The Analysis of a Novice Primary Teacher’s Mathematical Knowledge in Teaching: Area Measurement

  • Sümeyra Doğan Coşkun Gazi University
  • Mine Işıksal Bostan Middle East Technical University


The purpose of this paper is to investigate a novice primary teacher’s mathematical knowledge in teaching on area measurement.  Data was collected from a novice primary teacher of fourteen students in a primary school located in Ankara, Turkey using field notes, video recordings of lessons, and audio recordings of interviews before and after her teaching. Her teaching were analyzed according to dimensions of Knowledge Quartet (KQ) model which included Foundation, Transformation, Connection, and Contingency. Results revealed that the KQ model is an alternative and effective tool for the primary mathematics teaching. Specifically, the novice primary teacher’s mathematical knowledge in teaching for area measurement was found to be effective regarding the Foundation and Contingency dimensions. However, she lacked the ability to make connections and use appropriate representations and examples regarding the Connection and Transformation dimensions respectively.  Implications and suggestions for the improvement of teachers’ mathematical knowledge in teaching are presented.


Aaronson, D., Barrow, L., & Sander, W. (2007). Teachers and Student Achievement in the Chicago Public High Schools. Journal of Labor Economics, 25(1), 95–135.

Adams, T., & Harrell, G. (2003). Estimation at work. In NCTM Yearbook: Learning and teaching measurement (pp. 229-244). Reston, VA: NCTM.

Ball, D. L. (1991). Research on teaching mathematics: Making subject-matter knowledge part of the equation. Research on Teaching Mathematics, 2, 1-48.

Ball, D. L. (2003, February 6). Mathematics in the 21st century: What mathematical knowledge is needed for teaching mathematics? Secretary’s summit on mathematics. Washington, DC: U.S. Department of Education.

Ball, D. L., Thames, M.H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.

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

Bennett, A. B. Jr., & Nelson, L. T. (2001). Mathematics for Elementary Teachers: A Conceptual Approach (5th ed.). New York: McGraw-Hill.

Chappell, M. F. & Thompson, D. R. (1999). Perimeter or area? Which measure is it? MathematicsTeaching in the Middle School, 5(1), 20-23

Chen, J. C., Reys, B. J., & Reys, R. E. (2009). Analysis of the learning expectations related to grade 1–8 measurement in some countries. International Journal of Science and Mathematics Education, 7(5), 1013-1031.

Clements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 461–555). Charlotte, NC: Information Age.

Clements, D. H., & Stephan, M. (2004). Measurement in pre-K to grade 2 mathematics. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 299–320). Mahwah, NJ: Lawrence Erlbaum Associates.

Dickson, L. (1989). Area of a rectangle. In K. Hart, D. C. Johnson, M. Brown, L. Dickson, & R. Clarkson (Eds.). Children’s mathematical frameworks 8-13: A study of classroom teaching (pp.89-125). England, Windsor: NFER-Nelson Publishing Company.

Even, R. (1993). Subject-Matter Knowledge and Pedagogical Content Knowledge: Prospective Secondary Teachers And The Function Concept. Journal for Research in Mathematics Education, 24(2), 94-116.

Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164) New York: Macmillan.

Fernández-Balboa, J. M., & Stiehl, J. (1995). The Generic Nature of Pedagogical Content Knowledge among College Professors. Teaching and Teacher Education, 11, 293–306.

Gilbert, M. & Gilbert B. (2011). Examining the connection between teacher content knowledge and classroom practice. In B. Ubuz, (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, Vol 2, (p. 429) Ankara, Turkey: PME.

Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press, Columbia University.

Hart, K. M. (1984). Which comes first – Length, area, or volume? Arithmetic Teacher, 31(9), 16-27.

Hegarty, S. (2000). Teaching as a knowledge-based activity. Oxford Review of Education, 26(3-4), 451-465.

Hiebert, J. (1981). Cognitive development and learning linear measurement. Journal for Research in Mathematics Education, 12 (3), 197–211.

Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406.

Hirstein, J.J., Lamb, C.E.,& Osborne, A. (1978). Student misconceptions about area measure. Arithmetic Teacher, 25(6), 10–16.

Huang, H-M. E., & Witz, K. G. (2011). Developing children’s conceptual understanding of area measurement: A curriculum and teaching experiment. Learning and Instruction, 21, 1 – 13.

Kamii, C. (2006). Measurement of length: How can we teach it better? Teaching Children Mathematics, 13, 154-158.

Kenney, P. A., & Kouba, V. L. (1997). What do students know about measurement? In P. A. Kennedy & E. A. Silver (Eds.), Results from the Sixth Mathematics Assessment of the National Assessment of Education Progress, (pp. 141-163). Reston, Va.: National Council of Teachers of Mathematics.

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).Reston, VA: NCTM.

Lehrer, R., Jenkins, M., & Osana, H. (1998).Longitudinal study of children‘s reasoning about space and geometry. InR.Lehrer& D. Chazan (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space (pp. 137 –167). Mahwah, NJ: Erlbaum.

Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

Marks, R. (1990). Pedagogical content knowledge. From a mathematical case to a modified concept. Journal of Teacher Education, 41(3), 3-11.

Martin, G. W., & Strutchens, M. E. (2000). Geometry and measurement. In E. A. Silver & P. A. Kenney (Eds.), Results from the seventh mathematics assessment of the national assessment of educational progress (pp. 193-234). Reston, VA: National Council of Teachers of Mathematics.

McClain, K., Cobb, P., Gravemeijer, K., & Estes, B. (1999). Developing mathematical reasoning within the context of measurement. In: L. Stiff & F. R. Curcio (Eds.), Developing mathematical reasoning in grades K-12. Reston, VA: NCTM.

Menon, R. (1998). Preservice teachers’ understanding of perimeter and area. School Science and Mathematics, 98, 361–367.

Ministry of National Education. (2005). İkögretim Matematik Dersi Ögretim Programı ve Kılavuzu (1-5. sınıflar) [Primary schools mathematics program for 1-5 grades]. Devlet Kitapları Müdürlügü, Ankara.

Murphy, C. (2010). The Role of Subject Knowledge in Primary Students Teachers’ Approaches to Teaching the Topic Area. Proceedings of CERME 6, January 28- February 1st 2009, Lyon France From (Retrieved on 27 May 2015).

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Outhred, L. & Mitchelmore, M. C. (1996). Children’s intuitive understanding of area measurement. In L. Puig & A. Gutierrez (Eds.), Proceedings of the 20th conference of the International Group for the Psychology in Mathematics Education (Vol. 4, pp. 91-98). Valencia, Spain: university of Valencia.

Rowland, T. (2014). The Knowledge Quartet: The Genesis and Application of a Framework for Analysing Mathematics Teaching and Deepening Teachers’ Mathematics Knowledge. SISYPHUS Journal of Education, 1(3), 15-43.

Rowland, T., Huckstep, P., & Thwaites, A. (2003). The Knowledge Quartet. Proceedings of the British Society for Research into Learning Mathematics, 23(3), 97-102.

Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281.

Rowland, T., & Ruthven, K. (Eds). (2011). Mathematical knowledge in teaching. London: Springer.

Rowland, T., & Turner, F. (2007). Developing and Using The ‘Knowledge Quartet’: A Framework For The Observation Of Mathematics Teaching. The Mathematics Educator, 10(1), 107-124.

Rowland, T., & Zazkis, R. (2013). Contingency in the mathematics classroom: Opportunities taken and opportunities missed. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 137–153.

Rowland, T., Turner, F., Thwaites, A., & Huckstep, P. (2009). Developing Primary Mathematics Teaching: Reflecting on Practice with the Knowledge Quartet. London: Sage.

Sanders, W. L. (2000). Value-added assessment from student achievement data. Cary, NC: Create National Evaluation Institute.

Sgroi, L. S. (2001). Teaching Elementary and Middle School Mathematics: Raising the Standards. Belmont, California: Wadsworth.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

Simon, M. A. & Blume, G. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25, 472-494.

Stephan, M., & Clements, D.H. (2003). Linear and area measurement in prekindergarten to grade 2. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement. NCTM 2003 Yearbook (pp. 3–16). Reston, VA: NCTM.

Strutchens, M. E., Martin, W. G., & Kenney, P. A. (2003). What students know about measurement: Perspectives from the NAEP. In D. H. Clements & G. Bright (Eds.),Learning and Teaching Measurement: NCTM 2003 Yearbook (pp. 197-208). Reston: NCTM.

Tan-Sisman, G. & Aksu, M. (2009). Seventh grade students’ success on the topics of area and perimeter. İlköğretim-Online, 8(1), 243-253.

Tierney, C., Boyd, C. & Davis, G., (1990). Prospective primary teachers' conceptions of area. In G. Booker, P.Cobb, and T.N. de Mendicuti (Eds), Proceedings of the 14th Conference of the International Group for the Psychology of Mathematics Education with the North American Chapter 12th PME-NA, (Vol 2, pp. 307-315). Mexico: PME.

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). Elementary and middle school mathematics: Teaching developmentally – The Professional Development Edition. New York, NY: Pearson Education.

Watson, A. (2008). Developing and deepening mathematical knowledge in teaching: being and knowing. MKiT 6, Nuffield Seminar Series, 18th March, at University of Loughborough.

Woodward, E., & Byrd, F. (1983). Area: Included topic, neglected concept. School Science and Mathematics, 83(4), 343-347.

Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, CA: Sage.

Zacharos, K. (2006). Prevailing educational practices for area measurement and students‟ failure in measuring areas. Journal of Mathematical Behavior, 25, 224-239.