This paper reports findings related to the pursuit of describing a lived knowing for teaching mathematics. Specifically, we used an enactivist perspective to describe the knowing exhibited by three experienced high school teachers in their instructional actions while leading whole-class instruction on the topic of the equations of exponential…

Using a nested design and guided by the Social Control Theory, this study examined the factors that influence learners' achievement in mathematics in South Africa. The researchers collected data from 32 participants through an online questionnaire with open-ended and closed-ended questions. Quantitative data was analysed using SPSS to produce…

In the primary grades, engaging in counting collections provides students with regular opportunities to make sense of numbers in dynamic ways, build social skills, and communicate about mathematics. This article aims to guide elementary educators through a team's process of planning and implementing counting collections in kindergarten. Counting…

Students often instrumentally use variables and unknowns without considering the variational thinking behind them. Using parameters to modify the coefficients or unknowns in equations or systems of linear equations (without altering their structure) involves consciously incorporating variational thinking into problem-solving. We will test the…

Math skills are critical for students' success in other subjects and later in life, yet far too many teacher prep programs fail to give aspiring teachers the essential knowledge they need to be effective math teachers--undermining student learning before the first lesson even begins. To develop great math teachers, teacher prep programs must…

This is the executive summary for "Teacher Prep Review: Solving for Math Success." It provides key findings from the full report and recommendations.

In the last decade, researchers have focused more on how to provide instructional supports for mathematics writing (Powell et al., 2017). In this synthesis, we examined 22 studies about mathematics writing to determine the overall mathematics-writing and mathematics outcomes of mathematics-writing instruction, the mathematics-writing and…

Mathematical spaces often reinforce and perpetuate whiteness. Despite efforts to decenter whiteness in secondary and post-secondary classrooms, equity-oriented strategies can still perpetuate whiteness. In this action research study, I turned the lens of whiteness upon my instructional practices and curriculum. Using an analytic framework for…

Grades K-12 institutions in the United States continue to have a more culturally, linguistically, and racially diverse student population, with Hispanic and Asian students increasing in record numbers (United States Census Bureau, 2023). As a result, K-12 mathematics teachers are expected more than ever to design, select, and implement…

Fraction knowledge is an essential building block for successful completion of advanced mathematics courses and linked to the development of algebraic understanding. Many students, especially those with disabilities, experience significant difficulties developing fraction knowledge. Intensive fraction interventions have been shown to be effective…

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…

Inferentialism has emerged as a valuable theoretical resource in mathematics education. As a theory of meaning about the use and content of concepts, it offers a fresh perspective on traditional epistemological and linguistic questions in the field. Despite its emergence, important inferentialist ideas still need to be operationalized. In this…

Metacognition supports students in successfully working through struggle by equipping them with the tools to maintain an awareness of what they are doing and to change directions when needed to overcome obstacles. Thus, it is of little surprise that effective problem solvers spend a significant amount of time analyzing tasks relative to the amount…

Early intervention and identity-building can promote the idea among students that everyone is a math person. Natalie Parker-Holliman and Tenisha Marcel-Herbert share practical tools and strategies that schools and teachers can use to build students' confidence and strengthen their mathematical foundation. They highlight the significance of culture…

In this case study we explored how a mathematician's teaching of the Cauchy-Riemann (CR) equations actualized the virtual aspects of the equations. Using videotaped classroom data, we found that in a three-day period, this mathematician used embodiment to animate and bind formal aspects of the CR equations (including conformality), metaphors,…