The purpose of this article is to share how one teacher implemented exploratory writing within a mathematics lesson to support her third graders in making sense of fractions and communicating their mathematical ideas. The author defines exploratory writing, then describes the teacher's lesson while also presenting a general overview about how to…

Sequences are an important topic--not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns…

Argumentation is an important mathematical practice, highlighted by research and policy documents that describe ways to structure reform-oriented classrooms (Nardi and Knuth 2017; NCTM 2000; NGA Center and CCSSI 2010). Participating in argumentation can enhance students' mathematics learning as they make sense of mathematical ideas, provide…

Constructing formal geometry proofs in is an important topic in the mathematics curriculum. But students' difficulties with proof are well documented. This article focuses on proofs that use triangle congruence postulates in US high school geometry. Examining students' proof reasoning in one-on-one task-based interviews, we analyzed students' oral…

This paper investigates and considers factors that affect success in solving a stand-alone geometrical problem by 182 students of the 7th and 8th grades of elementary school. The starting point for consideration is a geometrical task from the National Secondary School Leaving Exam in Croatia (State Matura), utilising elementary-level geometry…

Lesson study is a Japanese concept to improve teaching and learning mathematics through a particular form of activity in which a group of teachers works collaboratively to plan, implement, observe, and reflect on the proposed research lessons. Although lesson study is internationally acknowledged as providing key learning opportunities for…

The purpose of this article was to evaluate the quality of research studies and the evidence base for algebra instruction for secondary students with learning disabilities (LD) from 2000 to 2020. We evaluated the quality of methodological rigor of a total of eight single subject and three group design research studies using the 2014 Council for…

This article presents the theoretical considerations leading to the design and development of a digital experience for teaching linear equations using a modified balance model for equation solving. We modified the balance to alter physics behaviour in a virtual reality (VR) experience, to strengthen students' schemes for solving linear equations…

Algebra is a gatekeeper. For the 6% of students with dyscalculia (i.e., mathematical learning disabilities), an inability to pass algebra may significantly limit academic and career opportunities. Unfortunately, prior research on dyscalculia has focused almost exclusively on elementary-aged students' deficits in speed and accuracy in arithmetic…

In March 2020, COVID-19 restrictions required our university courses to be offered in online mode only. This quick transition meant that lecturers were suddenly tasked with adapting their classroom-based teaching approaches and materials to the online space. For mathematics teacher educators (MTEs), whose on-campus classes were characterized by…

Many mathematics students require support for learning challenges, such as those invoked by mathematics anxiety. Support for these learning challenges is imparted through personal interactions between the student and the instructor, support staff or their peers. The online delivery of mathematics classes and support meetings reduced the quality of…

Research has revealed the extent and mechanism of the relation between language (dominated by alphabetic systems) and students' mathematics learning, but when it comes to Chinese language (an orthographic system), nature remains elusive. In this meta-analysis we aim to quantify the size of the relation between Chinese language and mathematics and…

The purpose of this study was firstly to investigate the mathematical metacognitive characteristics of high-efficiency students by comparing high-efficiency and low-efficiency students. Secondly, the aim was to explore the pathways of mathematical metacognition of efficient mathematics learners in mathematics achievement. In this study,…

This study attempts to describe characteristics of graph thinking in solving a mathematical problem. Three students at the 10th grade of senior-high schools were involved as the subject. The data was collected from the result of an optimization problem task (OPT), video recording, interviews, and field notes. The results showed two major…

The overall purpose of this study was to investigate the role of personal relevance in conceptual change. First, we used an experimental design to investigate the role of augmented activation--which directly implicated teachers' personal prior beliefs about mathematics learning and instruction--and refutational text manipulations on short and…