This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

Math fact fluency--the ability to quickly and accurately recall basic addition, subtraction, multiplication, and division facts--is a foundational mathematical skill. "Zaner-Bloser Building Fact Fluency (BFF)" was designed to build students' conceptual understanding of arithmetic operations and increase procedural fluency among…

Background: The COVID-19 pandemic and the shift to digital learning materials have dramatically reduced the use of paper-based textbooks in higher education. In the field of engineering, students need a comprehensive understanding of mathematical concepts, which can be achieved through the use of e-textbooks. These digital learning materials can…

The present study aimed to identify the errors made by pre-service elementary mathematics teachers while investigating the convergence of infinite series. A qualitative exploratory case study design was used with a total of 43 undergraduate students. Data were obtained from a test administered in a paper-and-pencil form consisting of seven…

Many studies have documented the challenges facing teachers who use digital technologies in their classrooms. This is especially true for digital technologies that offer new models or representations of school mathematics concepts. In this article, we report on a collaboration between teachers and researchers around the use of a novel touchscreen…

The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children's understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also…

Spatial reasoning, the ability to mentally represent and transform objects and their relations, is considered so closely connected to mathematics that there is no longer a question of whether the two are related. Instead, there remains debate about how to answer the question of why. This paper explores the way the two fields of mathematics…

Acknowledging the contribution of mathematicians to the mathematical education of teachers, we explore mathematicians' perspective on an envisioned Calculus course for prospective teachers. We analyzed semi-structured interviews with 24 mathematicians using the EDW (Essence-Doing-Worth) framework (Hoffmann & Even, 2018, 2019); and…

This is an article about abstraction, generalization, and the beauty of mathematics. We claim that abstraction and generalization in of itself may very well be a beauty of the human mind. The fact that we humans continue to explore and expand mathematics is truly beautiful and remarkable. Many years ago, our ancestors understood that seven stones,…

Within a study of student reasoning in abstract algebra, we encountered the claim "division and multiplication are the same operation." What might prompt a student to make this claim? What kind of influence might believing it have on their mathematical development? We explored the philosophical roots of "sameness" claims to…

In this study, we identify ways in which a sample of 18 graduates with mathematics-related first degrees found the nth term for quadratic sequences from the first values of a sequence of data, presented on a computer screen in various formats: tabular, scattered data pairs and sequential. Participants' approaches to identifying the nth term were…

This paper substantiates the notion of inclusive materialism by illustrating the role of signs and micro-perception in the learning process of multiplication. Inclusive materialism, offered by de Freitas and Sinclair, considers mathematical learning a process of becoming a learning assemblage, which embodies various materials in a Deleuzian sense.…

Binary operations are one of the fundamental structures underlying our number and algebraic systems. Yet, researchers have often left their role implicit as they model student understanding of abstract structures. In this paper, we directly analyze students' perceptions of the general binary operation via a two-phase study consisting of task-based…

The use of cartoons, songs, and quotes can be a useful way to engage students in discussion and learning key concepts about quantifying the uncertainty in statistical estimates.

The concept of determinant plays a central role in many linear algebra concepts and is also applied to other branches of mathematics and science. In this study, we focus on the application of determinant and inverse matrix concepts, in solving systems of equations by a group of 116 in-service mathematics teachers who were studying the topic at a…