The purpose of this article is to share how one teacher implemented exploratory writing within a mathematics lesson to support her third graders in making sense of fractions and communicating their mathematical ideas. The author defines exploratory writing, then describes the teacher's lesson while also presenting a general overview about how to…

Sequences are an important topic--not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns…

Mathematics assessments should allow all students opportunities to demonstrate their knowledge and skills as problem solvers. Looking at textbook word problems, the authors share a process for revising them using Universal Design for Learning (UDL). Outlined in detail here are problems for kindergarten, grades 5 and 7, and high school (algebra).

In this article, the author shares the Menu Writing project, designed to promote a meaningful, real-world connection to mathematics with the lives of students. The rationale for developing this project was two-fold: (1) to connect school mathematics to students' lived experiences to encourage and sustain students' interest, motivation, and…

Argumentation is an important mathematical practice, highlighted by research and policy documents that describe ways to structure reform-oriented classrooms (Nardi and Knuth 2017; NCTM 2000; NGA Center and CCSSI 2010). Participating in argumentation can enhance students' mathematics learning as they make sense of mathematical ideas, provide…

Probabilistic reasoning underpins much of middle school students' future work in data analysis and inferential statistics. Unfortunately for many middle school students, probabilistic reasoning is not intuitive. One specific area in which students seem to struggle is determining the probability of compound events (Moritz and Watson 2000). Research…

Black students in today's classrooms face major challenges unknown to white teachers. In this article, the authors share instructional practices, mindsets, and reflective questions that teachers can implement, practice, and respond to in order to support Black students to feel safe and welcome in their mathematics classrooms. In doing so, the…

To facilitate people using mathematical reasoning to compare risks associated with the COVID-19 pandemic, the National Science Foundation (NSF) funded the COViD-TASER (Creation of Visualizations of Data: The Application of STEM Education Research) research team to create the COVID-19 Relative Risk Tool (RRT). The RRT uses an interactive bar chart…

Reinhart's (2000) article "Never Say Anything a Kid Can Say!" shared the lessons he learned as he journeyed from a teacher-centered model of instruction to one that puts students at the center of the teaching and learning process. Within his narrative, he itemized the strategies he used and learned from, balanced recommendations with…

Students need to see the value in the lessons their teacher provide. As students begin to approach driving age, they may start to think about the make, model, color, and features they would want in a car; but do they think about the cost or how that cost depreciates over time? The author used these questions to develop a Desmos activity that would…

Quadratic modeling problems are commonplace in high school mathematics courses; they typically situate quadratic patterns of change and their corresponding parabolic graph within real-world contexts. Traditional approaches to this type of problem lend themselves to making connections across different representations (e.g., Garofalo and Trinter…

Data reasoning and digital literacy skills, especially the ability to find, represent, and accurately interpret the relevant data, are critical in workplaces and lifetime experiences. Given the importance of developing data reasoning skills from learners' experiences, this article aims to describe teacher and student actions that contributed to…

Using videos to supplement live instruction has gained momentum in the past year because teachers often scrambled to find ways to instruct students from different locations. The author, like many of her colleagues, began recording herself teaching short lessons and adding them to her Google Classroom library. But then she realized that despite her…

During the past year, teachers have expended much time and effort moving their mathematics instruction online. To do this, teachers had to build their content, pedagogical, and technological knowledge, or technological pedagogical content knowledge (TPACK). As teacher educators facilitating a professional learning sequence during the shift to…

Although many teachers recognize that they must adapt their instruction for the diverse and growing student population of multilingual learners across public schools in the United States, many report that they are unprepared to do this appropriately and productively (Banilower et al. 2013). This article aims to shed light on this issue.…