RESEARCH PAPER
Exploring Mathematics Learners’ Conceptual Understanding of Coordinates and Transformation Geometry through Concept Mapping
 
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University of South Africa, SOUTH AFRICA
 
 
Online publication date: 2019-11-07
 
 
Publication date: 2019-11-07
 
 
EURASIA J. Math., Sci Tech. Ed 2019;15(12):em1818
 
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ABSTRACT
In this article, we explored learners’ conceptual understanding of coordinates and transformation geometry through concept mapping. A qualitative case study was employed in this study, and data was collected using an investigative task, observation and reflective interviews on a sample of 34 Grade 12 mathematics learners. The study was guided by the following two research questions: What are the learners’ understanding of coordinate and transformation geometry? and How do concept maps improve learners’ understanding of coordinate and transformation geometry? The study revealed that, although some leaners struggled with linking words and omitted some concepts in their concept maps, there were some indications of conceptual understanding of coordinate and transformation geometry when the learners were probed during the interview. Thus, we argue that the learners’ conceptual understanding of coordinate and transformation geometry could be improved when they are taught, using concept mapping. The learners actively situated their knowledge of small pieces of coordinates and transformation geometry; and their understanding of coordinate and transformation geometry was expanded to show the conceptual structure of representing given information and a complete picture of the situation. It is therefore recommended that the teachers allow the learners to use the concept mapping strategy to construct their knowledge and that concept maps assist the learners in focusing on main ideas of identified concepts and explain the relationship.
REFERENCES (33)
1.
Asan, A. (2007). Concept Mapping in Science Class: A case Study of Fifth Grade Students. Educational Technology & Society, 10(1), 186-195.
 
2.
Borda, E. J., Burgess, D. J., Plog, C. J., & Luce, M. M. (2009). Concept Maps as Tools for Assessing Student’s Epistemologies of Science. Electronic Journal of Science Education, 13, 160-185.
 
3.
Chichekian, T., & Shore, B. M. (2013). Concept Maps Provide a Window onto Preservice Elementary Teachers’ Knowledge in the Teaching and Learning of Mathematics. Canadian Journal of Education, 36(3), 47-71.
 
4.
Creswell, J. W. (2007). Second Edition. Qualitative Inquiry & Research Design: Choosing among Five Approaches. London: SAGE Publications.
 
5.
Department of Education. (2009). Mathematics Intervention Guide: Limpopo Province. South Africa. Pretoria.
 
6.
Department of Education. (2010). Mathematics Subject Work schedule: Limpopo Province. South Africa. Pretoria.
 
7.
Grevholm, B. (2008). Concept maps as research tool in mathematics education. In Actes du colloque CMC 2008: Third International Conference on Concept Mapping.
 
8.
Hatano, G. (1996). A conception of knowledge acquisition and its implications for mathematics education. In L. Steffe, P. Nesher, P. Cobb, & G. Goldin (Eds.), Theories of mathematical learning (pp. 197–217). Hillsdale, NJ: Lawrence Erlbaum.
 
9.
Kharatmal, M. (2009). Concept Map for Eliciting Students’ understanding of Science. Indian Educational Review, 45(2), 31-43.
 
10.
Kilpatrick, J., Swafford, A., & Findell, B. (2002). Mathematics learning study committee. Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
 
11.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn Mathematics. Washington DC: National Research Council.
 
12.
Lincoln, Y. S., & Guba, E. (1985). Naturalistic Inquiry. Newbury Park, CA: Sages. https://doi.org/10.1016/0147-1....
 
13.
Machaba, F. (2014). Teachers’ and Facilitators’ Views on Grade 11 Learners’ Approaches to Solving Context-based Mathematics and Mathematical Literacy Tasks (Doctoral dissertation), Tshwane University of Technology.
 
14.
Machaba, F. M. (2016). The concepts of area and perimeter: Insights and misconceptions of Grade 10 learners. Pythagoras, 37(1), 1-11. https://doi.org/10.4102/pythag....
 
15.
Machaba, F. M. (2018). Pedagogical demands in mathematics and mathematical literacy: A case of mathematics and mathematical literacy teachers and facilitators. Eurasia Journal of Mathematics, Science and Technology Education, 14(1), 95-108. https://doi.org/10.12973/ejmst....
 
16.
Malatjie, J.F. (2012). Exploring learners’s conceptual understanding of coordinate and Transformation Geometry through concept –mapping (Masters Dissertation). Limpopo University.
 
17.
McMillan, J. H., & Schumacher, S. (1993).Research in Education: A conceptual introduction (3rd Edition). New York: Haper Collins Publishers.
 
18.
Mwakapenda, W. (2003, September). Concept mapping and context in mathematics education. In Proceedings of the 6th International Conference of the Mathematics Education into 21th Century Project (pp. 193-198).
 
19.
Mwakapenda, W., & Adler, J. (2003). Using concept mapping to explore student understanding and experiences of school mathematics. African Journal of Research in Mathematics, Science and Technology Education, 7(1), 51-62. https://doi.org/10.1080/102884....
 
20.
Naidoo, J., & Bansila, S. (2010). Transformation Geometry the VA Way. In M. D. de Villiers (Ed.), Mathematics: The Pulse of the Nation. Proceedings of 16th Annual Congress of the Association for Mathematics Education of South Africa (AMESA) (pp 323-331) George Campbell School of Technology Durban, KwaZulu-Natal, South Africa.
 
21.
New Jersey Assessment of Skills and Knowledge Spring. (2009). Grade 3 skills Technical Report. Spring.
 
22.
Novak, J. D. (n.d).The Theory Tnderlying Concept Maps and How to Construct them. Retrieved on September 7, 2009 from http://cmap.coginst.uwf.edu/in....
 
23.
Novak, J. D., & Cañas, A. J. (2008). The Theory Underlying Concept Maps and How to Construct and Use Them, Technical Report IHMC CmapTools 2006-01 Rev 01-2008, Florida Institute for Human and Machine Cognition.
 
24.
Piaget, J. (1964). Part I: Cognitive development in children: Piaget development and learning. Journal of research in science teaching, 2(3), 176-186. https://doi.org/10.1002/tea.36....
 
25.
Piaget, J. (1968). Six psychological studies. Trans. A. Tenzer.
 
26.
Pillay, E., & Bansilal, S. (2010). In M.D. de Villiers (Ed.), Mathematics: The Pulse of the Nation. Proceedings of 16th Annual Congress of the Association for Mathematics Education of South Africa (AMESA) (pp 298-306) George Campbell School of Technology Durban, KwaZulu-Natal, South Africa.
 
27.
Pirie, S. E. B., & Kieren, T. E. (1994). Growth in Mathematical Understanding: How can we Characterize it and How can we Represent it? Educational Studies in Mathematics, 26(3), 165-190. https://doi.org/10.1007/BF0127....
 
28.
Raymond, A. (1997). The use of Concept-Mapping in qualitative research: A multiple case study in Mathematics education. Focus on Learning Problems in Mathematics, 19(3), 1-28. https://doi.org/10.2307/749691.
 
29.
Roth, W. R., & Roychoudhury, A. (1992). The social construction of scientific concepts or the Concept Map as conscription device and tool for social thinking in high school science. Science Education, 76(5), 531-557. https://doi.org/10.1002/sce.37....
 
30.
Ruiz-Primo, M. A. (2004). Examining Concept Maps as an assessment tool. School of Education, Spain: Stanford University.
 
31.
Ruiz-Primo, M. A., & Shavelson, R. (1996). Problems and issues in the use of Concept Maps in science assessment. Journal of Research in Science Teaching, 33(6), 569-600. https://doi.org/10.1002/(SICI)...<569::AID-TEA1>3.0.CO;2-M.
 
32.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (Eds.). (2016). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Pearson Education.
 
33.
Yager, R. E. (1995). The Constructivist Learning Model: Towards real reform in Science Education. The Science Teacher, 58(6), 52-57.
 
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