Investigating Area and Volume Instruction for Prospective Teachers: A Lesson Experiment

Michelle Chamberlin; Megan Schnorenberg Candelaria

doi:10.29333/iejme/285

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Michelle Chamberlin, Megan Schnorenberg Candelaria

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Abstract

A lesson experiment was used to investigate how instruction impacted prospective elementary teachers' conceptual understandings of area and volume. Data sources included ten prospective teachers' work on a measurement pre-assessment, lesson activities, and three post-assessments as well as audio recordings of lesson activities. The qualitative analysis consisted of two steps: a "real-time" analysis within the constraints of the week surrounding the lesson and an "intensive-delayed" constant-comparative analysis over the next several months. Findings revealed the prospective teachers enhanced their understandings of area and volume. The lesson experiment led to instructional recommendations for improving the lesson in the future, such as the need to address prospective teachers‟ formulaic tendencies, interpretations about basic units, and perceptions of area and volume measurements as linear quantities. Implications include the value of lesson experiments as an iterative process to contribute to the shared knowledge base of mathematics teacher educators.

Keywords

Lesson Experiment
Prospective Teachers
Mathematics
Area
Volume
Qualitative Research

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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 9, Issue 2, October 2014, 113-134

https://doi.org/10.29333/iejme/285

Publication date: 12 Dec 2014

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References

Baturo, A., & Nason, R. (1996). Student teachers subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235-268. doi: 10.1007/BF00376322
Berenson, S., Van Der Valk, T. M., 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. doi: 10.1080/0261976970200203
Buck, R. E. (2004). Expanding mathematics preparation of elementary and middle school teachers. Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 14(2), 141-155. doi: 10.1080/10511970408984082
Chamberlin, M. T., & Powers, R. A. (2010). The promise of differentiated instruction for enhancing the mathematical understandings of college students. Teaching Mathematics and Its Applications: An International Journal of The Institute of Mathematics and Its Applications, 29(3), 113-139. doi: 10.1093/teamat/hrq009
Clarke, D. (1997). A compulsory mathematics unit for elementary preservice teachers: Content, pedagogy and assessment. Annual Conference of the Association of Mathematics Teacher Educators, Washington, DC.
Conference Board of the Mathematical Sciences (CBMS). (2001). The mathematical education of teachers. Washington, D.C.: Mathematical Association of America (MAA) in cooperation with American Mathematical Society (AMS).
Crespo, S., & Nicol, C. (2006). Challenging preservice teachers' mathematical understanding: The case of division by zero. School Science and Mathematics, 106(2), 84– 97. doi: 10.1111/j.1949- 8594.2006.tb18138.x
Delaney, S., Ball, D. L., Hill, H. C., Schilling, S. G., & Zopf, D. (2008). Mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11, 171- 197. doi: 10.1007/s10857-008-9072-1
Enochs, L. G., & Gabel, D. L. (1984). Preservice elementary teachers‟ conceptions of volume. School Science and Mathematics, 84(8), 670- 680. doi: 10.1111/j.1949- 8594.1984.tb09582.x
Hart, L. C. (2002). Preservice teachers' beliefs and practice after participating in an integrated content/methods course. School Science and Mathematics, 102(1), 4–14.
Hiebert, J., Morris, A., K., Berk, D., & Jansen, A. (2007). Preparing teachers to learn from teaching. Journal of Teacher Education, 58(1), 47-61. doi: 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.
Inskeep, J. E. (1976). Teaching measurement to elementary children. National Council of Teachers of Mathematics Yearbook (pp. 60- 86). Reston, VA: National Council of Teachers of Mathematics.
Lester, F. K., Jr., et al. (1992). Preparing elementary teachers to teach mathematics (PETTM): A problem-solving approach. (Final Report. Volume II: Content Component). Bloomington, IN: Indiana University, Mathematics Education Development Center.
Libeskind, S. (2011). Teaching mathematics for prospective elementary school teachers: What textbooks don‟t tell. Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 21(5), 473-484. doi: 10.1080/10511970903296106
Lubinski, C. A., & Otto, A. D. (2004). Preparing K-8 preservice teachers in a content course for standards-based mathematics pedagogy. School Science and Mathematics, 104(7), 336-336. doi: 10.1111/j.1949- 8594.2004.tb18252.x
Matthews, M., Rech, J., & Grandgenett, N. (2010). The impact of content courses on pre-service elementary teachers‟ mathematical content knowledge. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 1, Retrieved from http://www.k12prep.math.ttu.edu/journal/contentknowl edge/rech01/article.pdf
Matthews, M. E., & Seaman, W. I. (2007). The effects of different undergraduate mathematics courses on the content knowledge and attitude towards mathematics of preservice elementary teachers. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 1, Retrieved from http://www.k12prep.math.ttu.edu/journal/contentknowl edge/matthews01/article.pdf
McLeod, K., & Huinker, D. (2007). University of Wisconsin-Milwaukee mathematics focus courses: Mathematics content for elementary and middle grades teachers. International Journal of Mathematical Education in Science and Technology, 38(7), 949-962. doi: 10.1080/00207390701579498
Mewborn, D. S. (2001). Teachers‟ content knowledge, teacher education, and their effects on the preparation of elementary teachers in the United States. Mathematics Teacher Education and Development 3, 28- 36.
Mizell, J. A., & Cates, J. (2004). The impact of additional content courses on teacher candidates beliefs regarding mathematics content and pedagogy. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 4, Retrieved from http://www.eric.ed.gov/PDFS/EJ835512.pdf
Murphy, C. (2012). The role of subject knowledge in primary prospective teachers‟ approaches to teaching the topic of area. Journal of Mathematics Teacher Education, 15(3), 187- 206. doi: 10.1007/s10857-011-9194-8
National Commission on Mathematics and Science Teaching for the Twenty-First Century. (2000). Before it’s too late: A report to the nation. Jessup, MD: U.S. Department of Education. Retrieved from http://www.nationalmathandscience.org/si tes/default/files/resource/before%20its%20 too%20late.pdf
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2007). Mathematics teaching today. Reston, VA: Author.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, D.C.: Authors. Retrieved from http://www.corestandards.org
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, D.C.: U.S. Department of Education.
National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
O'Keefe, M., & Bobis, J. (2008). Primary teachers‟ perceptions of their knowledge and understanding of measurement. In M. Goos, R. Brown, & K. Makar (Eds.), Navigating Currents and Charting Directions (Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia) (pp. 391–398). Brisbane, Australia: Mathematics Education Research Group of Australasia.
Quinn, B., & Jadav, A.D. (1987). Causal relationship between attitude and achievement for elementary grade mathematics and reading. Journal of Educational Research, 80(6), 366-372.
Reinke, K. S. (1997). Area and perimeter: Preservice teachers‟ confusion. School Science and Mathematics, 97(2), 75-77.
Saiz, M. (2003). Primary teachers' conceptions about the concept of volume: The case of volume-measurable objects. Proceedings of the 27th International Group for the Psychology of Mathematics Education (pp. 95-102). Honolulu, HI: International Group for the Psychology of Mathematics Education.
Senk, S., Demir, M., Park, J., & Crespo, S. (2009). Pre-service elementary teachers' knowledge of geometry and measurement. In S. L. Swars, D. W. Stinson, & S. LemonsSmith (Eds.), Proceedings of the 31st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 569-576). Atlanta, GA: Georgia State University.
Sowder, J., Sowder, L., & Nickerson, S. (2009). Reconceptualizing mathematics for elementary school teachers. New York, NY: W. H. Freeman.
Strauss, A., & Corbin, J. (1998). Basics of qualitative research: Techniques and procedures for developing grounded theory (2nd ed.). London: Sage.
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., & Lovin, L. H. (2006). Teaching student-centered mathematics: Grades K-3. Columbus, OH: Allyn & Bacon.
Wiggins, G., & McTighe, J. (2005). Understanding by design (2nd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.
Woodward, E., & Byrd, F. (1983). Area: Included topic, neglected concept. School Science and Mathematics, 83(4), 343-347. doi: 10.1111/j.1949-8594.1983.tb10119.x
Zevenbergen, R. (2005). Primary pre-service teachers‟ understandings of volume: The impact of course and practicum experiences. Mathematics Education Research Journal, 17(1), 3-23. doi: 10.1111/j.1949-8594.1983.tb10119.x

How to cite this article

APA

Chamberlin, M., & Candelaria, M. S. (2014). Investigating Area and Volume Instruction for Prospective Teachers: A Lesson Experiment. International Electronic Journal of Mathematics Education, 9(2), 113-134. https://doi.org/10.29333/iejme/285

Vancouver

Chamberlin M, Candelaria MS. Investigating Area and Volume Instruction for Prospective Teachers: A Lesson Experiment. INT ELECT J MATH ED. 2014;9(2):113-34. https://doi.org/10.29333/iejme/285

AMA

Chamberlin M, Candelaria MS. Investigating Area and Volume Instruction for Prospective Teachers: A Lesson Experiment. INT ELECT J MATH ED. 2014;9(2), 113-134. https://doi.org/10.29333/iejme/285

Chicago

Chamberlin, Michelle, and Megan Schnorenberg Candelaria. "Investigating Area and Volume Instruction for Prospective Teachers: A Lesson Experiment". International Electronic Journal of Mathematics Education 2014 9 no. 2 (2014): 113-134. https://doi.org/10.29333/iejme/285

Harvard

Chamberlin, M., and Candelaria, M. S. (2014). Investigating Area and Volume Instruction for Prospective Teachers: A Lesson Experiment. International Electronic Journal of Mathematics Education, 9(2), pp. 113-134. https://doi.org/10.29333/iejme/285

MLA

Chamberlin, Michelle et al. "Investigating Area and Volume Instruction for Prospective Teachers: A Lesson Experiment". International Electronic Journal of Mathematics Education, vol. 9, no. 2, 2014, pp. 113-134. https://doi.org/10.29333/iejme/285