PRESERVICE MIDDLE SCHOOL MATHEMATICS TEACHERS’ KNOWLEDGE ABOUT STUDENTS’ MATHEMATICAL THINKING RELATED TO PERIMETER AND AREA

Year 2017, Volume: 6 , 61 - 67, 04.08.2017

Pınar Guner Didem Akyuz

Abstract

The
purpose of the current study is to examine preservice middle school mathematics
teachers’ knowledge about students’ mathematical thinking related to perimeter
and area and determine the consistency between this knowledge and students’
actual mathematical thinking. Case study, one of the qualitative research designs,
was used to gain an in-depth understanding of the situation. The study was
conducted with four senior preservice middle school mathematics teachers who
enrolled in the program of elementary mathematics education at a public
university. The data obtained through video recordings from the process of
planning, teaching and reflecting on two lessons towards perimeter and area.
The videos from teaching were used to identify students’ mathematical thinking,
difficulties, mistakes and misconceptions whereas the videos from planning and
reflecting were used to describe preservice teachers’ knowledge of students’
mathematical thinking. The data were analyzed through content analysis method.
The findings showed that students had lack of knowledge about the meanings of
the concepts of perimeter and area, made mistakes related to calculation and
use of measurement units. In addition to this, preservice teachers’ predictions
and expectations about students’ mathematical thinking were very limited.
Finally, it was observed that there were important differences between
students’ thinking ways, difficulties, misconceptions and possible mistakes and
preservice teachers’ expectations and predictions about these issues. 

Keywords

Knowledge of students’ thinking, preservice teachers, perimeter and area

References

• Ball, D. L., & McDiarmid, G. W. (1989). The Subject Matter Preparation of Teachers. Issue Paper 89-4. Baş, S., Erbaş, A. K. & Çetinkaya, B. (2011). Teachers’ knowledge about ninth grade students’ ways of algebraic thinking. Education and Science 36(159), 41-55. Baş, S. (2013). An Investigation of Teachers’ Noticing of Students’ Mathematical Thinking In The Context of A Professional Development Program. Unpublished doctoral dissertation. Middle East Technical University. Ankara, Turkey. Bergqvit, T. (2005). How students verify conjectures: Teachers’ expectations. Journal of Mathematics Teacher Education, 8, 171-191. Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: a knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3-20. Cavanagh, M. (2007). Year 7 students’ understanding of area measurement. Australian Association of Mathematics Teachers Inc., 136. Didiş, M., Erbaş, A., Çetinkaya, B., Çakıroğlu, E., & Alacacı, C. (2015). Öğrenci Çalışmalarını İncelemenin Öğrenci Düşünme Şekillerini Anlamadaki Rolü ile İlgili Matematik Öğretmen Adaylarının Düşünceleri. Turkish Journal of Computer and Mathematics Education, 6(2), 139-162. Doerr, H. M., & Lesh, R. (2003). A modeling perspective on teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 125–140). Mahwah, NJ: Lawrence Erlbaum. Goldsmith, L. T., & Seago, N. (2011). Using classroom artifacts to focus teachers‟ noticing: Affordances and opportunities. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 169-187). New York: Routledge. Hadjidemetriou, C., & Williams, J. (2002). Teachers’ pedagogical content knowledge: Graphs, from a cognitivist to a situated perspective. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3 (pp. 57-64). Norwich, UK: PME: Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7, 203-235. Kellogg, M. S. (2010). Preservice elementary teachers‟ pedagogical content knowledge related to area and perimeter: a teacher development experiment investigating anchored instruction with web-based microworlds. Unpublished doctoral dissertation. University of South Florida, USA. Kılıç, H. (2011). Preservice secondary mathematics teachers’ knowledge of students. Turkish Online Journal of Qualitative Inquiry, 2(2), 17–35. Martin, W. G., & Strutchens, M. E. (2000). Geometry and measurement. In E. A. Silver & P. A. Kennedy (Eds.), Results from the Seventh Mathematics Assessment of the National Assessment of Education Progress, (pp. 193-234). Reston, Va.: National Council of Teachers of Mathematics. Nathan, M. J., & Koedinger, K. R. (2000a). An investigation of teachers' beliefs of students' algebra development. Cognition and Instruction, 18(2), 209-237. Nathan, M. J., & Koedinger, K. R. (2000b). Teachers’ and researchers’ beliefs about the development of algebraic reasoning. Journal of Research in Mathematics Education, 31(2), 168-190. Reinke, K. S. (1997). Area and perimeter: Preservice teachers‟ confusion. School Science and Mathematics, 97, 75-77. Simon, M., & Blume, G. (1994). Mathematical modeling as a component of understanding ratio-as-measure: A study of prospective elementary teachers. Journal of Mathematical Behavior, 13, 183-197. Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5–25. Wallach, T., & Even, R. (2005). Hearing students: The complexity of understanding what they are saying, showing, and doing. Journal of Mathematics Teacher Education, 8(5), 393-417. Zacharos, K. (2006). Prevailing educational practices for area measurement and failure in measuring areas. Journal of Mathematical Behaviour, 25, 224-239. Zeytun, A., Çetinkaya, B., & Erbaş, A. K. (2010). Mathematics teachers’ covariational reasoning levels and their predictions about students’ covariational reasoning abilities. Educational Sciences: Theory & Practice, 10(3), 1573–1612.