Mathematical ideas are developed and spread during argumentative whole class discussions between a teacher and her students. The goal of the current study is to characterize how ideas about quadratic functions emerge and are spread during a whole-class discussion among ninth graders. To this end, we recorded both discussions between pairs of…

This article presents a theoretical-didactic perspective on the formation and development of concepts concerning mathematical objects as a result of research on didactic difficulties in dealing with concepts in school. The theoretical foundation that supports the research is based on the contributions of the materialist approach to the theory of…

Contribution: Using threshold concepts as the framework for curriculum design, a project on neural network methods for solving differential equations is presented, with a rich set of transformative concepts from mathematics and computer science. Projects of this kind complement a typical curriculum with expertise that is crucial for critique and…

Our mental representation of the infinite has received little research attention in cognitive psychology. In countably infinite sets, the infinity symbol (8) is presumed to be perceived as larger than any finite natural number. The present study sought to explore if the infinity symbol is processed as "larger than" natural numbers, and,…

In response to recent trends in the field of mathematics education, real-world contexts are frequently found in curricula and classrooms across the world. Numerous scholars contend that, in addition to making instruction more engaging and relevant, rich, imaginable contexts can provide a semantic grounding that helps students deeply understand…

The notion of definition is a central building block of mathematics. In addition to specific definitions, it is desirable that students learn about meta-mathematical aspects of definitions such as their role of classification, and about characteristics of definitions such as arbitrariness. We investigated how such meta-mathematical aspects emerge…

This paper aims to shed light on an overlooked but essential aspect of informal reasoning and its radical implication to mathematics education research: Decentralising mathematics. We start to problematise that previous studies on informal reasoning implicitly overfocus on what students infer. Based on Walton's distinction between reasoning and…

Middle school students (n = 144) worked with an applet specially designed to introduce the concept of function without using algebraic representations. The purpose of the study was to examine whether the applet would help students understand function as a relationship between a set of inputs and a set of outputs and to begin to develop a…

This article examines the integration of financial numeracy in secondary mathematics textbooks. It addresses the gap in literature on how financial concepts are portrayed in textbooks, contributing to the establishment of financial numeracy as a field of research and practice. The study analyzed financial numeracy tasks in three published textbook…

Most research on feedback in higher education focuses on evaluative feedback and its recipience, uptake, and enactment. Evaluative feedback information includes judgments, critiques and suggestions for improvement provided by a teacher, peer, self, pre-programmed automatic feedback, or artificial intelligence tutoring systems. In contrast, we…

This paper aims to reveal the potential of inferentialism, an emerging philosophy in mathematics education, to extend contemporary constructivist research regarding conceptual development. Going against the traditional view of a notion as the name of a corresponding concept and a constructivist way of naming second-order models, we provide a new…

The give-"n" task is widely used in developmental psychology to indicate young children's knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and…

Geometry and spatial reasoning form the foundations of learning in mathematics. However, geometry is a subject often ignored by curriculum writers and teachers until high school, leading to students lacking in critical skills in geometric reasoning. As the United States moves into a new curriculum epoch, heralding the commencement of the national…

The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…

How to influence and assess whether students engage in conceptual thinking are longstanding methodological problems in mathematics education. Recently, eye-tracking technology has fueled a discussion on whether eye movement analysis can support valid inferences about mathematical thinking. This study investigates whether eye movement analysis can…