Exploring Geometry Teaching Model: Polygon Pieces and Dictionary Tools for the Model

Shakespear Maliketi Chiphambo; Nosisi Nellie Feza

doi:10.29333/ejmste/8358

Full Text (PDF)

Shakespear Maliketi Chiphambo ¹ ^* , Nosisi Nellie Feza ¹

More Detail

¹ Walter Sisulu University, SOUTH AFRICA^* Corresponding Author

Abstract

Research reveals that many mathematics teachers find it difficult to stimulate learners' interest in learning geometry. One major reason suggested is that geometric concepts are not well conceptualised and comprehended by both learners and teachers. The study explored learners’ views on how polygon pieces and dictionary mediate learning of geometry. Nine Grade 8 learners were purposely selected from the cohort of 56 learners based on the diagnostic test results. By employing a qualitative approach through exploration data were gathered from semi- structured interviews and document analysis was implemented and reported in themes. The study found that polygon pieces with mathematics dictionary enhance learners’ learning of geometry through geometric inquiry. Polygon pieces assisted learners with geometric conceptualisation through cutting, constructing and measuring of angles and line segments. The dictionary enhanced learners’ geometric vocabulary by transferring informal vocabulary. We recommend mathematics teachers to integrate polygon pieces assisted by mathematics dictionary in the teaching and learning of mathematics.

Keywords

conceptual understanding
dictionary
polygon pieces
properties of triangles
unpack meaning

License

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

EURASIA J Math Sci Tech Ed, 2020, Volume 16, Issue 9, Article No: em1874

https://doi.org/10.29333/ejmste/8358

Publication date: 22 Jun 2020

Article Views: 2255

Article Downloads: 2164

Open Access References How to cite this article

References

Alex, J. K. (2012). The evaluation of an instructional framework using the van Hiele levels for learning and teaching geometry: A case study in five rural senior secondary schools. Unpublished doctoral dissertation, Walter Sisulu University, Mthatha, South Africa.
Alex, J. K., & Mammen, K. J. (2014). An assessment of the readiness of Grade 10 learners for geometry in the Context of Curriculum and Assessment Policy Statement (CAPS) Expectation. International Journal of Education Science, 7(1), 29-39. https://doi.org/10.1080/09751122.2014.11890167
Alex, J. K., & Mammen, K. J. (2016). Lessons learnt from employing van Hiele theory based instruction in senior school geometry classroom. Eurasia Journal of Mathematics, Science & Technology Education, 12(8), 2223-2236. https://doi.org/10.12973/eurasia.2016.1228a
Blanco, L. J. (2001). Errors in the Teaching/Learning of the Basic Concepts of Geometry. International Journal for Mathematics Teaching and Learning, pp. 1-11. Retrieved from http://www.cimt.org.uk/journal/lberrgeo.pdf
Bloor, M., & Wood, F. (2006). Keywords in Qualitative Methods: A Vocabulary of Research Concepts. London: Sage. https://doi.org/10.4135/9781849209403
Bowen, G. A. (2009). Document Analysis as a Qualitative Research Method. Qualitative Research Journal, 9(2), 27-40. https://doi.org/10.3316/QRJ0902027
Bussi, M. G. B., & Frank, A. B. (2015). Geometry in early years: sowing seeds for a mathematical definition of squares and rectangles. ZDM Mathematics Education, 47(3), 391-405. https://doi.org/10.1007/s11858-014-0636-5
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Gouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York, NY: MacMillan.
Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14(2), 133-148. https://doi.org/10.1007/s10857-011-9173-0
Corbin, J., & Strauss, A. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). Thousand Oaks, CA: Sage. https://doi.org/10.4135/9781452230153
Correa, C. A., Perry, M., Sims, L. M., Miller, K. F., & Fang, G. (2008). Connected and culturally embedded beliefs: Chinese and US teachers talk about how their learners best learn mathematics. Teaching and Teacher Education, 24, 140-153. https://doi.org/10.1016/j.tate.2006.11.004
Fraenkel, J. R., & Wallen, N. E. (2006). How to Design and Evaluate Research in Education (6^th ed.). New York, NY: McGraw-Hill.
Fujita, T., & Keith, J. (2003). The place of experimental tasks in geometry teaching: learning from the textbooks design of the early 20^th Century. Research in Mathematics Education, 5(1), 47–62. https://doi.org/10.1080/14794800008520114
Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine. https://doi.org/10.1097/00006199-196807000-00014
Hwang, W. Y., & Hu, S. S. (2013). Analysis of peer learning behaviours using multiple representations in virtual reality and their impacts on geometry problem solving. Computers & Education, 62(0), 308-319. https://doi.org/10.1016/j.compedu.2012.10.005
Lacey, A., & Luff, D. (2007). Qualitative data analysis. The NIHR RDS for the East Midlands / Yorkshire & the Humber.
Laski, E. V., Jor’dan, J. R., Daoust, C., & Murray, A. K. (2015). What makes mathematics manipulatives effective? Lessons from Cognitive Science and Montessori Education, 1-8. https://doi.org/10.1177/2158244015589588
LeCompte, M., & Goetz, J. P. (1982). Problems of reliability and validity in ethnographic research, Review of Educational Research, 52(1), 31-60. https://doi.org/10.3102/00346543052001031
Lewis, J., & Ritchie, J. (2003). Generalising from qualitative research. In J. Ritchie & J. Lewis (Eds.), Qualitative Research Practice: A Guide for Social Science Learners and Researchers (pp. 263-286). London: Sage.
Luria, A. R. (1976). Cognitive development: Its cultural and social foundations. Cambridge, MA: Harvard University Press.
Marshall, M. N. (1996). Sampling for qualitative research. Family Practice, 13, 522-525. https://doi.org/10.1093/fampra/13.6.522
Morin, J. E., & Franks, D, J. (2009) Why Do Some Children Have Difficulty Learning Mathematics? Looking at Language for Answers. Preventing School Failure: Alternative Education for Children and Youth, 54(2), 111-118. https://doi.org/10.1080/10459880903217861
Moss, J. Hawes Z, Naqvi S., & Caswell, B. (2015). Adapting Japanese Lesson Study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: a case study. ZDM Mathematics Education, 47, 377-390. https://doi.org/10.1007/s11858-015-0679-2
Puchner, L., Taylor, A., O’Donnell, B., & Fick, K. (2008). Teacher learning and mathematics manipulatives: A collective case study about teacher use of manipulatives in elementary and middle school mathematics lessons. School Science and Mathematics, 108, 313-325. https://doi.org/10.1111/j.1949-8594.2008.tb17844.x
Reddy, V., Visser, M., Winnaar, L., Arends, F., Juan, A., Prinsloo, C. H., & Isdale, K. (2016). TIMSS 2015: Highlights of Mathematics and Science Achievement of Grade 9 South African Learners. Human Sciences Research Council.
Riccomini, P. J., Smith, G. W., Hughes, E. M., & Fries K. M. (2015). The Language of Mathematics: The Importance of Teaching and Learning Mathematical Vocabulary. Reading & Writing Quarterly, 31(3), 235-252. https://doi.org/10.1080/10573569.2015.1030995
Shenton, A. K. (2004). Strategies for ensuring trustworthiness in qualitative research projects. Education for Information 22, 63-75. https://doi.org/10.3233/EFI-2004-22201
Steele, M. D. (2013). Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks. Journal of Mathematics Teacher Education, 16, 245-268. https://doi.org/10.1007/s10857-012-9230-3
Van den Heuvel‑Panhuizen, M., Elia, I., & Robitzsch, A. (2015). Kindergartners’ performance in two types of imaginary perspective‑taking. ZDM Mathematics Education, 47, 345-362. https://doi.org/10.1007/s11858-015-0677-4
Van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching children mathematics, 5(6), 310-317.
Van Teijlingen, E. R., & Hundley, V. (2001). The importance of pilot studies. In N. Gilbert (Ed.) Social Research update, University of Surrey.
Wiersma, W. (1991). Research Methods in Education: An Introduction, Boston: Allyn and Bacon.

How to cite this article

APA

Chiphambo, S. M., & Feza, N. N. (2020). Exploring Geometry Teaching Model: Polygon Pieces and Dictionary Tools for the Model. Eurasia Journal of Mathematics, Science and Technology Education, 16(9), em1874. https://doi.org/10.29333/ejmste/8358

Vancouver

Chiphambo SM, Feza NN. Exploring Geometry Teaching Model: Polygon Pieces and Dictionary Tools for the Model. EURASIA J Math Sci Tech Ed. 2020;16(9):em1874. https://doi.org/10.29333/ejmste/8358

AMA

Chiphambo SM, Feza NN. Exploring Geometry Teaching Model: Polygon Pieces and Dictionary Tools for the Model. EURASIA J Math Sci Tech Ed. 2020;16(9), em1874. https://doi.org/10.29333/ejmste/8358

Chicago

Chiphambo, Shakespear Maliketi, and Nosisi Nellie Feza. "Exploring Geometry Teaching Model: Polygon Pieces and Dictionary Tools for the Model". Eurasia Journal of Mathematics, Science and Technology Education 2020 16 no. 9 (2020): em1874. https://doi.org/10.29333/ejmste/8358

Harvard

Chiphambo, S. M., and Feza, N. N. (2020). Exploring Geometry Teaching Model: Polygon Pieces and Dictionary Tools for the Model. Eurasia Journal of Mathematics, Science and Technology Education, 16(9), em1874. https://doi.org/10.29333/ejmste/8358

MLA

Chiphambo, Shakespear Maliketi et al. "Exploring Geometry Teaching Model: Polygon Pieces and Dictionary Tools for the Model". Eurasia Journal of Mathematics, Science and Technology Education, vol. 16, no. 9, 2020, em1874. https://doi.org/10.29333/ejmste/8358