Mitigating Misconceptions of Preservice Teachers: The Relationship between Area and Perimeter


  • Sister Cecilia Anne Wanner Aquinas College


Preservice teachers often demonstrate misconceptions regarding the non-constant relationship between area and perimeter. The author presents a sequence of hands-on instructional tasks with pentominoes to promote deep conceptual understanding of this relationship.


Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. Raleigh, NC: Association of Mathematics Teacher Educators. Retrieved from

Brown, B. (2016). Tetris: The games people play. New York: First Second.

Conference Board of the Mathematical Sciences (CBMS). (2012). Issues in Mathematics Education: Vol. 17. The mathematical education of teachers II. Providence, RI: American Mathematical Society, in cooperation with Mathematical Association of America.

Gardner, M. (1957). Mathematical games: More about complex dominoes, plus the answers to last month’s puzzles. Scientific American, 197(6), 126-140.

Lappan, G., Fey, J. T., Fitzerald, W. M., Friel, S. N., & Phillips, E. D. (1998). Covering and surrounding: Two-dimensional measurement. New York: Addison Wesley Longman, Inc.

National Council of Teachers of Mathematics (NCTM). (2009). Puzzling pentominoes. Retrieved from

National Governors Association Center for Best Practices & Council of Chief State School Officers (NGA/CCSSO) (2010). Common core state standards for mathematics. Washington, DC: Author. Retrieved from Standards.pdf

Smith, M. S., Bill, V., & Hughes, E. K. (2008). Thinking through a lesson: Successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14, 132–138. doi:10.2307/41182652

Woodward, E., & Byrd, F. (2010). Area: Included topic, neglected concept. School Science and Mathematics, 83, 343–347. doi:10.1111/j.1949-8594.1983.tb10119.x




How to Cite

Wanner, S. C. A. (2019). Mitigating Misconceptions of Preservice Teachers: The Relationship between Area and Perimeter. Ohio Journal of School Mathematics, 82(1). Retrieved from