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…

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…

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…

The literature emphasizes the interest and need to learn the concept of continuity with understanding, although this meaning it is not consensual nor specified how it may emerge and be developed in the learning process. In this paper we report the results of a study aiming to analyse Brazilian preservice mathematics teachers' understanding of the…

"When you hear hoofbeats, look for horses, not zebras." This common saying in medicine (often attributed to Theodore Woodward, MD, of the University of Maryland School of Medicine) advises doctors to stick to the expected or likely diagnosis, rather than anticipating an unusual or atypical one. As a result, uncommon medical diagnoses are…

This article uses action-process-object-schema theory to study the mental constructions about the limit of series during a Calculus 1 course at a university. The researchers also used the theory's teaching methodology to teach the topic. A plethora of research on the limit concept is available and suggests that the concept is on record as being…

Two-hour long developmental teaching interviews were conducted with each of 14 sixth grade students, ages 11-12. The purposes of the interviews were to investigate how students solved arrangement problems (APs), and how their solutions of these problems differed from their solution of Cartesian product problems (CPPs). The 14 students represented…

This is an exploratory study considering instructional methods in mathematics education. The study examined misconceptions arising from selected assignments undertaken by sixty-five students. The students were attending a calculus mathematical course unit on limits of functions, in different academic areas offered at selected tertiary institutions…

A solid foundation in mathematics is beneficial not only for individuals' concurrent and later academic achievement, but also for future career success and financial stability. Rational number knowledge plays a pivotal role in mathematical success, yet it is often regarded as a challenging area to grasp comprehensively. The dissertation aims to…

Purpose: This study aimed to explore students' higher-order thinking skills development when they engaged in pattern blocks learning activities using Blended Learning Classroom teaching approaches through the Thailand Lesson Study Incorporated Open Approach model. Design/methodology/approach: The researchers utilized a multiple case research…

This article illustrates and differentiates the unique role cognitive interviews and think-aloud interviews play in developing and validating assessments. Specifically, we describe the use of (a) cognitive interviews to gather empirical evidence to support claims about the intended construct being measured and (b) think-aloud interviews to gather…

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

As soon as a new technology emerges, the education community explores its affordances and the possibilities to apply it in education. In this article, we analyze sessions with ChatGPT around topics in basic linear algebra. We reflect on the affordances and changes between two versions of ChatGPT since its worldwide publication in our area of…