A mathematical investigation (MI) encapsulates the reform movement in mathematics education by addressing content and process simultaneously and providing a novel opportunity for students to develop thinking skills and good mental habits. However, introducing MI to teachers and students who are used to routinised teaching approaches and…

As calls are made for reasoning-and-proving to permeate school mathematics, several textbook analyses have been conducted to identify reasoning-and-proving opportunities outside of high school geometry. This study looked within geometry, examining six geometry textbooks and characterizing not only the justifications given and the…

We analyze the interaction of 3 students working on mathematics problems over several days in a virtual math team. Our analysis traces out how successful collaboration in a later session is contingent upon the work of prior sessions and shows how the development of representational practices is an important aspect of these participants' problem…

A geometry textbook or mathematics journal that prints all the work that mathematicians use as they generate proofs of mathematical results would be rare indeed. The false starts, the tentative conjectures, and the arguments that led nowhere--these are conveniently omitted; only the final successful product is presented to the world. To students…

This study examined the improvement of students' comprehension of geometric concepts through analytical writing about their own misconceptions using a reflective tool called an ERNIe (acronym for ERror aNalyIsis). The purpose of this study was to determine whether the ERNIe process could be used to correct geometric misconceptions, as well as how…