Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

Contributor Notes

Megan H. Wickstrom, Department of Mathematical Sciences, Montana State University, Bozeman, MT, megan.wickstrom@montana.edu

Barrett, J. E., Cullen, C. J., Sarama, J., Clements, D. H., Klanderman, D., Miller, A. L., & Rumsey, C. (2011). Children’s unit concepts in measurement: A teaching experiment spanning grades 2 through 5. ZDM, 43(5), 637–650.

Barrett, J. E., Cullen, C. J., Sarama, J., Clements, D. H., Klanderman, D., Miller, A. L., & Rumsey, C. (2011). Children’s unit concepts in measurement: A teaching experiment spanning grades 2 through 5. )| false

Battista, M. T. (2007). The development of geometric and spatial thinking. In F.Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843–908). National Council of Teachers of Mathematics.

Battista, M. T. (2007). The development of geometric and spatial thinking. In F.Lester (Ed.), )| false

Battista, M. T., Clements, D. H., Arnoff, J., Battista, K., & Borrow, C. V. A. (1998). Students’ spatial structuring of 2D arrays of squares. Journal for Research in Mathematics Education, 29(5), 503–532.

Battista, M. T., Clements, D. H., Arnoff, J., Battista, K., & Borrow, C. V. A. (1998). Students’ spatial structuring of 2D arrays of squares. )| false

Baturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235–268.

Baturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. )| false

Browning, C., Edson, A.J., Kimani, P., & Aslan-Tutak, F. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on geometry and measurement. The Mathematics Enthusiast, 11(2), 333–384.

Browning, C., Edson, A.J., Kimani, P., & Aslan-Tutak, F. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on geometry and measurement. )| false

Clements, D. H., Sarama, J., & Miller, A. L. (2017). Area. In J. E.Barrett, D. H.Clements, & J.Sarama (Eds.), Children’s measurement: A longitudinal study of children’s knowledge and learning of length, area, and volume (JRME Monograph No. 16, pp. 71–81). National Council of Teachers of Mathematics.

Clements, D. H., Sarama, J., & Miller, A. L. (2017). Area. In J. E.Barrett, D. H.Clements, & J.Sarama (Eds.), )| false

Hong, D. S., Choi, K. M., Runnalls, C., & Hwang, J. (2018). Do textbooks address known learning challenges in area measurement? A comparative analysis. Mathematics Education Research Journal, 30(3), 325–354.

Hong, D. S., Choi, K. M., Runnalls, C., & Hwang, J. (2018). Do textbooks address known learning challenges in area measurement? A comparative analysis. )| false

Hong, D. S., & Runnalls, C. (2020). Examining preservice teachers’ responses to area conservation tasks. School Science and Mathematics, 120(5), 262–272.

Hong, D. S., & Runnalls, C. (2020). Examining preservice teachers’ responses to area conservation tasks. )| false

Huinker, D. (1998). Letting fraction algorithms emerge through problem solving. In L. J.Morrow & M. J.Kenney (Eds.), The teaching and learning of algorithms in school mathematics, NCTM 1998 yearbook (pp. 170–182). National Council of Teachers of Mathematics.

Huinker, D. (1998). Letting fraction algorithms emerge through problem solving. In L. J.Morrow & M. J.Kenney (Eds.), )| false

Kamii, C., & Kysh, J. (2006). The difficulty of “length × width". Is a square the unit of measurement?The Journal of Mathematical Behavior, 25(2), 105–115.

Kamii, C., & Kysh, J. (2006). The difficulty of “length × width". Is a square the unit of measurement?)| false

Lobato, J., & Walters, C. (2017). A taxonomy of approaches to learning trajectories and progressions. In J.Cai(Ed.), Compendium for research in mathematics education (pp. 74–101). National Council of Teachers of Mathematics.

Lobato, J., & Walters, C. (2017). A taxonomy of approaches to learning trajectories and progressions. In J.Cai(Ed.), )| false

Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K.Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 629–667). Information Age Publishing.

Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K.Lester, Jr. (Ed.), )| false

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.

Livy, S., Muir, T., & Maher, N. (2012). How do they measure up? Primary pre-service teachers’ mathematical knowledge of area and perimeter. )| false

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(5), 629–651.

Runnalls, C., & Hong, D. S. (2019). “Well - they understand the concept of area." Pre-Service teachers’ responses to student area misconceptions. )| false

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.

Simon, M. A., & Blume, G. W. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. )| false

Smith, J. P., III, Males, L. M., & Gonulates, F. (2016). Conceptual limitations in curricular presentations of area measurement: One nation’s challenges. Mathematical Thinking and Learning, 18(4), 239–270.

Smith, J. P., III, Males, L. M., & Gonulates, F. (2016). Conceptual limitations in curricular presentations of area measurement: One nation’s challenges. )| false

Stephan, M., & Clements, D. H. (2003). Linear, area, and time measurement in prekindergarten to grade 2. In D. H.Clements & G.Bright (Eds.), Learning and teaching measurement: 2003 yearbook (pp. 3–16). National Council of Teachers of Mathematics.

Stephan, M., & Clements, D. H. (2003). Linear, area, and time measurement in prekindergarten to grade 2. In D. H.Clements & G.Bright (Eds.), )| false

Wickstrom, M. H., Fulton, E.W., & Carlson, M. A. (2017). Pre-service teachers’ conceptions of tiling and relating area units. The Journal of Mathematical Behavior, 48, 112–136.

Wickstrom, M. H., Fulton, E.W., & Carlson, M. A. (2017). Pre-service teachers’ conceptions of tiling and relating area units. )| false