Construct maps and related item type frameworks, which respectively describe and identify common patterns in student reasoning, provide teachers with tools to support instruction built upon students' intuitive thinking. We present a methodological approach--embedded within common assessment development processes--for developing such construct maps…

This study investigates the potential of rehearsal interjections to provide opportunities for novice teachers and teacher educators to discuss topics related to teaching the practice of mathematical defining. Through analysis of video recordings of seven elementary novice teachers' rehearsals about geometric definitions, we identified the problems…

Ben Zunica describes a lesson in which computational thinking has been successful in assisting students to understand the process of simplifying surds. The strengths and limitations of this approach are discussed. The author concludes that computational thinking can assist in solidifying understanding of a range of mathematical processes for…

The purpose of this study is to investigate the reactions students with low interest in mathematics have to multiple mathematics tasks. Interest has been shown to influence students' engagement, motivation, and achievement (Renninger & Bachrach, 2015; Hidi & Harackiewicz, 2000; Kang & Keinonen, 2018). Therefore, understanding what…

The slow uptake of technology by mathematics teachers is in contrast with the rapid growth in the availability of different digital resources specifically designed to help teaching and learning mathematics. We refer to platforms that were designed to permit for mathematical communication between multiple users. We seek to explore the affordances…

The application of decomposition strategies (i.e., associative or distributive strategies) in two-digit multiplication problem solving supports algebraic thinking skills essential for later complex mathematical skills like solving algebra problems. Use of such strategies is also associated with improved accuracy and speed in mathematical problem…

Mathematics teachers, are always making and remaking their curricula to better serve the needs of their students. Sometimes, these revisions happen while they are teaching a new task. At other times, as they grow in their thinking, they become aware that some of the tasks they've used for years--and might even name as favorites for their potential…

Empirical studies demonstrate that students have some difficulties with the mathematical modeling process. Studies contain various applications for developing students' modeling competencies. This study investigated video-based modeling tasks' impact on modeling competencies with a descriptive design. In this context, it aims to compare…

We contribute to the understanding of teacher noticing by focusing on what a teacher may notice in students' mathematical contributions in the context of problem-based lessons. Complementing approaches to research on noticing that focus on individual teachers' perceptual, cognitive, or situated skills, this conceptual article offers four…

Music provides an excellent setting for students to explore trigonometric functions in a setting which is independent of their utility in resolving triangles. In this paper, we present several investigations using trigonometric functions to model musical phenomena. From a mathematical technology point of view, most examples require only function…

Many scholars have argued that mathematics classrooms often offer narrow conceptions of mathematical excellence, recognizing only some kinds of thinking and some kinds of people as valuable, and conflating mathematical aptitude with overall intelligence. Play offers the potential to disrupt such classroom mathematical practices, by offering new…

Spatial ability is a multifaceted construct with demonstrated ties to success in mathematics and gesture production. Recent empirical work has also begun investigating whether targeted interventions for spatial ability can transfer to mathematics but are often limited to specific populations and specific math outcomes. Spatial anxiety has been…

This study explored the math course taking patterns of Nebraska's secondary students from 2014-2020 using statewide data. Three course taking patterns were identified and examined. There are nuanced differences through these pathways based and race and gender. Student success through the pathways is dependent on course placement in the first year…

With democracy in mind, promoting students' cognitive, personal, and social development can inform and shape the mathematics curriculum and classroom practice with the goal of their becoming more capable, self-reflective, and socially aware human beings. Toward that realization, their mathematics experience could include: heuristics, as it…

Math-anxious people consistently underperform in math. The most widely accepted explanation for "why" this underperformance occurs is that math-anxious people experience heightened anxiety when faced with math, and this in-the-moment anxiety interferes with performance. Surprisingly, this explanation has not been tested directly. Here,…