Using teaching representations is one of the common means for preparing pre-service mathematics teachers (PSTs) to learn how to teach mathematics meaningfully. However, turning PSTs' attention to the mathematical objects that students engage with during the lesson is a challenging pursuit. This paper suggests using the Realization Tree Mediator…

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…

In this paper, I share an activity that reinforces students' understanding of translations, reflections, and rotations via body movement. As a result of this activity, students gain a different perspective compared to previous explorations on paper, communicate mathematics, and visualize transformations as rigid motions on the plane. Furthermore,…

In this paper I describe classroom experiences with pre-service secondary mathematics teachers (PSMTs) investigating and extending patterns embedded in the Pythagorean configuration. This geometric figure is a fruitful source of mathematical tasks to help students, including PSMTs, further develop habits of mind such as visualization,…

In the art classroom--where art, identity, and culture are inextricably linked--racially and culturally responsive teaching play a critical role in how teachers interact with students and ultimately how students themselves come to understand cultural diversity, social inclusion, and antiracist behaviors. It is important that teachers understand…

Each year at Bath University the Open University's Centre for Mathematics Education runs a one-week summer school for Key Stage 3 teachers as well as those aspiring to become teachers. For many of the participants, the course is a case of dipping their toe in the water towards a longer-term goal of taking an Advanced Diploma (or perhaps a masters)…

This article describes how spatial instruction with preservice teachers can be implemented in a middle-grades mathematics methods class. A "Reflect and Discuss" section is included for professional development study. (Contains 4 figures.)

Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by…