A teacher of mathematics knows mathematics as a teacher and as a mathematician. Whilst the existing research on teacher knowledge contributes to our understanding of the ways of knowing mathematics as a teacher, little is known about ways of knowing mathematics as a mathematician. Guided by the conceptual framework of mathematical practices (MPs)…

Opportunities to closely monitor and evaluate students' mathematical thinking enables accurate interpretations of their conceptual understanding. This methodological paper reports on a novel and versatile analysis approach to extract student thinking during mathematical games through the generation of Dynamic Learning Artefacts (DLAs).…

It is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing…

Purpose: Music could be a challenger for mathematics and a potential candidate for the title "The Universal Language." This paper aims to discuss the primary objectives of engaging with music, including the therapeutic benefits. Similarities, between mathematics and music and how studying one might enhance one's abilities of the other…

The aim of this study was to investigate current trends in research of math anxiety (MA) through bibliometric perspective. Three main clusters were formed based on author keywords: cognitive correlates (working memory, attention, numerical cognition, mental arithmetic), psychological factors and effects (self-concept and self-efficacy, motivation,…

This study aimed to investigate secondary mathematics teachers' noticing of students' mathematical thinking in the context of a professional development (PD) program utilizing modeling-based teacher investigations. The PD program was conducted with two groups of mathematics teachers from two public high schools. It included seven 1-month-long…

This study investigates the mediating roles of mathematics interest and perseverance on the effects of cognitive activation on mathematics achievement. We analysed data from a large-scale survey involving 25,969 eighth grade students from 86 schools in central China. The results show that (1) cognitive activation had a direct and positive effect…

Mathematical problem-solving places heavy demands on children's developing working memory capacity. This review examines how offloading numerical information using embodied (e.g. finger counting) or external tools (e.g. manipulatives) can reduce cognitive load and improve mathematical task performance. Strategic offloading emerges in childhood;…

This paper aims at defining and exploring design principles in a distance technological setting for an educational activity for mathematics undergraduate students, devoted to the construction of basic concepts in general topology, the promotion of problem-solving processes, the development of metacognitive aspects, and, in general, the development…

This research focuses on a dual mediation model designed to describe the learning process of sixth grade students practicing mathematics to improve Mathematics Operation Proficiency while experiencing different forms of feedback. The variables of interest in this study are the predictor variable feedback type, the mediating variables of Affective…

Process data from educational assessments enhance the understanding of how students answer cognitive items. However, effectively making use of these data is challenging. We propose an approach to identify solution patterns from operation sequences and response times by generating networks from process data and defining network features that…

Over four decades of conceptual change studies in education have been based on the assumption that learners come to science classrooms with functionally fixated intuitive ideas. However, it is largely ignored that such pre-instructional conceptions are probabilistic, reflecting some aspects of an idiosyncratic sampling of their experiences and…

Although the importance of problem solving as an essential component of mathematics learning and doing has consistently been recognized, recent research has only just begun to identify and describe the complex set of variables influencing the endeavor. Therefore, the aim of this study was to empirically investigate the relationships between…

Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in…

We offer a new angle to explain the comprehension of mathematical infinity. We use Action-Process-Object-Schema (APOS) theory to explore the construction of different aspects of the cognitive Object related to this notion. We focus our attention on different ways of interacting with infinity, and how to act on infinite entities. Our aim is to shed…