Grade 9 Mathematics Learners’ Strategies in Solving Number-Pattern Problems

Erica Dorethea Spangenberg; Aphane Koko Pithmajor

doi:10.29333/ejmste/8252

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Erica Dorethea Spangenberg ¹ ^* , Aphane Koko Pithmajor ¹

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¹ University of Johannesburg, SOUTH AFRICA^* Corresponding Author

Abstract

Many Grade 9 mathematics learners face difficulties in solving number-pattern problems due to insufficient exposure to strategies in solving such problems. The aim of this exploratory qualitative study was to investigate Grade 9 mathematics learners’ strategies in solving number-pattern problems. The problem-solving conceptual framework of Singer and Voica (2013) highlighting four indicators, namely decoding, representing, processing and implementing, underpinned the study. Ninety Grade 9 learners were purposively selected from three rural schools (30 from each school) to participate. Qualitative data were collected through a written activity and semi-structured one-on-one interviews. The study found that learners utilise four main strategies to solve number-pattern problems, namely (1) direct counting; (2) direct proportion; (3) recursive strategy; and (4) mental image representation. Knowledge about learners’ strategies can assist teachers in their pedagogies to teach number-pattern problems. The study adds to the research on problem solving, specifically pertaining to number patterns.

Keywords

learners
mathematics
number-pattern
problem solving
strategies

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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 7, Article No: em1862

https://doi.org/10.29333/ejmste/8252

Publication date: 10 May 2020

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Article Downloads: 3206

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References

Ahmad, A., Tarmizi, R. A., & Mawawi, M. (2010). Visual representations in mathematical word problem solving among Form Four students in Malacca. Procedia - Social and Behavioral Sciences, 8, 356-361. https://doi.org/10.1016/j.sbspro.2010.12.050
Akkan, Y. (2013). Comparison of 6th-8th graders’ efficiencies, strategies and representations regarding generalization patterns. Bolema: Boletim de Educação Matemática, 27(47), 703-732. https://doi.org/10.1590/S0103-636X201300040000
Anderson, J. (2009). Mathematics Curriculum Development and the Role of Problem Solving. 2009 National Biennial Conference of the Australian Curriculum Studies Association: Curriculum, 1-8. Retrieved from https://www.acsa.edu.au/pages/images/JudyAnderson-MathematicsCurriculumDevelopment.pdf
Barbosa, A., Vale, I., & Palhares, P. (2012). Pattern Tasks: Thinking processes used by 6th grade students. Revista Latinoamericana de Investigación En Matemática Educativa, 15(3), 273-293. Retrieved from https://www.redalyc.org/jatsRepo/335/33524579002/html/index.html
Becker, J. R., & Rivera, F. (2005). Generalization strategies of beginning high school algebra students. In H. Chick & J. L. Vincent (Eds.), Proceeding of the 29th Conference of the International Group for the Psychology of Mathematics Education (pp. 121-128). Melbourne, Australia: University of Melbourne. Retrieved from https://www.emis.de/proceedings/PME29/PME29RRPapers/PME29Vol4RossiBeckerRivera.pdf
Biddlecomb, B., & Carr, M. (2011). A longitudinal study of the development of mathematics strategies and underlying counting schemes. International Journal of Science and Mathematics Education, 9(1), 1-24. https://doi.org/10.1007/s10763-010-9202-y
Boonen, A. J. H., van der Schoot, M., van Wesel, F., de Vries, M. H., & Jolles, J. (2013). What underlies successful word problem solving? A path analysis in sixth grade students. Contemporary Educational Psychology, 38(3), 271-279. https://doi.org/10.1016/j.cedpsych.2013.05.001
Clement, J. J. (2008). Does decoding increase word problem solving skills? (University of Nebraska-Lincoln, Lincoln, NE). Retrieved from https://digitalcommons.unl.edu/mathmidactionresearch/32/
Department of Basic Education. (2011). Curriculum and Assessment Policy Statement: Further Education and Training Phase. Grades 10-12 Mathematical Literacy. Retrieved from https://www.education.gov.za/Portals/0/CD/NationalCurriculumStatementsandVocational/CAPSFET_MATHEMATICALLITERACY_GR10-12_Web_DDA9.pdf?ver=2015-01-27-154330-293
Duru, A., Peker, M., Bozkurt, E., Akgün, L., & Bayrakdar, Z. (2011). Pre-service primary school teachers’ preference of the problem solving strategies for word problems. Procedia - Social and Behavioral Sciences, 15, 3463-3468. https://doi.org/10.1016/j.sbspro.2011.04.319
Garcia-Cruz, J. A. A., & Martinon, A. (1997). Actions and invariant in schemata in linear generalising problems. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education (pp. 289-286). Retrieved from https://jagcruz.webs.ull.es/Articulos/pme97.pdf
Govender, V. G. (2012). Using the South African mathematics challenge to develop pre-service mathematics teachers’ problem-solving abilities. In M. Lebitso, & A. Maclean (Eds.), 20th Annual National Congress of the Association for Mathematics Education of South Africa (AMESA): Demystifying mathematics (pp. 87-104). Kimberley, South Africa: AMESA. Retrieved from http://www.amesa.org.za/AMESA2014/Proceedings/images/Front%20Matter%202014%20AMESA.pdf
Güner, P., Ersoy, E., & Temiz, T. (2013). 7th and 8th Grade students’ generalization strategies of patterns. International Journal of Global Education, 2(4), 39-54. Retrieved from http://www.ijtase.net/ojs/index.php/ijge/article/view/284/348
Ibrahim, B., & Rebello, N. S. (2013). Role of mental representations in problem solving: Students’ approaches to nondirected tasks. Physical Review Special Topics - Physics Education Research, 9(2), 1-17. https://doi.org/10.1103/PhysRevSTPER.9.020106
Jan, S., & Rodrigues, S. (2012). Students’ difficulties in comprehending mathematical word problems in English language learning contexts. International Researchers, 1(3), 152-160. Retrieved from http://www.iresearcher.org/150-160 Salma.pdf
Jupri, A., & Drijvers, P. (2016). Student Difficulties in Mathematizing Word Problems in Algebra. EURASIA Journal of Mathematics, Science & Technology Education, 12(10), 2481-2502. https://doi.org/10.12973/eurasia.2016.1299a
Jurdak, M. E., & El Mouhayar, R. R. (2014). Trends in the development of student level of reasoning in pattern generalization tasks across grade level. Educational Studies in Mathematics, 85(1), 75-92. https://doi.org/10.1007/s10649-013-9494-2
Killen, R. (2007). Teaching strategies for outcomes-based education (2nd ed.). Cape Town: Juta.
Lannin, J., Barker, D., & Townsend, B. (2006). Algebraic generalisation strategies: Factors influencing student strategy selection. Mathematics Education Research Journal, 18(3), 3-28. https://doi.org/10.1007/BF03217440
Liljedahl, P. (2004). Repeating pattern or number pattern: The distinction is blurred. Focus on Learning Problems in Mathematics, 26(3), 24-42. Retrieved from http://www.peterliljedahl.com/wp-content/uploads/JA-FLPM-2004.pdf
Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem Solving in Mathematics Education. In Problem Solving in Mathematics Education. ICME-13 Topical Surveys. (pp. 1-39). https://doi.org/10.1007/978-3-319-40730-2_1
Mahlobo, N., & Nthombela, R. (2014). How I teach patterns in a Grade one class. In M. Lebitso & A. Maclean (Eds.), The 20th Annual National Congress of the Association for Mathematics of South Africa: Demystifying mathematics (pp. 186-189). Retrieved from http://www.amesa.org.za/AMESA2014/Proceedings/images/FrontMatter2014AMESA.pdf
Maluleka, B. K. (2013). Improving Grade 9 learners’ mathematical processes of solving word problems. (Master’s dissertation). University of Limpopo, Mankweng, South Africa. Retrieved from http://hdl.handle.net/10386/965
Schumacher, R. F., & Fuchs, L. S. (2012). Does understanding relational terminology mediate effects of intervention on compare word problems? Journal of Experimental Child Psychology, 111(4), 607-628. https://doi.org/10.1016/j.jecp.2011.12.001
Singer, F. M., & Voica, C. (2013). A problem-solving conceptual framework and its implications in designing problem-posing tasks. Educational Studies in Mathematics, 83(1), 9-26. https://doi.org/10.1007/s10649-012-9422-x
Tambychik, T., & Meerah, T. S. M. (2010). Students’ Difficulties in Mathematics Problem-Solving: What do they Say? Procedia - Social and Behavioral Sciences, 8, 142-151. https://doi.org/10.1016/j.sbspro.2010.12.020
Van Staden, S., & Motsamai, P. (2017). Differences in the quality of school-based assessment: Evidence in Grade 9 mathematics achievement. Pythagoras, 38(1), a367. https://doi.org/10.4102/pythagoras.v38i1.367

How to cite this article

APA

Spangenberg, E. D., & Pithmajor, A. K. (2020). Grade 9 Mathematics Learners’ Strategies in Solving Number-Pattern Problems. Eurasia Journal of Mathematics, Science and Technology Education, 16(7), em1862. https://doi.org/10.29333/ejmste/8252

Vancouver

Spangenberg ED, Pithmajor AK. Grade 9 Mathematics Learners’ Strategies in Solving Number-Pattern Problems. EURASIA J Math Sci Tech Ed. 2020;16(7):em1862. https://doi.org/10.29333/ejmste/8252

AMA

Spangenberg ED, Pithmajor AK. Grade 9 Mathematics Learners’ Strategies in Solving Number-Pattern Problems. EURASIA J Math Sci Tech Ed. 2020;16(7), em1862. https://doi.org/10.29333/ejmste/8252

Chicago

Spangenberg, Erica Dorethea, and Aphane Koko Pithmajor. "Grade 9 Mathematics Learners’ Strategies in Solving Number-Pattern Problems". Eurasia Journal of Mathematics, Science and Technology Education 2020 16 no. 7 (2020): em1862. https://doi.org/10.29333/ejmste/8252

Harvard

Spangenberg, E. D., and Pithmajor, A. K. (2020). Grade 9 Mathematics Learners’ Strategies in Solving Number-Pattern Problems. Eurasia Journal of Mathematics, Science and Technology Education, 16(7), em1862. https://doi.org/10.29333/ejmste/8252

MLA

Spangenberg, Erica Dorethea et al. "Grade 9 Mathematics Learners’ Strategies in Solving Number-Pattern Problems". Eurasia Journal of Mathematics, Science and Technology Education, vol. 16, no. 7, 2020, em1862. https://doi.org/10.29333/ejmste/8252