The majority of studies about mathematical knowledge for teaching (MKT) have been conducted in the US, with little research on MKT being performed in the Middle East. Accordingly, this study contributed to the cross-national MKT literature by translating, adapting, and validating a novel US teacher knowledge instrument for use in Kuwait. Both…

Productive problem solving, concept construction, and sense making occur through the core process of abstraction. Although the capacity for domain-general abstraction is developed at a young age, the role of abstraction in increasingly complex and disciplinary environments, such as those encountered in undergraduate STEM education, is not well…

U.S. students have consistently demonstrated poor performance in spatial reasoning in standardized testing (e.g., National Assessment of Educational Progress). One possible reason is students' lack of conceptual understanding of measurement concepts (length, area, volume, capacity). This paper describes different ways that mathematics textbooks…

In this article, we question the prevalent assumption that teaching and learning mathematics should always entail movement from the concrete to the abstract. Such a view leads to reported difficulties in students moving from manipulatives and models to more symbolic work, moves that many students never make, with all the implications this has for…

The Three-Square Puzzle shows a remarkable relationship between three angles. What happens when the number of squares increases? This article explores that question and brings in Fibonacci and Lucas sequences.

The rules of indices, e.g. a[superscript n] b[superscript n] = (ab)[superscript n], are a particularly important part of elementary algebra. This paper reports results from a textbook analysis which examined how the shift from integer to rational exponents in the rules of indices is discussed in school textbooks. The analysis also considered…

The calculus concepts of concavity and inflection points are critical for a complete understanding of quantities' behavior, making them important topics of research for those interested in the intersections of STEM disciplines. This study seeks to provide insight into this area by reporting on trends in students' concept projections of these…

This paper describes a research project implemented in a course of Real Analysis II. The aim of this project is to analyse students' comprehension of the limiting behaviour of a function from "R"[superscript 2] to "R" at a point "P"[subscript 0] focusing on the formal definitions. Alternative definitions and other…

This study was conducted with the aim of investigating the current knowledge of Primary Teachers and Primary Pre-service Teachers on the misconceptions of primary school students about the subject of fractions. The qualitative research method of case study was used to conduct the research. The data were collected with semi-structured forms that…

Combination problems are a cornerstone of combinatorics courses, but little research has been done examining the ways that students perceive and differentiate among different combination problems. In this article, we investigate how mathematics education students (n = 18) in a discrete mathematics course view two categorically different…

We present exploratory analyses of three cases in which groups of four (quartets) worked with video recordings of choreographed performances from the opening ceremony of the 2016 Rio Olympic Games. We asked quartets to view the recordings, explain what performers were doing by reenacting what they noticed in the video, and create their own…

The fundamental theorem of calculus (FTC) plays a crucial role in mathematics, showing that the seemingly unconnected topics of differentiation and integration are intimately related. Indeed, it is the fundamental theorem that enables definite integrals to be evaluated exactly in many cases that would otherwise be intractable. Students commonly…

How students' rigid perceptions of mathematics persist over years has been a conundrum. Students not only think that only one solution exists for a mathematical task (Schoenfeld 1985) but also rigidly fuse mathematical concepts with specific tasks. Students deserve to learn a variety of mathematical strategies to flexibly deploy at will. Teaching…

Psychological studies of early numerical development fill a void in mathematics education research. However, conflations between magnitude awareness and number, and over-attributions of researcher conceptions to children, have led to psychological models that are at odds with findings from mathematics educators on later numerical development. In…

The motivation behind this examination is to present the theoretical structure of Modeling Activities, which is believed to be a vital device for mathematics instruction. Modeling activities are defined as activities to figure out complex problems faced in real life situations that require the creation of a mathematical model as a product. In…