Backward transfer is defined as the influence that new learning has on individuals' prior ways of reasoning. In this article, we report on an exploratory study that examined the influences that quadratic functions instruction in real classrooms had on students' prior ways of reasoning about linear functions. Two algebra classes and their teachers…

This study identifies characteristics of polygon class learning opportunities for 8-9-year-old children during the whole-class instruction. We consider the interplay between the geometrical tasks demanding different ways of reasoning, features of children's geometrical thinking, and the teacher's moves to identify characteristics of learning…

This work is the result of a pre-experiment carried out as part of a master's course, dealing with the study of the parabola through different mathematical views. It aims to recognize possible didactic obstacles in its teaching, based on intuitive manifestations in the resolution of a didactic situation based on GeoGebra software. The methodology…

The concrete-representational-abstract (CRA) approach is an instructional framework for teaching math wherein students move from using concrete materials to solve problems to using visual representations of the materials, and finally abstract concepts. This study provides a literature synthesis and meta-analysis of the effectiveness of the CRA…

Mathematical abstraction constitutes the foundational cornerstone for the establishment and evolution of mathematical disciplines, serving as the pathway through which mathematical concepts emerge. As one of the information technologies widely applied in mathematics education, the Dynamic Mathematics Systems (DMS) have been found to have a…

The research on mathematical argumentation has mainly adopted a dialectic lens which focuses on understanding the abstract and logical development of reasoning in argumentation. However, this approach may have overlooked other key aspects of mathematical argumentation, including the unfolding of the meaning-making experience and process during…

Students need a robust understanding of the derivative for upper-division mathematics and science courses, including thinking about derivatives as ratios of small changes in multivariable and vector contexts. In "Raising Calculus to the Surface" activities, multivariable calculus students collaboratively discover properties of…

Tentativeness is often framed as a deficit, synonymous with timidity or a lack of confidence. In this article, I situate the notion of tentativeness in an enactivist framework and describe its role as both a strategy and affordance in a spatial visualization exercise. Drawing on insights from mathematics education and ecological psychology, I…

This paper presents data from the first of three iterations of teaching experiments conducted with secondary teachers. The purpose of the experiments was to investigate how teachers' combinatorial reasoning could support their development of algebraic structure, specifically structural relationships between the roots and coefficients of…

Since formal mathematics is discussed in terms of abstract symbols, many students face difficulties to acquire a clear understanding of mathematical concepts and ideas. Transforming abstract or dis-embodied representations of mathematical concepts and ideas into embodied representations is a strategy to make mathematics more tangible and…

This work is part of an investigation conducted in Italy, which aims to explore the effects of instruction on secondary school students' combinatorial reasoning. We gave a questionnaire adapted from Navarro-Pelayo's research to two groups of students with and without instruction on combinatorics in order to analyse the students' performances and…

Many educators and professional organizations recommend Quantitative Reasoning as the best entrylevel postsecondary mathematics course for non-STEM majors. However, novice and veteran instructors who have no prior experience in teaching a QR course often express their ignorance of the content to choose for this course, the instruction to offer…

Covariational reasoning is a cognitive activity that attends to two or more varying quantities and how their changes are related to each other. Previous studies indicate that covariational reasoning seems to have levels. Content analysis was used to examine the pedagogy and development of covariational reasoning levels in the sections that…

This research aims to analyze the results of studies conducted in Turkey on reasoning skills in mathematics teaching and to reveal what kind of trend there is in this field. Within the scope of this study, databases were searched with the keywords "reasoning"(muhakeme, akil yürütme) and "reasoning skill" (Muhakeme becerisi,…

The authors define two mathematical cognitive verbs which are fundamental to the development of mathematical thinking and reasoning. They distinguish between 'describing' and 'explaining' in relation to doing mathematics, rather than using them interchangeably.