Challenging to learn, proof can be equally challenging to teach. Insights gleaned about students’ conceptions of proof from 10 high school students who completed four proof-related tasks during one-on-one interviews led to a few instructional takeaways for teachers.

Crowley, Mary L.1987. “The van Hiele Model of the Development of Geometric Thought." In Learning and Teaching Geometry, K–12, edited by Mary M.Lindquist, pp. 1–16. Reston, VA: National Council of Teachers of Mathematics.

Crowley, Mary L.1987. “The van Hiele Model of the Development of Geometric Thought." In )| false

Ellis, Amy B., Kristen N.Bieda, and Eric J.Knuth. 2012. Developing Essential Understanding of Proof and Proving for Teaching Mathematics in Grades 9–12. Reston, VA: National Council of Teachers of Mathematics.

Ellis, Amy B., Kristen N.Bieda, and Eric J.Knuth. 2012. )| false

Knuth, Eric J., Jeffrey M.Choppin, and Kristen N.Bieda. 2009. “Proof: Examples and Beyond." Mathematics Teaching in the Middle School15, no. 4 (November): 206–11.

Mason, John, and DavidPimm. 1984. “Generic Examples: Seeing the General in the Particular." Educational Studies in Mathematics15, no. 3 (August): 277–89.

Soucy McCrone, Sharon M., and Tami S.Martin. 2009. “Chapter 12: Formal Proof in High School Geometry." In Teaching and Learning Proof across the Grades: A K–16 Perspective, edited by Despina A.Stylianou, Maria L.Blanton, and Eric J.Knuth. New York: Routledge.

Soucy McCrone, Sharon M., and Tami S.Martin. 2009. “Chapter 12: Formal Proof in High School Geometry." In )| false

Stylianou, Despina A., Maria L.Blanton, and OuraniaRotou. 2015. “Undergraduate Students’ Understanding of Proof: Relationships between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof." International Journal of Research in Undergraduate Mathematics Education1, no. 1: 91–134.

Stylianou, Despina A., Maria L.Blanton, and OuraniaRotou. 2015. “Undergraduate Students’ Understanding of Proof: Relationships between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof." )| false

Van Hiele, Pierre M.1984. “The Child’s Thought and Geometry." In English Translation of Selected Writings of Dina van Hiele-Geldof and Pierre M. van Hiele, edited by DavidFuys, DorothyGeddes, and RosamondWelchman Tishler, pp. 243–52. Brooklyn, NY: City University of New York. ERIC/SMEAC.

Van Hiele, Pierre M.1984. “The Child’s Thought and Geometry." In )| false