The relationship between grade 11 learners’ procedural and conceptual knowledge of algebra

Munyaradzi Chirove(1*), Ugorji Iheanachor Ogbonnaya(2)

(1) Department of Science, Mathematics & Technology Education, University of Pretoria, South Africa
(2) Department of Science, Mathematics & Technology Education, University of Pretoria, South Africa
(*) Corresponding Author

Abstract

The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners’ procedural and conceptual knowledge of algebra has not been well explored. This research paper examined the relationship between Grade 11 learners’ procedural and conceptual knowledge of algebra. Data for the study was collected using an algebra test administered to 181 grade 11 learners in Gauteng province, South Africa. Descriptive statistics and Pearson’s correlation coefficient were used to analyse the data in SPSS. The study revealed that the learners have low levels of both procedural and conceptual knowledge of algebra. However, they displayed better procedural knowledge than the conceptual knowledge of algebra. In addition, a statistically significant moderate positive linear relationship was found between the learners’ procedural and conceptual knowledge of algebra.

Keywords

Algebra, conceptual knowledge, procedural knowledge, mathematics, South Africa

Full Text:

PDF

References

Ai-Muatawah, M., Thomas, R., Eid, A., Mahmond, E. Y., & Fateel, M. J. (2019). Conceptual understanding, procedural knowledge and problem-solving skills in mathematics: High school graduates work analysis and standpoints. International journal of education and practice, 7(3), 258-273. https://doi.org/10.18488/journal.61.2019.73.258.273

Chinnappan, M., & Forrester, T. (2014). Generating procedural and conceptual knowledge of fractions by preservice teachers. Mathematics education research journal, 26(4), 871-896.

Crooks, N. M., & Alibali, M. W. (2014). Defining and measuring conceptual knowledge in mathematics. Developmental review, 34, 344-377.

Cummings, K. (2015). How does tutoring to develop conceptual understanding impact student understanding? In BSU Honors Program Theses and Projects, Item 96. Bridgewater: Bridgewater State University. Retrieved from http://vc.bridgewedu/honors_proj/96

De Jong, T., & Ferguson-Hestler, M. (1996). Types and qualities of knowledge. Educational psychologist, 31(2), 105-113. https://doi.org10.1207/s15326985ep3102_2

Department of Basic Education. (2019). Report on the 2019 national senior certificate diagnostic report, part 1. Gauteng, South Africa: Department of basic education.

Donevska-Todorova, A. (2016). Procedural and conceptual understanding in undergraduate linear algebra. First conference of international network for didactic research in university mathematics. Montpeller. Retrieved from https://hal.archives-ouvertertes.fr/hal-01337932

Egodawatte, G. (2011). Secondary school students’ misconceptions in Algebra. Unpublished doctoral thesis. Toronto: University of Toronto.

Egodawatte, G., & Stoilescu, D. (2015). Grade 11 students’ interconnected use of conceptual knowledge, procedural skills, and strategic competences in algebra: A mixed method study of error analysis. European journal of science and mathematics education, 3(3), 289-305. https://doi.org/10.30935/scimath/9438

Engelbrecht, J., Harding, A., & Potgieter, M. (2006). Undergraduate students’ performance and confidence in procedural and conceptual mathematics. International journal of mathematical education in science and technology, 36(7), 701-712. https://doi.org/10.1080/00207390500271107

Faulkenberry, E. (2003). Secondary mathematics preservice teachers' conceptions of rational numbers. Unpublished doctoral dissertation. Oklahoma: Oklahoma State University.

Figueras, H., Males, L., & Otten, S. (2008). Algebra students’ simplification of rational expressions. Retrieved February 27, 2016, from www.msu.edu

Forrester, P. A., & Chinnappan, M. (2010). The predominance of procedural knowledge in fractions. In I. Sparrow, B. Kissane, & C. Hurst, Shaping the future of mathematics education MERGA33 (pp. 185-192). Fremantle: Merga Inc.

Ghazali, N. H., & Zakaria, E. (2011). Students’ procedural and conceptual understanding of mathematics. Australian journal of basic and applied sciences , 5(7), 684-691.

Haapasalo, L., & Kadijevich, D. (2000). Two types of mathematical knowledge and their relation. Journal for mathematics education., 21(2), 139-157. https://doi.org/10.1007/bf03338914

Hardin, L. E. (2002). Educational strategies. Problem solving concepts and theories. Journal of veterinary medical education, 30(3), 227-230.

Hiebert, J. (2013). Conceptual and procedural knowledge: The case of mathematics. Routledge. https://doi.org/10.4324/9780203063538

Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert, Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Erlbaum.

Ho, T. M. (2020). Measuring conceptual understanding, procedural fluency and integrating procedural and conceptual knowledge in mathematical problem solving. International journal of scientific research and management, 8(5), 1334-1350. https://doi.org/10.18535/ijsrm/v8i05.el02

Hodgen, J., & Jones, I. (2013). Measuring conceptual understanding: The case of fractions . Proceedings of the 37th conference of the international group for the Psychology of Mathematics Education. Kiel, Germany: PME.

Huang, T., Liu, S., & Lin, C. (2007). Preservice teachers’ mathematical knowledge of fractions. Research in higher education journal, 1-8.

Hurrell, D. P. (2021). Conceptual knowledge OR Procedural knowledge OR Conceptual knowledge AND Procedural knowledge:Why the conjunction is important for teachers. Australian journal of teacher education, 46(2), 57-71. https://doi.org/10.14221/ajte.2021v46n2.4

Kadijevich, D. M. (2018). Relating procedural and conceptual knowledge. Teaching of mathematics, 21(1), 15-18.

Khashan, K. H. (2014). Conceptual and procedural knowledge of rational number for Riyadh elementary school teachers. Journal of education and human development, 3(4), 181-197. https://doi.org/10.15640/jehd.v3n4a17

Kieran, C. (2013). The false dichotomy in mathematics education between conceptual understanding and procedural skills: An example from algebra. In K. Leatham, Vital directions for mathematics education research. New York: Springer. https://doi.org/10.1007/978-1-4614-6977-3

Lenz, K., & Wittmann, G. (2021). Individual differences in conceptual and procedural fraction knowledge: What makes the difference and what does it look like? International electronic journal of mathematics education, 16(1), em0615. https://doi.org/10.29333/iejme/9282

Long, C. (2005). Mathematics concepts in teaching: Procedural and conceptual knowledge. Pythagoras(62), 59-65. https://doi.org/10.4102/pythagoras.v0i62.115

Mabilangan, R. A., Limjap, A. A., & Belecina, R. R. (2011). Problem solving strategies of high school students on non-routine problems: A case study. A journal of basic education., 5, 23-46.

Maulina, R., Zubainur, C. M., & Bahrun. (2020). Conceptual and procedural knowledge of junior high school students through realistic mathematics education (RME) approach. Journal of Physics: Conference series 1460 012017, 1-6. https://doi.org/10.1088/1742-6596/1460/1/012017

Nahdi, D. S., & Jatsunda, M. G. (2020). Conceptual understanding and procedural knowledge: A case study on learning mathematics of fractional material in elementary school. Journal of Physics: Conference series 1477 042037, 1-5. https://doi.org/10.1088/1742-6596/1477/4/042037

Ndemo, Z., & Ndemo, O. (2018). Secondary school students’ errors and misconceptions in learning algebra. Journal of education and learning, 12(4), 690-701. https://doi.org/10.11591/edulearn.v12i4.9556

Oregon department of Education. (1991). Oregon Mathematics problem solving rubrics. Retrieved May 29, 2021, from https://web.njit.edu/~ronkowit/presentations/ rubrics/samples/math_probsolv_chicago.pdf

Rittle-Johnson, B., & Alibali, M. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of educational psychology, 91(1), 175-189. https://doi.org/10.1037/0022-0663.91.1.175

Rittle-Johnson, B., & Schneider, M. (2012). Developing conceptual and procedural knowledge of mathematics. In R. Cohen Kadosh, & A. Dowker, Oxford handbook of numerical cognition. Oxford: University press.

Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of educational psychology, 93(2), 346-362. https://doi.org/10.1037//0022-0663.93.2.346

Schneider, M., & Stern, E. (2010). The developmental relations between conceptual and procedural knowledge: A multimethod approach. Developmental Psychology, 46(1), 178-192. https://doi.org/10.1037/a0016701

Schneider, M., Rittle-Johnson, B., & Star, J. R. (2011). Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge. Developmental psychology, 47(6), 1525-1538. https://doi.org/10.1037/a0024997

Schwartz, J. E. (2008). Elementary mathematics pedagogical content knowledge: Powerful ideas for teachers. Virginia: Allyn and Bacon.

Simpson, A., & Zakaria, N. (2004). Making the connection: Procedural and conceptual students’ use of linking words in solving problems. . Proceedings of the 28th conference of the international group for the psychology of mathematics education, 4, pp. 201-208.

Star, J. R. (2005). “Re-conceptualising” procedural knowledge. Journal for research in mathematics education, 36(5), 404-411.

Star, J. R. (2007). Foregrounding procedural knowledge. Journal for research in mathematics education, 38(2), 132-135.

Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J., McCallum, W. G., Porath, J., & Zbiek, R. M. (2015). Teaching strategies for improving algebra knowledge in middle and high school students (NCEE 2014-4333). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. Retrieved from http://whatworks.ed.gov

Star, J. R., & Seifert, C. (2006). The development of flexible procedural knowledge in equation solving. Contemporary educational psychology, 31(3), 280-300. https://doi.org/10.1016/j.cedpsych.2005.08.001

Star, J. R., & Stylianides, G. J. (2013). Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian journal of science, mathematics and technology education, 13(2), 169-181. https://doi.org/10.1080/14926156.2013.784828

Syam, A. S. (2019). How students understand the linear equation and inequalities (Factual, Conceptual, Procedural Knowledge). Proceedings of the 1st Vocational Education International Conference (VEIC 2019).379, pp. 119-125. Amsterdam: Atlantis Press SARL. https://doi.org/10.2991/assehr.k.191217.020

Tesfayi, A., Arefayne, N., & Micael, K. (2020). Early Grade Children Procedural and Conceptual Knowledge in Number Pattern Concept at Halaba. Developing Country Studies, 10(12), 1-8. https://doi.org/10.7176/DCS/10-12-01

Tularam, G. A., & Hulsman, K. (2013). A study of first year tertiary students’ mathematical knowledge- conceptual and procedural knowledge, logical thinking and creativity. Journal of mathematics and statistics, 9(3), 219-237. https://doi.org/10.3844/jmssp.2013.219.237

Zakaria, E., & Zaini, N. (2009). Conceptual and procedural knowledge of rational numbers in trainee teachers. European journal of social sciences, 9(2), 202-217.

DOI: 10.23917/jramathedu.v6i4.14785

Article Metrics

Abstract view(s): 549 time(s)
PDF: 401 time(s)

Refbacks

  • There are currently no refbacks.