Lesson Experiment Cycles: Examining Factors that Affect Prospective Teachers’ Learning of Area Measurement

Michelle Chamberlin

doi:10.29333/iejme/11469

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Michelle Chamberlin ¹ ^*

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¹ University of Wyoming, USA^* Corresponding Author

Abstract

For teachers to provide students with meaningful instruction in area measurement, teachers need robust understandings of area. Here, I describe two cycles of a lesson experiment used to investigate prospective teachers’ understandings of area units in an undergraduate mathematics class. For each cycle, I collected and analyzed the prospective teachers’ written work and videotaped class discussions. The first cycle yielded a learning trajectory for helping prospective teachers better understand area units, which led to more teachers attaining the lesson goals in the second cycle. The paper articulates these classroom lessons and the lesson experiment process for fellow mathematics instructors and teacher educators.

Keywords

lesson experiment
prospective teachers
area measurement
undergraduate mathematics classes
teacher preparation

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 17, Issue 1, February 2022, Article No: em0665

https://doi.org/10.29333/iejme/11469

Publication date: 03 Jan 2022

Article Views: 1395

Article Downloads: 867

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Battista, M. T. (2003). Understanding students’ thinking about area and volume measurement. In D. H. Clements (Ed.), Learning and teaching measurement (2003 yearbook) (pp. 122-142). National Council of Teachers of Mathematics.
Baturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31, 235-268. https://doi.org/10.1007/BF00376322
Bilir, C. K. (2018). Pre-service teachers’ understanding the measurement of the area of rectangles [Doctoral dissertation, Purdue University]. https://search.proquest.com/docview/2051466222
Berenson, S., van der Valk, T., Oldham, E., Runesson, U., Moreira, C. Q., & Broekman, H. (1997). An international study to investigate prospective teachers’ content knowledge of the area concept. European Journal of Teacher Education, 20(2), 137-150. https://doi.org/10.1080/0261976970200203
Browning, C., Edson, A. J., Kimani, P. M., & Aslan-Tutak, F. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on geometry and measurement. The Mathematics Enthusiast, 11(2), 333-384.
Chamberlin, M. T., & Candelaria, M. S. (2018). Learning from teaching teachers: A lesson experiment in area and volume with prospective teachers. Mathematics Teacher Education and Development, 20(1), 86-111.
Conference Board of the Mathematical Sciences (CBMS). (2012). The mathematical education of teachersII. Mathematical Association of America in cooperation with the American Mathematical Society. http://www.cbmsweb.org/archive/MET2/met2.pdf
Hiebert, J., & Morris, A. (2009). Building a knowledge base for teacher education: An experience in K-8 mathematics teacher preparation. The Elementary School Journal, 109(5), 475-490. https://doi.org/10.1086/596997
Hiebert, J., Morris, A., K., Berk, D., & Jansen, A. (2007). Preparing teachers to learn from teaching. Journal of Teacher Education, 58(1), 47-61. https://doi.org/10.1177/0022487106295726
Hiebert, J., Morris, A. K., & Glass, B. (2003). Learning to learn to teach: An “experiment” model for teaching and teacher preparation in mathematics. Journal of Mathematics Teacher Education, 6, 201-222. https://doi.org/10.1023/A:1025162108648
Jansen, A., Bartell, T., & Berk, D. (2009). The role of learning goals in building a knowledge base for elementary mathematics teacher education. The Elementary School Journal, 109(5), 525-536. https://doi.org/10.1086/597000
Lehrer, R. (2003). Developing understanding of measurement. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 179-192). National Council of Teachers of Mathematics.
Lehrer, R., Jacobson, C., Thoyre, G., Kemeny, V., Strom, D., Horvath, J., Grance, S., & Koehler, M. (1998a). Developing understanding of geometry and space in the primary grades. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 169-200). Lawrence-Erlbaum.
Lehrer, R., Jaslow, L., & Curtis, C. (2003). Developing an understanding of measurement in the elementary grades. In D. H. Clements (Ed.), Learning and teaching measurement (2003 yearbook) (pp. 100-121). National Council of Teachers of Mathematics.
Lehrer, R., Jenkins, M., & Osana, H. (1998b). Longitudinal study of children’s reasoning about space and geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 137-167). Lawrence-Erlbaum.
Livy, S., Muir, T., & Maher, N. (2012). How do they measure up? Primary pre-service teachers’ mathematical knowledge of area and perimeter. Mathematics Teacher Education and Development, 14(2), 91-112.
National Governors Association Center for Best Practices (NGA Center) & Council of Chief State School Officers (CCSSO). (2010). Common core state standards for mathematics. http://www.corestandards.org/
Phelps, C. M., & Spitzer, S. M. (2012). Systematically improving lessons in teacher education: What’s good for prospective teachers is good for teacher educators. The Teacher Educator, 47(4), 328-347. https://doi.org/10.1080/08878730.2012.707759
Reinke, K. S. (1997). Area and perimeter: Preservice teachers’ confusion. School Science and Mathematics, 97(2), 75-77. https://doi.org/10.1111/j.1949-8594.1997.tb17346.x
Reynolds, A., & Wheatley, G. H. (1996). Elementary students’ construction and coordination of units in an area setting. Journal for Research in Mathematics Education, 27, 564-581. https://doi.org/10.2307/749848
Runnalls, C., & Hong, D. S. (2019). “Well, they understand the concept of area”: Pre-service teachers’ responses to student area misconceptions. Mathematics Education Research Journal, 32, 629-651. https://doi.org/10.1007/s13394-019-00274-1
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge. https://doi.org/10.4324/9780203883785
Simon, M. A. (2011). Studying mathematics conceptual learning: Student learning through their mathematical activity. In L. R. Wiest & T. Lamberg (Eds.), Proceedings of the 33^rd annual meeting of the north American chapter of the international group for the psychology of mathematics education (pp. 31-43). http://www.pmena.org/pmenaproceedings/PMENA%2033%202011%20Proceedings.pdf
Simon, M. A., & Blume, G. W. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25(5), 472-494. https://doi.org/10.2307/749486
Sowder, J., Sowder, L., & Nickerson, S. (2014). Reconceptualizing mathematics for elementary school teachers. Freeman.
Stephan, M., & Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. In D. H. Clements (Ed.), Learning and teaching measurement (2003 yearbook) (pp. 3-16). National Council of Teachers of Mathematics.
Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). SAGE.
Tatto, M. T., Schwille, J., Senk, S. L., Ingvarson, L., Rowley, G., Peck, P., Bankow, K., Rodriguez, M., & Reckase, M. (2012). Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries: Findings from the IEA Teacher Education and Development Study in Mathematics (TEDS-M). International Association for the Evaluation of Educational Achievement (IEA).
Tierney, C., Boyd, C., & Davis, G. (1990). Prospective primary teachers’ conceptions of area. In G. Booker, P. Cobb, & T. D. Mendecuti (Eds.), Proceedings of the 14th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 307–315). Mexico: International Group for the Psychology of Mathematics Education.
Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Pearson.

How to cite this article

APA

Chamberlin, M. (2022). Lesson Experiment Cycles: Examining Factors that Affect Prospective Teachers’ Learning of Area Measurement. International Electronic Journal of Mathematics Education, 17(1), em0665. https://doi.org/10.29333/iejme/11469

Vancouver

Chamberlin M. Lesson Experiment Cycles: Examining Factors that Affect Prospective Teachers’ Learning of Area Measurement. INT ELECT J MATH ED. 2022;17(1):em0665. https://doi.org/10.29333/iejme/11469

AMA

Chamberlin M. Lesson Experiment Cycles: Examining Factors that Affect Prospective Teachers’ Learning of Area Measurement. INT ELECT J MATH ED. 2022;17(1), em0665. https://doi.org/10.29333/iejme/11469

Chicago

Chamberlin, Michelle. "Lesson Experiment Cycles: Examining Factors that Affect Prospective Teachers’ Learning of Area Measurement". International Electronic Journal of Mathematics Education 2022 17 no. 1 (2022): em0665. https://doi.org/10.29333/iejme/11469

Harvard

Chamberlin, M. (2022). Lesson Experiment Cycles: Examining Factors that Affect Prospective Teachers’ Learning of Area Measurement. International Electronic Journal of Mathematics Education, 17(1), em0665. https://doi.org/10.29333/iejme/11469

MLA

Chamberlin, Michelle "Lesson Experiment Cycles: Examining Factors that Affect Prospective Teachers’ Learning of Area Measurement". International Electronic Journal of Mathematics Education, vol. 17, no. 1, 2022, em0665. https://doi.org/10.29333/iejme/11469