Historically, educators have held up the study of Euclidean geometry as a model of learning deductive reasoning rooted in axioms. However, axioms based solely on the Elements may not get a high school student all the way to clean, rigorous proofs of congruence and similarity from a transformation approach. While Euclid did allude to superposition […]

Graduate-level geometry courses in mathematics departments introduce contemporary approaches in professional research areas such as combinatorial geometry and computational geometry. Like other advanced studies of mathematics, contemporary geometry employs rigorous methods grounded on formal definitions and proofs. Contemporary geometry courses can provide secondary mathematics teachers with a unique opportunity for professional development that can advance their knowledge and […]

Authors of the MODULE(S²) Project Geometry materials will share how the educative curriculum materials were conceived and provide a brief tour through the materials. The MODULE(S²) Project Geometry materials include three modules designed for use with prospective secondary mathematics teachers:  Axiomatic Systems, Transformational Geometry, and Similarity and Measurement. Throughout the materials, connections are made to […]

The Japanese approach to problem-based lessons is well known for the selection of interesting, challenging problems, the highly-planned teacher moves, and the facilitation of student attempts toward solving the problem. This talk will revolve around one geometry problem, taken from a Japanese 8th-grade lesson filmed for the TIMSS video study, as a case of how […]

In this talk, I will share how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in number theory and geometry). I will portray the progression of Theo’s set-based model from […]

Galileo proposed a geometric model to explain how much force is required to break a horizontal beam that is secured at one end and pushed down at the other—a cantilever.  Preservice teachers at LSU investigated and tested Galileo’s model using styrofoam beams.  They found that Galileo’s model predicts a strength that is 3 times as great as actually observed.  […]

Members of the Transformations Working Group will discuss their lesson study that has now been taught three times in various settings. The purpose of the lesson was to foster normative precision in describing and defining geometric transformations, including symmetries, and to foster dispositions to attend to prospective students’ mathematical identities. We call it the “Adinkra” […]

In this talk, I will describe a sequence of investigative activities in dynamic geometry (Geometer’s Sketchpad) developed and enacted in a Geometry course. The specific example of investigative sequence will focus on similarity theorems from Euclidean geometry perspective. While all students can benefit learning Geometry from inquiry-based perspective, this approach may be particularly appropriate for […]

Results from a qualitative study about proof in high school geometry will be shared. First, a Common Core geometry textbook was analyzed for its proof-related contents. Then, inservice and preservice secondary mathematics teacher participants were administered a content assessment and interviewed regarding their knowledge, beliefs, and goals for teaching proof.

This talk will make an argument that it is essential to provide opportunities for prospective secondary mathematics teachers to connect advanced mathematics content to secondary mathematics teaching practice, if these courses are to be useful to them as prospective teachers. Then, we will review curricular materials intended for use in advanced mathematics courses in which […]