Non-Euclidean Geometry Lesson Promotes Mathematical Reasoning

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Derek A. Williams Montana State University, Bozeman, MT

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Kelly Fulton Bozeman High School, Bozeman, MT

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Travis Silver Pine Hills Correctional Facility, Miles City, MT

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Alec Nehring Montana State University, Bozeman, MT

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A two-day lesson on taxicab geometry introduces high school students to a unit on proof.

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

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  • Hanna, Gila. 1995. “Challenges to the Importance of Proof." For the Learning of Mathematics 15, no. 3 (November): 4249.

  • Hanna, Gila. 2002. “Proof, Explanation and Exploration: An Overview." Educational Studies in Mathematics 44 (December): 523.

  • Knuth, Eric J. 2002. “Teachers’ Conceptions of Proof in the Context of Secondary School Mathematics." Journal of Mathematics Teacher Education 5, no. 1 (March): 6188.

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  • Krause, Eugene F. 1973. “Taxicab Geometry." Mathematics Teacher 66, no. 8 (December): 695706.

  • National Governors Association Center for Best Practices (NGA Center) and Council of Chief State School Officers (CCSSO). 2010. Common Core State Standards for Mathematics. Washington, DC: NGA Center and CCSSO. http://www.corestandards.org.

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  • Sinclair, Nathalie, David Pimm, and Melanie Skelin. 2012. Developing Essential Understanding of Geometry: Grades 9–12, edited by Rose Mary Zbiek. Reston, VA: National Council of Teachers of Mathematics.

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