RESEARCH PAPER
Exploring Grade Nine Geometry Spatial Mathematical Reasoning in the South African Annual National Assessment
 
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Department of Mathematics Science and Technology Education, University of Limpopo, SOUTH AFRICA
2
Center of Academic Excellence, University of Limpopo, SOUTH AFRICA
Online publish date: 2019-05-23
Publish date: 2019-05-23
 
EURASIA J. Math., Sci Tech. Ed 2019;15(11):em1772
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ABSTRACT
The purpose of this study was to explore geometry spatial mathematical reasoning in Grade nine Annual National Assessments, South Africa. Conceptual Blending was the guiding theory. Document analysis within the exploratory case study was used to explore available data, the 2014 Annual National Assessment learners’ scripts (n=1250). Results revealed that on average 70.5 percent of the total number of learners remembered and blended irrelevant prior knowledge not reflective to the contexts of the geometry problems. For learners who recalled the correct prior knowledge, its manipulation was either fragmented or irrelevant. The use of recalled information in wrong contexts could be due to the incorrect manipulation of the meaning of the problems. Also, responses reveal challenges on the quality of mathematics education on geometry. Therefore, the teaching and learning of geometry should focus on empowering learners with skills of recalling, blending and on manipulating problems in their contexts.
 
REFERENCES (60)
1.
Ally, N., & Christiansen, M. (2013). Opportunities to develop mathematical proficiency in Grade 6 mathematics classroom in Kwazulu-Natal. Perspectives in Education, 31(3), 106-121. Retrieved from http://perspectives-in-educati....
 
2.
Amir-Mofidi, S., Amiripour, P., & Bijan-zadeh, M. (2012). Instruction of mathematical concepts through analogical reasoning skills. Indian Journal of Science and Technology, 5(6), 2916-2922. https://doi.org/10.17485/ijst/....
 
3.
Bansilal, S. (2017). The Difficulty level of a national assessment of Grade 9 mathematics: The case of five schools. South African Journal of Childhood Education, 7(1), 1-8. https://doi.org/10.4102/sajce.....
 
4.
Battista, M. T. (1990). Spatial visualisation and gender differences in high school geometry. Journal for Research in Mathematics Education, 21(1), 47-60. https://doi.org/10.2307/749456.
 
5.
Brodie, K. (2010). Teaching Mathematical Reasoning in secondary classrooms, 1st Edition. Dordrecht, Springer. https://doi.org/10.1007/978-0-....
 
6.
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. Handbook of research on mathematics teaching and learning, 420-464.
 
7.
Creswell, J. (2014). Educational research: Planning, conducting and evaluating quantitative and qualitative research, 4th Edition. New Jersey, Pearsons Education.
 
8.
Department of Basic Education (DBE). (2011). Curriculum and assessment policy statements Grades 7-9. Pretoria. Retrieved from http://www.education.gov.za.
 
9.
DBE. (2014a). The annual national assessment of 2014 diagnostic report intermediate and senior phases mathematics. Pretoria. Retrieved from http://www.education.gov.za.
 
10.
DBE. (2014b). Report on the annual national assessment of 2014: Grades 1 to 6 & 9, Pretoria. Retrieved from http://www.education.gov.za.
 
11.
DBE. (2015). Annual National Assessment 2015 Grade 9 Mathematics Test, Pretoria. Retrieved from www.education.gov.za.
 
12.
Dhlamini, Z. B., & Luneta, K. (2016). Exploration of the levels of mathematical proficiency displayed by grade 12 learners in responses to matric examinations. International Journal of Educational Sciences, 12(2), 231-246. https://doi.org/10.1080/097511....
 
13.
Dunne, T., Long, C., Graig, T., & Venter, E. (2012). Meeting the Requirements of both Classroom-Based and Systemic Assessment of Mathematics Proficiency: The Potential of Rasch Measurement Theory. Pythagoras, 33(3), Art. #19, 16 pages. http://doi.org/10.4102/pythago....
 
14.
Eccles, P. J. (2007). An introduction to mathematical reasoning, numbers, sets and functions. New York, Cambridge University Press. Retrieved from https://www.maths.manchester.a....
 
15.
Eppe, M., Maclean, E., Confalonieri, R., Kutz, O., Schorlemmer, M., Plaza, E., & Kuhnberger, K. (2018). A computational framework for conceptual blending. Artificial Intelligence, 256, 105-129. https://doi.org/10.1016/j.arti....
 
16.
Fauconnier, G., & Turner, M. (2002). The way we think: Conceptual blending and the mind’s hidden complexities. New York, Basic Books. Retrieved from https://www.amazon.com/Way-We-....
 
17.
Figueiredo, C., Leite, C., & Fernandes, P. (2016). The curriculum in school external evaluation frameworks in Portugal and England. Comparative & International Education, 11(3), 282-297. https://doi.org/101177/1745499....
 
18.
Foster, C. (2018). Developing mathematical fluency: Comparing exercises and rich tasks. Educational Studies in Mathematics, 97, 121-141. https://doi.org/10.1007/s10649....
 
19.
Fujita, T., Kondo, Y., Kumakura, H., & Kunimune, S. (2017). Students’ geometry thinking with cube representations: Assessment framework and empirical evidence. Journal of Mathematical Behavior, 46, 96-111. https://doi.org/10.1016/j.jmat....
 
20.
Gerson, H., & Walter, J. (2008). How blending illuminates understanding of calculus. In Electronic proceedings for the eleventh special interest group o the mathematical association of America on research in undergraduate mathematics. Retrieved from http://rume.org/crume2008/Proc....
 
21.
Gibbs, G. R. (2012). Different approaches to coding. Sociological Methodology, 42, 82-84. https://doi.org/10.1177/008117....
 
22.
Gorard, S. (2005). The advantages of the mean deviation. British Journal of Educational Studies, 53(4), 417-430. https://doi.org/10.1111/j.1467....
 
23.
Graven, M., & Venkat, H. (2014). Primary teachers’ experiences relating to the administration processes of high-stakes testing: The case of mathematics annual national assessments. African Journal of Research in Mathematics, Science and Technology Education, 18(3), 299-310. Retrieved from https://doi.org/10.1080/102884....
 
24.
Hegarty, M., & Waller, D. (2004). A dissociation between mental rotation and perspective-taking spatial abilities. Intelligence, 32, 175-191. https://doi.org/10.1016/j.inte....
 
25.
Heyd-Metzuyanim, E., Munter, C., & Greeno, J. (2018). Conflicting frames: a case of misalignment between professional development efforts and a teacher’s practice in a high school mathematics classroom. Educational Studies in Mathematics, 97, 21-37. https://doi.org/10.1007/s10649....
 
26.
Hombo, M. (2003). NAEP and No Child Left behind: Technical Challenges and Practical Solutions. Theory Into Practice, 42(1), 59-65. Retrieved from https://www.jstor.org/stable/1....
 
27.
Jonsson, B., Norqvist, M., Liljekvist, Y., & Lithner, J. (2014). Learning mathematics through algorithmic and creative reasoning. The Journal of Mathematical Behavior, 36, 20-32. https://doi.org/10.1016/j.jmat....
 
28.
Johnson, S. (2017). Design challenges for national assessment in this accountability era: A background paper commissioned by Cambridge Assessment. Cambridge, UK: Cambridge Assessment. Retrieved from http://www.cambridgeassessment....
 
29.
Kanjee, A., & Moloi, Q. (2016). A standard-based approach for reporting assessment results in South Africa. Perspectives in Education, 34(4), 29-51. https://doi.org/10.18820/25195....
 
30.
Kellaghan, T., Greaney, V., & Murray, S. T. (2009). Using the results of a national assessment of educational achievement. Washington, DC, World Bank. Retrieved from http://hdl.handle.net/10986/26....
 
31.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). (Eds.). Adding it up: Helping children learn mathematics, Washington D.C: National Academy Press, 115-155. https://doi.org/10.17226/9822.
 
32.
Klenowski, V., & Wyatt-Smith, C. (2012). The impact of high stakes testing: the Australian story. Assessment in Education: Principles, Policy and Practice, 19(1), 65-79. https://doi.org/10.1080/096959....
 
33.
Koichu, B., & Leron, U. (2015). Proving as problem solving: The role of cognitive decoupling. The Journal of Mathematics Behavior, 40, 233-244. https://doi.org/10.1016/j.jmat....
 
34.
Komatsu, K., Jones, K., Ikeda, T., & Narazaki, A. (2017). Proof validation and modification in secondary school geometry. Journal of Mathematical Behavior, 47, 1-15. https://doi.org/10.1016/j.jmat....
 
35.
Lachmy, R., & Koichu, B. (2014). The interplay of empirical and deductive reasoning in proving ‘if’ and ‘only if’ statements in a dynamic geometry environment. Journal of Mathematical Behavior, 36, 150-165. https://doi.org/10.1016/j.jmat....
 
36.
Lee, K. (2016). Students’ proof schemes for mathematical proving and disproving of propositions. The Journal of Mathematical Behavior, 41, 26-44. https://doi.org/10.1016/j.jmat....
 
37.
Lee, C. Y., & Chen, M. J. (2015). Effects of worked examples using manipulatives on fifth graders’ learning performance and attitude toward mathematics. Journal of Educational Technology & Society, 18(1), 264-275. Retrieved from http://www.jstor.org/stable/je....
 
38.
Lehrer, R. (2012). Longitudinal study of children’s reasoning about space and geometry. In Designing learning environments for developing understanding of geometry and space (pp. 151-182). Routledge. Retrieved from https://psycnet.apa.org/record....
 
39.
Long, C., & Wendt, H. (2017). A comparative investigation of South Africa’s high performing learners on selected TIMSS items comprising multiplicative concepts. African Journal of Research in Mathematics, Science and Technology Education, 21(2), 109-124. https://doi.org/10.1080/181172....
 
40.
Mabotja, S., Chuene, K., Maoto, S., & Kibirige, I. (2018). Tracking Grade 10 learners’ geometric reasoning through folding back. Pythagoras, 39(1), a371. https://doi.org/10.4102/ pythagoras.v39i1.371.
 
41.
Markovits, H., & Doyon, C. (2011). Using analogy to improve abstract reasoning in adolescents: Not as easy as it looks. European Journal of Psychology of Education, 26(3), 355-372. https://doi.org/10.1007/s10212....
 
42.
Maoto, S., Masha, K., & Mokwana, L. (2018). Teachers’ learning and assessing of mathematical processes with emphasis on representations, reasoning and proof. Pythagoras, 39(1), https://doi.org/10.4102/pythag....
 
43.
McHugh, M. L. (2012). Interrater reliability: The kappa statistic. Biochemia Medica, 22(3), 276-82. https://doi.org/10.11613/BM.20....
 
44.
Munzer, S., Fehringer, B., & Kuhl, F. T. (2018). Specificity of mental transformations involved in understanding spatial structures. Learning and Individual Differences, 61, 40-50. https://doi.org/10.1016/j.lind....
 
45.
Otten, O., Bleiler-Baxter, S. K., & Engledowl, C. (2017). Authority and whole-class proving in high school geometry: The case of Ms. Finley. The Journal of Mathematical Behavior, 46, 112-127. https://doi.org/10.1016/j.jmat....
 
46.
Pedemonte, B., & Balacheff, N. (2016). Establishing links between conceptions, argumentation and proof through the ck¢-enriched Toulmin Model. The Journal of Mathematical Behavior, 41,104-122. https://doi.org/10.1016/j.jmat....
 
47.
Pittalis, M., & Christou, C. (2010). Types of reasoning in 3D geometry thinking and their relation with spatial ability. Educational Studies in Mathematics, 75(2), 191-212. https://doi.org/10.1007/s10649....
 
48.
Pournara, C., Mpofu, S., & Sanders, Y. (2015). The Grade 9 maths ANA - What can we see after three years? Learning and Teaching of Mathematics, 18, 34-41. Retrieved from https://hdl.handle.net/10520/E....
 
49.
Resnick, B. L., & Schantz, E. (2017). Testing, teaching, learning: who is in charge? Assessment in Education: Principles, Policy & Practice, 24(3), 424-432. https://doi.org/10.1080/096959....
 
50.
Spaull, N. (2016). Disentangling the language effect in South African schools: Measuring the impact of ‘language of assessment’ in Grade 3 literacy and numeracy. South African Journal of Childhood Education, 6(1). Retrieved from https://doi.org/10.4102/sajce.....
 
51.
Sidney, P. G., & Alibali, M. W. (2015). Making connections in math: Activating a prior knowledge analogue matters for learning. Journal of Cognition and Development, 16(1), 160-185. https://doi.org/10.1080/152483....
 
52.
Singh, K. (2007). “Quantitative social research methods” New Delhi: SAGE Publications. https://doi.org/10.4135/978935....
 
53.
Surtees, A., Apperly, I., & Samson, D. (2013). Similarities and differences in visual and spatial perspective-taking processes. Cognition, 129, 426-438. https://doi.org/10.1016/j.cogn....
 
54.
Umugiraneza, O., Bansilal, S., & North, D. (2018). Exploring teachers’ descriptions of ways of working with the curriculum in teaching mathematics and statistics. African Journal of Research in Mathematics Science and Technology Education, 22(1), 70-80. https://doi.org/10.1080/181172....
 
55.
Usiskin, Z. (1987). “Resolving the continuing dilemmas in school geometry”. In M. M. Lindquist and A. P. Shulte (Eds), Learning and Teaching Geometry, K-12. Reston, VA, National Council of Teachers of Mathematics. Retrieved from https://books.google.co.za/boo....
 
56.
Yazan, B. (2015). Three approaches to case study methods in education: Yin, Merriam, and Stake. The Qualitative Report, 20(2), 134-152. Retrieved from https://nsuworks.nova.edu/tqr/....
 
57.
Yin, R. K. (1984). Case study research: design and methods. Beverly Hills, Calif: Sage Publications. Retrieved from https://evaluationcanada,ca/sy....
 
58.
Yoon, C., Thomas, M. O. J., & Dreyfus, T. (2011). Grounded blends and mathematical gesture spaces: Developing mathematical understanding via gestures. Educational Studies in Mathematics, 78, 371-393. https://doi.org/10.1007/s10649....
 
59.
Yopp, D. A. (2015). Prospective elementary teachers’ claiming in responses to false generalizations. The Journal of Mathematical Behavior, 39, 79-99. https://doi.org/10.1016/j.jmat....
 
60.
Zandieh, M., Roh, K. H., & Knapp, J. (2014). Conceptual blending: Student reasoning when proving “conditional implies conditional” statements. The Journal of Mathematical Behavior, 33, 209-229. https://doi.org/10.1016/j.jmat....
 
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