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

Sister Cecilia Anne Wanner


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.

Full Text:



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


  • There are currently no refbacks.

Copyright (c) 2019 Sister Cecilia Anne Wanner

The Ohio Journal of School Mathematics is published by the Ohio Council of Teachers of Mathematics and hosted by The Ohio State University Libraries.

If you encounter problems with the site or have comments to offer, including any access difficulty due to incompatibility with adaptive technology, please contact

ISSN 2472-5986 (print)
ISSN 2472-601X (online)