We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

Constructing formal geometry proofs in is an important topic in the mathematics curriculum. But students' difficulties with proof are well documented. This article focuses on proofs that use triangle congruence postulates in US high school geometry. Examining students' proof reasoning in one-on-one task-based interviews, we analyzed students' oral…

Building on prior work visualizing player behavior using interaction networks [1], we examined whether measures of implicit science learning collected during gameplay were significantly related to changes in external pre-post assessments of the same constructs. As part of a national implementation study, we collected data from 329 high school…

Mathematics teachers play a unique role as experts who provide opportunities for students to engage in the practices of the mathematics community. Proof is a tool essential to the practice of mathematics, and therefore, if teachers are to provide adequate opportunities for students to engage with this tool, they must be able to validate student…