What I wish I had known about teaching proof before I taught geometry
The history and the mathematics used by Newton and Leibniz in their invention of calculus. The exploration of this topic is intended to show students that mathematics is a human invention. Suggestions are made to help teachers incorporate the mathematics and the history into their own lessons.
Michelle Cirillo and Heather Thompson
Michelle Cirillo and Jenifer Hummer
Use these ideas to diagnose and address common conceptual obstacles that inhibit students' success.
Michelle Cirillo, Beth Herbel-Eisenmann, and Corey Drake
Michelle Cirillo, Corey Drake, and Beth Herbel-Eisenmann
Corey Drake, Michelle Cirillo, and Beth Herbel-Eisenmann
“Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well” (The Teaching Principle, NCTM 2000, p. 16).
Samuel Otten, Michelle Cirillo, and Beth A. Herbel-Eisenmann
Reconsider typical discourse strategies when discussing homework and move toward a system that promotes the Standards for Mathematical Practice.
Beth A. Herbel-Eisenmann, Michael D. Steele, and Michelle Cirillo
We describe our ongoing efforts to design materials for supporting secondary mathematics teachers in using a set of Teacher Discourse Moves purposefully in order to develop classroom discourse that is both productive and powerful for students' learning. We focus on secondary mathematics classroom discourse because mathematical language and meanings get increasingly complex beginning in middle school, and most discourse-related work in mathematics education has focused on elementary school classrooms. We make explicit both the concepts we use and the translation of these theoretical concepts into ideas useful for practice. This article contributes to ongoing discussions about making visible the work of developing research-based professional development materials.