Author Pam Harris argues that teaching real math--math that is free of distortions--will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math…

This article shares activities that engage students in quality peer dialogue to build up and break down networks, revealing underlying structure and equivalence. These investigations offer students three kinds of mathematical arguments: (1) proofs of impossibility; (2) proofs by induction; and (3) proofs by exhaustion. The authors describe a…

This article suggests ways teachers can share picturebook biographies to introduce students to the Standards for Mathematical Practice (SMPs). The SMPs, the foundation of mathematical proficiency, specify ways of thinking and working in which every learner needs to engage. The authors believe biography breaks support students' learning and love…

This classroom-based action research investigates the impact of teaching problem-solving heuristics on preservice teachers' mathematical creativity, self-efficacy, and problem-solving beliefs. The study was conducted with seven preservice teachers at a state university in the Philippines, using a Plan-Do-Study-Act (PDSA) cycle. Participants were…

Mathematical representation is one of the skills that students need to master because it can help them in various problem-solving tasks. This research is a literature review of articles related to mathematical representation in mathematics education. The articles are those published in journals indexed by Scopus from 2020 to 2024. The results of…

Effective feedback is essential for refining instructional practices in mathematics education, and researchers often turn to advanced natural language processing (NLP) models to analyze classroom dialogues from multiple perspectives. However, utterance-level discourse analysis encounters two primary challenges: (1) multifunctionality, where a…

This meta-analysis examines the impact of technology in statistics learning, comparing experimental and control groups across 34 studies, resulting in 55 effect sizes. The random effects model revealed a significant standardized mean difference (gRE = 0.50, 95% CI [0.35, 0.64], p < 0.01), indicating a positive effect of using technology in…

Considering its relationships with real life and mathematics, mathematical modeling is one of the most effective ways of learning and teaching mathematics. In this study, the effect of teaching with mathematical modeling on students' mathematics achievement was examined using the meta-analysis method. An effect size of 51 was achieved with 45…

Several studies on student's understanding of the concept of the tangent line agree that the difficulties students have when dealing with lines tangent to curves at inflection points or tangent lines that have more than one point in common with the curve are due to a misconception of tangency that is limited to the geometric relationship between…

Students' sense of belonging in the mathematics classroom can be supported and increased by building mathematics tasks that connect to and incorporate aspects of students' identities and sense of selves (e.g., their names, images, and ages). This article shares one commonly used mathematics task and highlights how it can be used to create…

This study explores the cognitive structures of pre-service primary teachers regarding fraction comparison, using Vinner's concept-image framework to analyze how these pre-service teachers mobilize their knowledge to compare fractions. The mixed-methods approach, combining both quantitative and qualitative analyses (including a questionnaire),…

Research on teachers' noticing of student mathematical thinking has typically focused on how a teacher attends to, interprets, and determines a response to an individual student contribution in isolation from the broader mathematical classroom context. This research focus is not nuanced enough, however, to fully account for the complex noticing…

In this article we review the research on the flexible or adaptive use of solution strategies in school mathematics, with a focus on the most recent work in the field. After a short introduction, we provide an overview of the various ways in which strategy flexibility has been conceptualized and investigated in the research literature. Then we…

Given that early career elementary teachers face pressure to plan pedagogy that provides equitable opportunities to learn mathematics for understanding, it is important to consider their mathematics lesson planning practices. This study uses interview data to compare the planning practices of four early career teachers (ECTs) who consistently…

Using the sawtooth map as the basis of a coupled map lattice enables simple analytic results to be obtained for the global Lyapunov spectra of a number of standard lattice networks. The results presented can be used to enrich a course on chaos or dynamical systems by providing tractable examples of higher dimensional maps and links to a number of…