Geometry

Like classrooms, professional development (PD) workshops can be organised as dialogic and inclusive spaces, where the verbal contributions of the participants are critical for driving the inquiry and meeting the intended learning goals. Also, similar to how students interact during instruction, teachers’ verbal contributions during workshops may be uneven in their frequency and focus, with some individuals speaking up on particular topics, while others remain relatively silent. This study examines the nature and variation of teachers’ verbal participation during whole-group discussions as part of a weeklong mathematics PD programme.

This study examines technology-enhanced teacher responses and students’ written mathematical explanations to understand how to support effective teacher responding and the centering of students’ mathematical ideas. Although prior research has focused on teacher noticing and responding to students’ mathematical ideas, few studies have explored the revisions that students make to their written explanations after teacher responding and very few explore this in authentic classroom contexts.

This study examines technology-enhanced teacher responses and students’ written mathematical explanations to understand how to support effective teacher responding and the centering of students’ mathematical ideas. Although prior research has focused on teacher noticing and responding to students’ mathematical ideas, few studies have explored the revisions that students make to their written explanations after teacher responding and very few explore this in authentic classroom contexts.

There is strong empirical evidence in support of learning from comparisons in mathematics education research. The Animated Contrasting Cases in Geometry project seeks to extend this research and transform the learning of geometry for middle school students by designing a supplementary digital animated curriculum. This paper focuses on the Transformations unit, which is one of four units.

In this collection of materials, four geometric topics are covered in animated, digital materials. There are also paper-based materials for the four geometric topics: Angles, Transformations, Pythagorean Theorem, and Volume. These topics are discussed in scenarios of contrasting cases, where two fictional students each present a unique method or solution strategy to the same problem. The goal is then to analyze both methods and discuss similarities and differences, strengths and weaknesses of each. 

This peer-reviewed research journal publication addresses one of the grant goals with respect to how students performed on a set of proof tasks.

Students who earned high marks during the proof semester of a geometry course were interviewed to understand what high-achieving students actually took away from the treatment of proof in geometry. The findings suggest that students had turned proving into a rote task, whereby they expected to mark a diagram and prove two triangles congruent.

Presentation slides and handout from the 2019 NCTM Regional Conference in Nashville, TN.

Linear Algebra and Geometry is aimed at preservice and practicing high school mathematics teachers and advanced high school students looking for an addition to or replacement for calculus. The materials are organized around carefully sequenced problems that help students build both the tools and the habits that provide a solid basis for further study in mathematics. Requiring only high school algebra, it uses elementary geometry to build the beautiful edifice of results and methods that make linear algebra such an important field.