In this paper, we discuss the utilization of an innovative learning tool, the Sphero BOLT robot, in a 10-day algebra-based mathematics education course for graduate students. Students created routes for their BOLTs to travel and determined ways to measure the distance, rate, and time of their robots' movements. The student prompt, sample student…

Problem solving is an important aspect of the mathematics classroom and teachers should work to promote problem solving in their classrooms. The purpose of this explanatory mixed-methods study was to examine mathematics preservice teachers' (PSTs) problem-solving performance and connect it with their K-12 and tertiary education problem-solving…

As institutions strive to improve teaching and learning for all, educators must consider equitable instruction. This includes equitable distributions of authority and agency among students. The authors define distribution of authority as shared opportunities for decision-making in enacting mathematical tasks and agency as the power to carry out…

The aim of this study was to examine 6th-grade students' mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations,…

Purpose: Previous research focused on graphical skills of the students, which remains a gap that exists, and there has not been comprehensive research on students' graphical literacy abilities. The present study aims to picture graphical literacy levels of the 8th grade students concerning the "reading," "interpreting,"…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

This study investigated preservice middle school mathematics teachers' (PSTs) understanding of proportional and nonproportional relationships and their abilities to differentiate these relationships from each other. The PSTs' abilities to interpret and represent proportional and nonproportional situations and solution strategies were also…

Number sense has been considered as one of the most important mathematical notions to be addressed in school mathematics in the 21st century. In this paper, we identify how students of a public middle school, located in a rural area in Mexico, showed several aspects of number sense by performing tasks involving arithmetic operations in a shopping…

Learning progressions (LPs) have seen a growing interest in recent years due to their potential benefits in the development of formative assessments for classroom use. Using an LP as the backbone of an assessment can yield diagnostic classifications of students that can guide instruction and remediation. In operationalizing an LP, assessment items…

We report on a teaching experiment with pre-service teachers (PSTs) intended to support their understanding of the validity of mathematical arguments, and their ability to formulate mathematical arguments by conducting case analysis. PSTs used Toulmin's framework (1958/2003) and engaged in collective argumentation while solving crypto-arithmetic…

Although numerous studies have investigated how technology affects academic achievement, very few have focused on the purpose of the use of technology in mathematics education. This current study examines how student teachers (STs) benefit from GeoGebra as one of the Dynamic Geometry Software (DGS) while solving continuity problems. In order to…

Blended learning models can help teachers leverage the power of technology to customize student learning and differentiate instruction for students at varying achievement levels. Research on the effectiveness of blended learning in K-12 education has largely relied on case studies, and findings suggest differences in achievement outcomes based on…

Engaging in argumentation can lead to an increase in the development of critical-thinking skills, not to mention academic achievement, emotional maturity, and academic and communication skills. If argumentation is such an effective format for developing rigorous academic ideas, how might it be used in discussion-oriented classrooms to engage…

Drawing upon task-based learning designs from second language acquisition, we critique how mathematics education has primarily conceived of tasks as problems to be solved. We extend the notion of communicative gaps (e.g., opinion and information) into a framework that considers the flows of information that tasks structure and facilitate. We then…