Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

Fractions are among the most problematic concepts that children encounter in their primary school years because of the many different conceptions of fractions. Textbook analyses have tried to provide insights into how fractions are introduced, focusing on the different concepts and representations of fractions. In this paper, we contribute to…

Is children's literature only beneficial to children? Or do the benefits of children's literature also extend to the knowledge and mathematical skills of the teachers who employ it and reflect on it? This study seeks to investigate the role of picturebooks on the mathematical knowledge of preschool teacher candidates. For this purpose, in-depth…

In this paper the author explores and demonstrates the vital role mathematics plays in technology by showing how algebra, and in particular Boolean algebra, has become an essential part of how computers and computer languages work. Both Boolean logic and algebra are core competencies in Computer Science at the university level which may encourage…

Fractions are an imperative skill for students to master to achieve success in future mathematics concepts and classes. Yet many students, especially those experiencing math difficulties and/or characteristics of emotional and behavioral disorders, continue to exit elementary school without a concrete foundation of fractions skills required to…

Due to the learning paradox, students cannot have real difficulty in understanding a mathematical concept that they have not yet understood. There is a gap between real difficulties, directly experienced by students, and illusionary ones, only observed by researchers. This paper aims to offer a critical reflection on our understanding of the term…

"Epistemological justification" is a way of thinking that manifests itself through perturbation-resolution cycles revolving around the question "why and how was a piece of mathematical knowledge conceived?" The paper offers a conceptual framework for constituent elements of epistemological justification. The framework provides:…

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

The use of scientific calculators in teaching parabola functions has been shown to have significant effect in learner performance. This study examined the effectiveness of scientific calculators' usage in the teaching and learning of Grade 11 parabola functions to improve learner performance. Bandura's observational learning theory underpinned…

This scholarly inquiry critically examines the pedagogical aspects pertaining to the instruction and acquisition of Abstract Algebra within the realm of University Mathematics Education (UME). Drawing upon multiple lenses, including epistemological, cognitive, phenomenological, and institutional perspectives, this study investigates the formidable…

In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating…

This paper is devoted to the design, description and validation of the Android application TEAtreves, which focuses on structured arithmetic problem-solving for students with autism spectrum disorder (ASD). The application contains multiple adaptations to make it suitable for users with ASD. Validation was carried out with five students with ASD,…

Prompting learners to generate examples has been proposed as an effective way of developing understanding of a new concept. However, empirical support for this approach is lacking. This article presents two empirical studies on the use of example-generation tasks in an online course in introductory university mathematics. The first study compares…

The purpose of this article is to conduct a mathematical and phenomenological comparison of three concepts: (1) the finite limit of a function at a point, (2) the finite limit of a sequence, and (3) the infinite limit of a sequence. Additionally, we aim to analyse the presence of these concepts in Spanish textbooks. The methodology employed is…

This paper describes an interdisciplinary collaboration of faculty and students from chemistry and mathematics to develop and implement an activity showcasing the relevance of calculus in chemistry to first-semester calculus students. The activity focuses on using calculus optimization methods to maximize the ground-state radial probability…