Mathematical identity is a socio-motivational construct known to be a predictor of mathematical achievement. Students who identify positively with mathematics are more likely to pursue advanced courses and Science, Technology, Engineering, and Mathematics (STEM)-related occupations. Although mathematical identity is shaped by a myriad of internal…

This study explores peer feedback in a combined fifth and sixth-grade classroom. Drawing on Hattie and Timperley's (2007) model for feedback, we analyzed 334 peer feedback comments gathered during six mathematics lessons. Our analysis revealed evidence of peer feedback being beneficial to the students who provide it as well as those who receive…

In this paper I discuss the possibilities for exploring the hundred chart kinesthetically with elementary preservice teachers using a life-size hundred chart--an innovative tool, homemade from a shower curtain--to build quantity sense. Preservice teachers explored creative approaches to teach mathematics using the life-size hundred chart and…

This study reports on efforts over several years to design and implement a yearlong intervention intended to support secondary mathematics teachers in their early years of teaching. The intervention is designed to retain early career mathematics teachers in the professions by engaging them in the development of meaningful professional…

Two case studies were conducted to examine whether inquiry-based learning (IBL) can help students in understanding normal distributions, and to determine if IBL methods have any effect on students' conceptual and computational capabilities. There were 16 students in the traditional class and 17 students in the IBL-implemented class who…

Game-based learning has received more focus as a way to engage students and increase interest in mathematics. Game-based learning should be integrated with effective practices for teaching mathematics, though these is a need for further research on effective implementation models. The purpose of this article is to describe two modes of game-based…

An increasing number of students are "hyper-accelerating" their study of formal Algebra I to Grade 7 or earlier to maintain a competitive edge in the race to calculus. However, there is a lack of evidence that these students construct the conceptual foundations necessary for persistence in advanced mathematics. This paper maps the drive…

Teaching gerrymandering in our high school geometry classrooms provides students with a unique opportunity to use mathematics to describe, analyze and make sense of the world around them. Our purpose is to provide our students the opportunity to apply learned definitions and formulas of area and perimeter to a sociopolitical context. We present a…

Physical models for exploring multiplication are fixtures in elementary classrooms. The most widely used physical models of multiplication are collections of discrete things, such as Cuisenaire rods, Unifix Cubes, or Base-10 Blocks. But discrete physical models are limited in the products they can represent. By contrast, pictorial models, such as…

This conversation is a slightly modified version of an interview with Dr. Peter Liljedahl, Professor of Mathematics Education. The interview was conducted by "JMETC" Guest Editors on March 8, 2021 and was based on Dr. Liljedahl's December 7, 2020 colloquium presentation "Building Thinking Classrooms: A Case of Results First…

"Algebra-as-gatekeeper" is a powerful paradigm that structures students' experiences within mathematics class, as well as their future educational trajectories. In this paper, I show how modeling--when conceived as a culturally relevant practice--can support students to make sense of the key ideas of algebra as well as develop positive…

While a growing body of research examines teachers' facilitation of discourse-rich classrooms, surprisingly little research is devoted to learners' responsibilities in such classrooms. In this paper, we share a theoretical model for explaining students' responsibilities in yielding mathematical learning in discourse-rich classrooms. These…

This classroom study immersed high school geometry students in the creative and intellectually challenging design task of developing unique logos using mathematics and technology. The students applied and deepened their knowledge of transformations while using dynamic geometry software. One of the main aims of the task was to elevate student…

Postsecondary mathematics classrooms continue to become more diverse, which implores educators to continue to incorporate more diverse modes of assessment to support all learners. However, researchers have found that mathematics assessment at the postsecondary level has remained mostly stagnant, with traditional, closed-book exams dominating the…

The non-learning of school mathematics is now almost universally taken for granted, but this does not have to happen. This article takes a critical look at the root of this non-learning by pointing to the flagrant defects in the kind of mathematics--to be called TSM--that is predominant in almost all the school textbooks. By analyzing how the long…