Task-relevant actions can facilitate mathematical thinking, even for complex topics, such as mathematical proof. We investigated whether such cognitive benefits also occur for action predictions. The action-cognition transduction (ACT) model posits a reciprocal relationship between movements and reasoning. Movements--imagined as well as real ones…

Extant research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and extent of this relationship requires a detailed elaboration. This is especially true when adidactical problem-posing arises within a problem-solving context. In this study, we analyze the scripting journey used by two…

It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral…

Responsive teaching is a highly effective strategy that promotes student learning. In math classrooms, teachers might funnel students towards a normative answer or focus students to reflect on their own thinking, deepening their understanding of math concepts. When teachers focus, they treat students' contributions as resources for collective…

Prior studies show that elementary school children generally "lack" formal understanding of inverse relations. This study goes beyond lack to explore what children might "have" in their existing conception. A total of 281 students, kindergarten to third grade, were recruited to respond to a questionnaire that involved both…

This study aimed to reveal the conceptual and operational conceptions of sixth-grade students in the process of division. The focus of the study included the strategies used in the division process, the students' understanding of the division algorithm, and their ability to interpret the remainder in a real-life context. Being qualitative in…

This paper presents strategies identified in Mexican rural school students in seeking structure on equivalence tasks that involve the equal sign and tasks that do not. The results arise from the pilot study of a research project on the structure of numbers and numerical operations -- a key aspect of early algebraic thinking. [For the complete…

In this article, the authors present a brief description of the different views of the "nature of mathematics" (NOM), share a five-point view of NOM that undergirds the teaching profession's guiding documents, and describe ways of providing opportunities for teachers and students to have conversations in the classroom that build…

This study highlights the importance of an educational design that includes robotics and programming through a visual programming language as a means to enable students to improve substantially their understanding of the elements of logic and mathematics. Gaining an understanding of computational concepts as well as a high degree of student…

Assessment data from the United States and international reports of student achievement indicate that upper elementary students are failing to meet basic levels of proficiency in fractions and writing, and that this is particularly prevalent with students with or at-risk for learning disabilities in mathematics. Proficiency with fractions has been…

Permutations and combinations are used to solve certain kinds of counting problems, but many students have trouble distinguishing which of these concepts applies to a given problem. An "order heuristic" is usually used to distinguish the two, but this heuristic can cause confusion when problems do not explicitly mention order. This…

This study is part of a larger research program aimed at studying mental mathematics with objects other than numbers. It concerns operations on functions in a graphical environment with Grade-11 students. Grounded in the enactivist theory of cognition, particularly in problem-posing, the study aims to characterize students' mathematical activity…

A renewed emphasis was placed on ratio and proportional reasoning in the middle grades in the Common Core State Standards for Mathematics (CCSSM). The expectation for students includes the ability to not only compute and then compare and interpret the results of computations in context but also interpret ratios and proportions as they are…

This research was designed to investigate the conceptualisations and thinking strategies Indigenous Australian students use in counting tasks. Eighteen Aboriginal students, in years 1 to 11 at a remote community school, were interviewed using standard counting tasks and a "counting" task that involved fetching "maku" (witchetty…

The intention of the present study is to know how the pupils can learn to make a group of ten to understand the idea of unitizing. The pupils were given a contextual problem "Counting the Beads" in order to promote their understanding about the idea of unitizing. The process of designing the problem was based on the 5 tenets of…