Comparing grades 10 – 12 mathematics learners’ non-routine problem solving

David Mogari; Munyaradzi Chirove

doi:10.12973/eurasia.2017.00946a

Full Text (PDF)

David Mogari ¹ ^* , Munyaradzi Chirove ¹ ^*

More Detail

¹ University of South Africa, South Africa
^* Corresponding Author

Abstract

The study, which is derived from a larger study, compares grades 10 – 12 mathematics learners’ non-routine problem solving. An exploratory study was conducted on a convenience sample drawn from three high performing high schools located in Tshwane North District, Gauteng province of South Africa.Learners wrote a non-routine problem solving test. Findings revealed that the 11th grade learners obtained the highest mean score while that of the 10th grade learners was the lowest. High school learners’ level of strategy use on solving non-routine problems improved significantly as they progress from grade 10 to higher grades. No significant difference was discovered as learners progress from grade 11 to 12.

Keywords

non-routine problems
non-routine mathematical problem solving
and problem solving strategies

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

https://doi.org/10.12973/eurasia.2017.00946a

EURASIA J Math Sci Tech Ed, 2017 - Volume 13 Issue 8, pp. 4523-4551

Publication date: 21 Jul 2017

Article Views: 3773

Article Downloads: 3787

Open Access References How to cite this article

References

AMESA (2013). A report on the 2013 Mathematics & Mathematical Literacy Grade 12 Examination Papers. Retrieved from www.amesa.org.za on 2014/07/31.
Arslan, C. & Altun, M. (2007). Learning to solve non-routine mathematical problems. Elementary Education Online 6(1), 50-66.
Bansilal, S., Brijlall, D., & Mkhwanazi, T. (2014). An exploration of common content knowledge of high school mathematics teachers. Perspectives in Education 32(1), 30 – 46.
Branca, N. A. (1980). Problem solving as a Goal, Process and Basic Skill. In Krulik, S, & Rey, R. E. Problem solving in school mathematics, National Council of Teachers of Mathematics, 1980 Yearbook. Virginia: NCTM.
Brunning, R. H., Schraw, G. J., & Ronning, R. R. (1999). Cognitive Psychology and instruction (3rd Ed.). New Jersey: Prentice-Hall Inc.
Carson, J. (2007). A problem with problem solving: Teaching thinking without teaching knowledge. The Mathematics Educator 17(2), 7-14.
CDE (2013). Mathematics outcomes in South African schools: What are the facts? What should be done? CDE Insights. Johannesburg: Centre for Development and Enterprise.
Cherry, K. (2011). What is problem-solving? Retrieved from http://psychology.about.com/od/problemsolving/f/problem-solving-steps.htm on 2011/06/29.
Depaepe, F. (2009). The culture and practices in sixth-grade mathematics classrooms: An attempt to unravel relationships between social and individual aspects in problem-solving lessons. Retrieved fromhttp://lirias-kuleuven.be/bitstream/.../233766/.../doctoraat+Fien+Depaepe.pdf on 2011/03/29.
Department of Basic Education (2011). Curriculum and Assessment Policy Statement Grades 10-12: Mathematics. Pretoria: Government Press.
Department of Basic Education (2014). Report on the annual national assessments of 2014: Grade 1-6 & 9. Pretoria: Government Press.
Department of Basic Education (2015). National senior certificate examinations 2015. diagnostic report. www.education.gov.za.
Department of Basic Education (2016). National senior certificate examinations 2016. diagnostic report. www.education.gov.za.
Elia, I., Van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics.ZDM Mathematics Education, 41: 605-618.
Engel, A. (1998). Problem-solving strategies. New York: Springer-verlag.
Ewen, I. (1996). Strategies for problem solving. In Posameties, A. S., & Schulz, W. The art of problem solving: A resource for the mathematics teacher. California: Corwin Press, Inc.
Gilfeather, M., & Regass, J. (1999). Routine and non-routine problem solving; Mathematics experience based approach (MEBA); Pentathlon Institute, Inc.
Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spartial representations and mathematical problem solving.Journal of Educational Psychology, 91(4), 684-689.
HSRC (2012). Towards equity and excellence.Highlights from TIMSS 2011: SA Perspective. Pretoria: HSRC Press.
Kirkley, J. (2003). Principles of teaching problem solving; Technical Paper #4.doi:10.1.1.117.8503.
Kolovou, A., Van den Heuvel-Panhuizen, M., Bakker, A., & Elia, I. (2011). An ICT environment to assess and support students’ mathematical problem-solving performance in non-routine puzzle-like word problems. ICME 11.
Lester, F. K. (2013). Thoughts about research on mathematical problem-solving instruction. The Mathematics Enthusiast, 10(1/2), 245-278.
Logsdon, A. (2007). How to solve math word problems- learn the SQRQCQ strategy to solve math problems. Retrieved from http://learningdisadisabilities.about.com/od/insttructionalmaterials/ht /sqrqcq.html on 2011/04/01.
Lucangeli, D., & Cabrele, S. (2006). The relationship of metacognitive knowledge, skills and beliefs in children with and without mathematics learning disabilities. In A. Desoete& M. Veenman (eds). Metacognition in Mathematics Education. New York: Nova Science Publishers, Inc.
Mabilangan, R. A., Limjap, A. A., &Belecina, R. R. (2011). Problem solving strategies of high school students on non-routine problems: A case study. Journal of Basic Education, 5, 23-46.
Malouff, J. (2011). Psychology-Over fifty problem solving solvingstrategies explained. Retrieved from http://www.une.edu.au/bcss/psychology/john.malouff/problem-solving.php on 2011/04/01.
Maree, K., Aldous, C., Hattingh, A., Swanepoel, A, & Van der Linde, M. (2006). Predictors of learner performance in mathematics and science according to a large-scale study in Mpumalanga.South African Journal of Education, 26(2), 229-252.
Mogari, D., & Lupahla, N. (2013). Mapping a group of Northern Namibian grade 12 learners’ algebraic non-routine problem solving skills.African Journal of Research in Mathematics, Science and Technology Education, 17(1/2), 94-105.
Muis, K. R. (2004). Epistemic styles and mathematics problem solving: Examining relations in the context of self –regulated learning. Retrieved from http://ir.lib.sfu.ca/bitstream/1892/9935/1/b37359599.pdf on 2011/03/30.
Muller, R. (2014). Truth about SA’s mathematics, science education quality. Retrieved May 18 2016 from http://mybroadband.co.za/news/government/103677-truth-about-sas....
National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
OECD (2009). Pisa 2009 assessment framework – key competencies in reading, mathematics and science. Paris: OECD.
Polya, G. (1985). How to solve it (2nded). Princeton, NJ: Princeton University Press.
Russell, D. (2007). Problem solving strategies. Retrieved April 01 2011 from http://math.about.com/cs/testprep/∞/ps.html.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In Grouws, D. A. (Ed.). Handbook for research on mathematics teaching and learning (pp. 334-370). New York: Macmillan.
Stephenson, D. (2001). Math problem solving techniques: Eighty problem solving strategies and practice activities for 9 to 12 year olds. Greenwood, WA: Ready-Ed Publishers. ISBN: 186397 1106.
Van den Heuvel-Panhuizen, M., Kolovou & Robitzsch, A. (2013). Primary school students’ strategies in early algebra problem solving supported by an online game. Educational Studies in Mathematics 84: 281 – 307.
Webb, N.L. (2010). Content complexity and depth-of-knowledge as applicable to research and practice. In D. Mogari; A. Mji; F. Mundalamo & U.I. Ogbonnaya (eds). Proceedings of ISTE2010 International Conference: Towards Effective Teaching and Meaningful Learning in MST, pp. 1 – 19.
Yazgan, Y. (2013). Non-routine mathematical problem-solving at high school level and its relation with success on university entrance exam. US-China Education Review 3(8): 571 – 579.
Yazgan, Y. (2015). Sixth graders and non-routine problems: Which strategies are decisive for success? Academic journals. Vol. 10(13), pp. 1807-1816.
Zanzali, N. A. A., & Nam, L. L. (1997). Evaluating the levels of problem solving abilities in mathematics. Retrieved April 01 2011 from http://math.unipa.it/~grim/jzanzalinam.PDF.

How to cite this article

APA

Mogari, D., & Chirove, M. (2017). Comparing grades 10 – 12 mathematics learners’ non-routine problem solving. Eurasia Journal of Mathematics, Science and Technology Education, 13(8), 4523-4551. https://doi.org/10.12973/eurasia.2017.00946a

Vancouver

Mogari D, Chirove M. Comparing grades 10 – 12 mathematics learners’ non-routine problem solving. EURASIA J Math Sci Tech Ed. 2017;13(8):4523-51. https://doi.org/10.12973/eurasia.2017.00946a

AMA

Mogari D, Chirove M. Comparing grades 10 – 12 mathematics learners’ non-routine problem solving. EURASIA J Math Sci Tech Ed. 2017;13(8), 4523-4551. https://doi.org/10.12973/eurasia.2017.00946a

Chicago

Mogari, David, and Munyaradzi Chirove. "Comparing grades 10 – 12 mathematics learners’ non-routine problem solving". Eurasia Journal of Mathematics, Science and Technology Education 2017 13 no. 8 (2017): 4523-4551. https://doi.org/10.12973/eurasia.2017.00946a

Harvard

Mogari, D., and Chirove, M. (2017). Comparing grades 10 – 12 mathematics learners’ non-routine problem solving. Eurasia Journal of Mathematics, Science and Technology Education, 13(8), pp. 4523-4551. https://doi.org/10.12973/eurasia.2017.00946a

MLA

Mogari, David et al. "Comparing grades 10 – 12 mathematics learners’ non-routine problem solving". Eurasia Journal of Mathematics, Science and Technology Education, vol. 13, no. 8, 2017, pp. 4523-4551. https://doi.org/10.12973/eurasia.2017.00946a