Introductory calculus is mandatory for postsecondary science, technology, engineering, and mathematics (STEM) majors (Bressoud, 2015); however, many students do not persist through introductory calculus to further STEM study (Rasmussen et al., 2019). One reason for this may be that students struggle with the prior mathematical knowledge required…

Motivation is known to fluctuate, often declining, over time. Research on how motivation changes across school years is ubiquitous, yet little research examines changes in motivation within one school year. In this study, we model how third- through fifth-grade students' mathematics motivation (i.e., expectancies and values) changes over two years…

A major challenge faced by elementary education programs is the vast amount of content preservice teachers must master in various subject areas. With limited time and coursework, how can teacher preparation programs scaffold meaningful experiences and provide a progression of opportunities to aid preservice teachers in mastering this content and…

This study aims to examine the types of mathematical connections that pre-service mathematics teachers use in their instructions and their opinions on the mathematical connection. For this purpose, a total of 60 pre-service mathematics teachers made lesson plans related to a learning objective from the Turkish middle school mathematics curriculum.…

As a significant tool to integrate information technology and education, dynamic mathematical software (DMS) has been widely concerned in recent years. However, how to better apply it to instruction practice deserves further exploration. Thus, we adopted the meta-analysis method to analyze the DMS-based experiments published between 2000 and 2020.…

Choosing an unsuitable method of delivering material is one of the factors that gives students difficulties in applying concepts in solving mathematical problems. Strong mathematical concepts will help students develop their mathematical thinking skills, including geometric thinking skill. The use of ethnomathematics combined with worked example…

Drawing on autobiographical essays written by master's students in mathematics preparing to become teachers, we investigate what mathematical identity these students articulate and how. By means of a discursive thematic analysis centered on the notion of ascesis, we show that the participants' identity revolves around a characterization of…

Analogy has played an important role in developing modern mathematics. However, it is unclear to what extent students are granted opportunities to productively reason by analogy. This article proposes a set of lessons for introducing topics in ring theory that allow students to engage with the process of reasoning by analogy while exploring new…

The Building Painted Cubes Task is a groupworthy algebraic task. Students build cubes using linking unit cubes, search for algebraic patterns, and report findings on posters. This task can create spaces for students to see themselves as doers of mathematics.

Undergraduate mathematics tutoring centres are prevalent in many countries; however, there is limited research-based evidence on effective organizational structures for these centres. In this study, we consider two research questions. First, how can the quantitative and qualitative data from 10 mathematics tutoring centres be organized for…

In this paper, we draw on recent research on so-called Fermi problems and situate the fundamental principles underlying this type of tasks and their use from a task design perspective. We use the models and modelling perspective on teaching and learning to elaborate on aspects related to the design of single-use, as well as sequences of, Fermi…

Understanding randomness is essential for modern life, as it underpins decisions under uncertainty. It is also an essential part of both the mathematics and science curricula in schools. Yet, research has shown that many people consider randomness difficult to perceive and argue about, with a number of different and contradictory views on the…

Reversibility thinking carried out mentally in mathematical operations has an important role in the process of understanding concepts as it involves developing a thinking process from beginning to end and from end to beginning. This qualitative research aims to describe students' reversible thinking processes in solving algebra problems,…

We describe how an instructor integrated embodiment to teach the Fundamental Homomorphism Theorem (FHT) and preliminary concepts in an undergraduate abstract algebra course. The instructor's use of embodiment reduced levels of abstraction for formal definitions, theorems, and proofs. The instructor's simultaneous use of various forms of embodiment…

This study examined the mediator role of mathematics motivation and the moderator role of mathematics anxiety (MA) in the relationship between metacognition (MC) and mathematical resilience (MR). The participants are 202 gifted students. Data were collected through the "Metacognitive Awareness Scale," "MR Scale," "Revised…