We compared students' learning gains in authentic seventh-grade classrooms (N = 144) in 4 different interventions that incorporated a computer game that aims to teach players to solve linear equations. Significantly higher learning gains were measured in the implementations that were specifically designed to mediate the attribution of algebraic…

This study was framed within a quantitative research methodology to develop a concise measure of calculus self-efficacy with high psychometric properties. A survey research design was adopted in which 234 engineering and economics students rated their confidence in solving year-one calculus tasks on a 15-item inventory. The results of a series of…

This informal essay is based on a presentation James Tanton gave at the Australian Association of Mathematics Teachers (AAMT) 'Why Maths?' Conference in 2019. It begins by offering two first steps to problem-solving that Tanton believes are key for finding success--and joy--in doing mathematics: (1) Be human! Have an emotional reaction to the…

The purpose of this qualitative study was to analyze the relationship between argumentation and proof in terms of verbal, visual, and algebraic representations of mathematical concepts. We conducted task-based interviews based on geometric locus problems with six undergraduate mathematics teachers while they were working in pairs. We identified…

MathCheck is a relatively new online tool that gives students feedback on their solutions to elementary university mathematics and theoretical computer science exercises. MathCheck was designed with constructivism learning theory in mind and it differs from other online tools as it checks the solutions step by step and shows a counter-example if…

When teaching through problem solving, effective mathematics teachers need to lead discussions that assist students in making connections between different solution strategies. However, while teaching a methods course for preservice teachers (PSTs), we noticed that after solving a problem and presenting various solution strategies, many PSTs…

The purpose of the current study is to examine the ways in which preservice middle school mathematics teachers (PMSMT) apply and represent algebraic reasoning in their solution processes for the problems in the concept of sets. This model provides detailed information about the reasoning made through the process of the solution of set problems.…

Solving word problems is challenging in elementary schools, both for the teacher in teaching students to solve word problems and for the student in learning to solve them. This paper examines how the ideas of learning trajectory and variation pedagogy could be integrated as an instructional principle for teaching this content in the context of…

Inquiry-oriented teaching is a specific form of active learning gaining popularity in teaching communities. The goal of inquiry-oriented classes is to help students in gaining a conceptual understanding of the material. My research focus is to gauge students' performance and conceptual understanding in inquiry-oriented linear algebra classes. This…

The need to raise achievement levels in mathematics and science has led instructional design researchers to focus on the factors that enhance achievement in these subjects. Understanding of students toward mathematics achievement may guide educators in their efforts to promote achievement by designing learning models that provide the most…

Learning Disabilities in Mathematics (LDM) or dyscalculia are a frequent and disruptive problem within schools. Nevertheless, this problem has received little attention from researchers and practitioners, if compared with the number of studies published on disabilities in reading. Therefore, teachers do not have enough guidance to help children…

This research aims to analyze ways of understanding of students with mathematics learning disabilities when learning fraction. The research was conducted in an Inclusive Junior High School in the West Java Province, Indonesia. This study is qualitative, with the single-case (holistic) designs. The case will focus on three students who suspected of…

The aim of the study reported in this paper was to explore and enhance experienced school mathematics teachers' knowledge of students'thinking, as it is manifested in practice. Data were collected from records of classroom observations, interviews with participating teachers, and weekly teacher-researcher meetings organized in the school. In this…

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning, and that these pedagogies effectively support students' learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a…