportional reasoning. We then continue with the…

This article gives a general overview of an alternative instructional sequence that can be used to teach integer concepts and operations. The sequence follows three heuristics from Realistic Mathematics Education (RME) that encourage curricula to be reinforced with real-world applications (financial net worth): move students gradually, yet…

This document is the fourth volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 42 research reports by presenters with last names beginning between Mul and Wu:…