Developing Preservice Teachers’ Understanding of Area Through a Units Intervention

Author:
Megan H. Wickstrom Montana State University, Bozeman

Search for other papers by Megan H. Wickstrom in
Current site
Google Scholar
PubMed Close
Volume/Issue:
Volume 10: Issue 2
Page(s):
143–170
DOI:
https://doi.org/10.5951/MTE.2020.0056
Restricted access
NCTM members GET ACCESS here
Subjects:
Grade(s) or Audience, Grades 3-5, Math Coordinator/Math Coach/Department Chair, Higher Education, Math Topic, Geometry, Geometric Measurement & Dimension, 3-D Shapes/Spatial Visualization, Measurement, Number, Number & Operations, Number & Operations—Fractions, Other Topic, Connections, Representations, Teaching and Learning Instruction, Manipulatives, Research, Qualitative Research
Keywords:
Teachers; Area Model; Visual Representations

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

  • Collapse
  • Expand
Mathematics Teacher Educator
Cover Mathematics Teacher Educator
  • 1.

    Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. Available online at amte.net/standards

    • Search Google Scholar
    • Export Citation
  • 2.

    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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 3.

    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.

    • Search Google Scholar
    • Export Citation
  • 4.

    Battista, M. T. (2012). Cognition-based assessment and teaching of geometric measurement: Building on students’ reasoning. Heinemann.

    • Search Google Scholar
    • Export Citation
  • 5.

    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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 6.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 7.

    Beckmann, S. (2018). Mathematics for elementary teachers with activities (5th ed.) Pearson.

  • 8.

    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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 9.

    Clements, D. H. , & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89.

  • 10.

    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.

    • Search Google Scholar
    • Export Citation
  • 11.

    Cullen, A. L. , & Barrett, J. E. (2020). Area measurement: Structuring with nonsquare units. Mathematical Thinking and Learning, 22(2), 85–115.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 12.

    Empson, S. B. , & Levi, L. (2011). Extending children’s mathematics: Fractions and decimals. Heinemann.

  • 13.

    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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 14.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 15.

    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.

    • Search Google Scholar
    • Export Citation
  • 16.

    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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 17.

    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.

    • Search Google Scholar
    • Export Citation
  • 18.

    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.

    • Search Google Scholar
    • Export Citation
  • 20.

    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.

    • Search Google Scholar
    • Export Citation
  • 21.

    Menon, R. (1998). Preservice teachers’ understanding of perimeter and area. School Science and Mathematics, 98(7), 361–368.

  • 22.

    Miles, M. B. , Huberman, A. M. , & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook. SAGE Publications.

  • 23.

    Reinke, K. S. (1997). Area and perimeter: Preservice teachers’ confusion. School Science and Mathematics, 97(2), 75–77.

  • 30.

    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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 24.

    Sarama, J. , & Clements, D. H. (2009). Early childhood mathematics education research learning trajectories for young children. Routledge.

  • 25.

    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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 26.

    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.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 27.

    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.

    • Search Google Scholar
    • Export Citation
  • 28.

    Tierney, C. , Boyd, C. , & Davis, G. (1990). Prospective primary teachers’ conception of area [Conference presentation]. Fourteenth psychology in mathematics education conference, Mexico (Vol. 2).

    • Search Google Scholar
    • Export Citation
  • 29.

    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.

    • Crossref
    • Search Google Scholar
    • Export Citation
Copyright:
The National Council of Teachers of Mathematics, Inc. All rights reserved. 2022
Page Count:
28
Article Category:
Research Article
Print Publication Date:
01 Feb 2022
Online Publication Date:
01 Feb 2022
All Time Past Year Past 30 Days
Abstract Views 33394 32425 638
Full Text Views 589 202 3
PDF Downloads 607 118 4
EPUB Downloads 0 0 0