This study reviews the literature on error patterns in mathematics among students with mathematics difficulty. We analyzed and synthesized the findings from 17 studies, focusing on the characteristics of error analysis studies, the mathematics topics examined, and the specific error patterns identified. The results revealed the following: (a) the…

Mathematical flexibility is thought to be a critical component of mathematical proficiency, and the term "mathematical flexibility" has been used by teachers, researchers, and policy makers for more than 2 decades. Although there seems to be consensus on the importance of mathematical flexibility as a construct, the way it is defined and…

The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…

Mathematical flexibility has been widely acknowledged as an important learning goal in mathematical education and has received increasing research attention in order to explore its nature, facilitating mechanisms, and promotion interventions. Given that researchers conceptualize, assess, and explain flexibility in mathematical problem solving from…

The concrete-representational-abstract (CRA) approach is an instructional framework for teaching math wherein students move from using concrete materials to solve problems to using visual representations of the materials, and finally abstract concepts. This study provides a literature synthesis and meta-analysis of the effectiveness of the CRA…

Since its first notable appearance in the "Second Handbook of Research on Mathematics Teaching and Learning," the phrase productive struggle has garnered support from a few, yet very influential, educational researchers. However, since the phrase was popularized by Hiroko Warshauer in 2011, examinations of the productive struggle have…

Counting is foundational to success with mathematics. In this synthesis, we analyzed 17 studies about counting-focused interventions for preschool and kindergarten students with mathematics difficulty or at-risk of mathematics difficulty. All interventions addressed several components of counting, including stable order, one-to-one correspondence,…

Mathematics is an essential subject in schools, helping develop cognitive skills such as critical analysis, logical reasoning, and problem-solving. However, academic achievement in mathematics often declines, with some students having difficulty understanding mathematical ideas. Many factors influence mathematics achievement, including students'…

Understanding rational numbers is critical for secondary mathematics achievement. However, students with mathematics difficulties (MD) struggle with rational number topics, including fractions, decimals, and percentages. The purpose of this systematic review was to describe the instructional foci of rational number interventions, determine the…

Mathematics plays many roles in physics and physics education. While these roles have previously been extensively discussed in the physics education research community, no systematic picture of the multifaceted considerations has yet been formed. To gain a comprehensive overview of the previous studies on the topic, we conducted a systematic…

This review study synthesises the literature on how computational thinking (CT) and mathematical thinking (MT) are integrated into mathematics education research with a focus on tasks. A review of 28 relevant articles on the Web of Science Core Collection database indicated that (1) CT helps students develop and apply mathematical concepts and…

This paper reports a systematic literature review of the balance model, an often-used aid to teach linear equations. The purpose of the review was to report "why" such a model is used, "what" types of models are used, and "when" they are used. In total, 34 peer-reviewed journal articles were analyzed, resulting in a…

Mathematics teaching and learning goes beyond computations and procedures; it rather includes complex problem-solving and critical thinking. Kilpatrick, Swafford, and Findell (2001) identify five mathematical competencies that are present in mathematics learning: conceptual understanding, procedural fluency, adaptive reasoning, strategic…

This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications…

We review literature relevant to using technology in the teaching/learning of mathematics to highlight four roles of effective technology use: (a) promoting cycles of proof; (b) presenting and connecting multiple representations; (c) supporting case-based reasoning; and (d) serving as a tutee. We then discuss how they intersect with good…