Groupwork provides opportunities to learn important communication and collaboration skills, but how can we ensure all students are participating equitably while also engaging with the academic content when working in groups? Group-worthy tasks provide participation structures needed for students to engage with the content as well as develop and…

The short activity presented in this article continues a discussion related to the value of golden ratio explorations in secondary mathematics, and acts as a companion to the earlier paper in this journal (Crawley, 2023). Exploring meaningful ways in which teachers can elicit students' interest and engagement in mathematics is vital, and…

How we should teach mathematics has long been debated by advocates of different instructional approaches. These debates can lead to tensions that are difficult to navigate for those who are new to (or even veterans of) the profession. Educators often propose a "balance" of different approaches as a solution. Charles Munter considers…

Mark Creager noticed that how we teach students to reason mathematically may be counter-productive to our teaching goals. Sometimes a linear approach, focusing on sub-processes leading to a proof works well. But not always. Students should be made aware that reasoning is not always a straight forward process, but one filled with false starts and…

Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help…

Teaching requires attention to individual student needs by providing both adequate challenge and sufficient support to help students successfully gain academic skills (Shurr et al., 2019). The learning stages framework divides typical learning into four distinct stages: acquisition, fluency, maintenance, and generalization (Collins, 2012; Haring…

A rigorous and axiomatic-deductive approach is emphasized in teaching mathematics at university-level. Therefore, the secondary-tertiary transition includes a major change in mathematical thinking. One viewpoint to examine such elements of mathematical thinking is David Tall's framework of the three worlds of mathematics. Tall's framework…

There is a large body of research on how to improve student learning through active learning and metacognition. However, without well-structured guidelines, students do not tend to actively engage with the taught material, peers, and the instructor at a desirable metacognitive level (Deslauriers et al., 2019). To address this problem, a…

Teachers spend a lot of time talking about students: They talk about how students learn, how to best plan lessons for them, and how to understand their written work using different protocols. Instead of hypothesizing about what a student might do on a task or why a student made a certain mistake, why aren't teachers just asking the student?…

Successful math word-problem solving is difficult for some students. Getting the right answer involves students engaging correctly in an amalgamation of actions. Schema instruction is an instructional approach aimed at supporting students in identifying the underlying math problem structure to yield an appropriate solution plan. The focus of this…

In this article, the authors identify and explore the work that teachers can do to support students to build and critique arguments with particular attention to critiquing arguments. Additionally, they seek to describe how the types of arguments students engage with and the work that teachers do to support this engagement change across grade…

In this paper, we will discuss a type of activity that lets the mathematics classroom become a place where students can learn more than mathematical content. Specifically, students can learn interdisciplinary skills in the area of communication (both verbal and non-verbal) and debate skills that are often taught in communication or English…

Despite growing attention to identifying equitable teaching practices that provide all students opportunities to engage in mathematical thinking and reasoning (Tan and Kastberg 2017; NCTM 2014), students with disabilities have had limited opportunities to take on the role of doers of mathematics and to see themselves or have others see them as…

In many prekindergarten classes, children begin the day by singing a song as part of their opening routine. In reflecting on opening routines in public prekindergarten classrooms across Michigan, the authors have been struck by how often small changes in teachers' routines or materials could enrich the mathematical engagement of children. The goal…

The transition to online learning has highlighted the pervasiveness of the digital divide as more than inequitable access to computers and internet (Hohlfeld et al. 2017). Even when students have laptops and physical connectivity, their participation depends on teachers who position them as mathematically competent (Berry 2018; Langer Osuna 2017)…