Addressing mathematics learning challenges through concept-based instruction: A study in Limpopo Province, South Africa

Mildret Ncube; Kakoma Luneta

doi:10.31129/LUMAT.12.4.2319

Authors

Mildret Ncube University of Johannesburg, South Africa https://orcid.org/0009-0005-0530-8148
Kakoma Luneta University of Johannesburg, South Africa https://orcid.org/0000-0001-9061-0416

DOI:

https://doi.org/10.31129/LUMAT.12.4.2319

Keywords:

concept, conceptual understanding, procedural understanding, concept-based instruction, constructivism

Abstract

Continuous poor performance of learners in mathematics motivated the study reported in this paper. The purpose of the study was to investigate the challenges that concept-based instruction could address in trying to improve learners’ performance in mathematics by equipping them with conceptual understanding. The study adopted a qualitative case study design approach that involved an interpretivist paradigm. Tests, questionnaires and semi-structured interviews were the data sources of this inquiry. Constructivism theoretically underpinned this study in a bid to bring up the importance of creating knowledge for oneself through linking new information to prior knowledge. The study involved 35 learners who were purposefully selected from a township school in Limpopo Province, South Africa. All the 35 learners wrote the test twice and completed a questionnaire. Six learners were selected for interviews for clarification of how they had arrived at their solutions and provision of more information. The study revealed the following mathematics learning challenges: poor mathematics background; too many rules and long steps involved; boredom and attitude; educator’s pace versus learners’ pace; and lack of variety of activities to reduce boredom. It was concluded that concept-based instruction has the potential to address challenges encountered by learners in learning mathematics.

References

Achmetli, K., Schukajlow, S. & Rakoczy, K. (2019). Multiple solutions for real-world problems, experience of competence and students’ procedural and conceptual knowledge. International Journal of Science and Mathematics Education, 17, 1605–1625.

Adak, S. (2017). Effectiveness of Constructivist Approach on Academic Achievement in Science at Secondary Level. Educational Research and Reviews, 12(22), 10741079.

Ala-Mutka, K. (2011). Mapping digital competence: Towards a conceptual understanding. Sevilla: Institute for Prospective Technological Studies, 7–60.

Al-Qatawneh, K.S. (2012). Effect of concept-based curriculum and instruction on motivating learners of English as a foreign language. Science Journal of Psychology, 2012.

Andamon, J., & Tan, D.A. (2018). Conceptual understanding, attitude and performance in mathematics of grade 7 students. International Journal of Scientific & Technology Research, 7(8), 96–105.

Assem, H. D., Nartey, L., Appiah, E., & Aidoo, J. K. (2023). A review of students’ academic performance in physics: Attitude, instructional methods, misconceptions and teachers qualification. European Journal of Education and Pedagogy, 4(1), 84–92. https://doi.org/10.24018/ejedu.2023.4.1.551

Attard, C. (2012). Applying a framework for engagement with mathematics in the primary classroom. Australian Primary Mathematics Classroom, 17(4), 22–27.

Balta, J.Y., Supple, B., & O'Keeffe, G.W. (2021). The universal design for learning framework in anatomical sciences education. Anatomical Sciences Education, 14(1), 71–78.

Borji, V., Radmehr, F., & Font, V. (2021). The impact of procedural and conceptual teaching on students' mathematical performance over time. International Journal of Mathematical Education in Science and Technology, 52(3), 404–426.

Brown, A.L., & Palincsar, A.S. (2018). Guided, cooperative learning and individual knowledge acquisition (pp. 393–451). Routledge.

Brussow, J. A., Roberts, K., Scaruto, M., Sommer, S., & Mills, C. (2019). Concept-based curricula: A national study of critical concepts. Nurse Educator, 44(1), 15.

Buehl, D. (2023). Classroom strategies for interactive learning. Routledge. https://doi.org/10.4324/9781032680842.

Cevikbas, M., & Kaiser, G. (2020). Flipped classroom as a reform-oriented approach to teaching mathematics. Zdm, 52(7), 1291–1305.

Chand, S., Chaudhary, K., Prasad, A., & Chand, V. (2021). Perceived Causes of Students' Poor Performance in Mathematics: A Case Study at Ba and Tavua Secondary Schools. Frontiers in Applied Mathematics and Statistics, NA-NA.

Chappell, K. K., & Kilpatrick, K. (2003). Effects of concept-based instruction on students’ conceptual understanding and procedural knowledge of calculus. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 13(1), 17–3.

Chew, S. L., & Cerbin, W. J. (2021). The cognitive challenges of effective teaching. The Journal of Economic Education, 52(1), 17–40. https://doi.org/10.1080/00220485.2020.1845266.

Clark, K. R. (2018). Learning theories: constructivism. Radiologic Technology, 90(2), 180–182.

Chinn, S. (2020). The trouble with maths: A practical guide to helping learners with numeracy difficulties. Routledge.

Colgan, L. (2014). Hey, It's Elementary-Improving Mathematics Achievement With (Im) Possible Thoughts. Gazette-Ontario Association for Mathematics, 52(4), 15.

Demby, A. (1997). Algebraic procedures used by 13-to-15-year-olds. Educational Studies in Mathematics, 33(1), 45–70.

Dignath, C., & Buttner, G. (2018). Teachers’ direct and indirect promotion of self-regulated learning in primary and secondary school mathematics classes–insights from video-based classroom observations and teacher interviews. Metacognition and Learning, 13(2), 127–157.

Durmus, S. & Karakirik, E. (2006). Virtual Manipulatives in Mathematics Education: A Theoretical Framework. Turkish Online Journal of Educational Technology-TOJET, 5(1), 117–123.

Erickson, F. (2012). Qualitative research methods for science education. In Second International Handbook of Science Education (pp. 1451–1469). Springer, Dordrecht.

Filippello, P., Buzzai, C., Messina, G., Mafodda, A. V., & Sorrenti, L. (2020). School refusal in students with low academic performances and specific learning disorder. The role of self-esteem and perceived parental psychological control. International Journal of Disability, Development and Education, 67(6), 592–607.

Fair, D. L., & Stott, A. E. (2021). A Longitudinal case study of mathematics and mathematical literacy achievement of boys at a high quintile school in South Africa. African Journal of Research in Mathematics, Science and Technology Education, 25(2), 137–147. https://doi.org/10.1080/18117295.2021.1932331

Ghazali, N. H. C., & Zakaria, E. (2011). Students’ procedural and conceptual understanding of mathematics. Australian Journal of Basic and Applied Sciences, 5(7), 684–691.

Giddens, J. F. (2019). Concepts for Nursing Practice E-Book. Elsevier Health Sciences.

Godino, J. D. (1996, July). Mathematical concepts, their meanings and understanding. In PME Conference (Vol. 2, pp. 2–417). The Program Committee of the 18th PME Conference.

Guner, N. (2020). Difficulties Encountered by High School Students in Mathematics. International Journal of Educational Methodology, 6(4), 703–713.

Gutknecht, A. J., Wibral, M., & Makkeh, A. (2021). Bits and pieces: Understanding information decomposition from part-whole relationships and formal logic. Proceedings of the Royal Society A, 477(2251), 20210110.

Higgins, B., & Reid, H. (2017). Enhancing “conceptual teaching/learning” in a concept-based curriculum. Teaching and Learning in Nursing, 12(2), 95–102.

Iji, C., Abah, J., & Anyor, J. (2018). Educational Cloud Services and the Mathematics Confidence, Affective Engagement, and Behavioral Engagement of Mathematics Education Students in Public Universities in Benue State, Nigeria. International Journal of Teaching and Learning in Higher Education, 30(1), 47–60.

Isaqjon, T. (2022). Strategies and techniques for improving EFL learners’ reading skills. https://doi.org/10.5281/zenodo.7277769.

Jacinto, H., & Carreira, S. (2023). Knowledge for teaching mathematical problem-solving with technology: An exploratory study of a mathematics teacher’s proficiency. European Journal of Science and Mathematics Education, 11(1), 105–122.

Jesionkowska, J., Wild, F., & Deval, Y. (2020). Active learning augmented reality for STEAM education—A case study. Education Sciences, 10(8), 198. https://www.mdpi.com/journal/education.

Kaufman, D. M. (2018). Teaching and learning in medical education: How theory can inform practice. Understanding medical education: Evidence, theory, and practice, 37–69.

Kacerja, S. (2012). Real-life contexts in mathematics and students’ interests: An Albanian study. Doctoral thesis. University of Agder. http://hdl.handle.net/11250/139703

Keller, L., Cortina, K. S., Müller, K., & Miller, K. F. (2022). Noticing and weighing alternatives in the refection of regular classroom teaching: Evidence of expertise using mobile eye-tracking. Instructional Science, 50(2), 251–272. https://doi.org/10.1007/s11251-021-09570-5.

Kenedi, A. K., Helsa, Y., Ariani, Y., Zainil, M., & Hendri, S. (2019). Mathematical Connection of Elementary School Students to Solve Mathematical Problems. Journal on Mathematics Education, 10(1), 69–80.

Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. Second Handbook of Research on Mathematics Teaching and Learning, 2, 707–762.

Kleine, C. (2019). Premodern Intercultural and Interreligious Dialogues and the Formation of Comparative Concepts: How Encounters Between European missionaries and Japanese in the 16th and 17th centuries changed the conceptual world. Part I. NotaBene, 44.

Korn, J. (2014). Teaching conceptual understanding of mathematics via a hands-on approach.

Kunwar, R., Shrestha, B. K., & Sharma, L. (2021). Are Teachers Aware of Mathematics Learning Disabilities? Reflections from Basic Level Schoolteachers of Nepal. European Journal of Educational Research, 10(1), 367–380.

Mahlangu, T. (2021). The role of mathematical tasks in providing Grade 10 learners an opportunity to learn trigonometry (Master's thesis, University of Pretoria (South Africa).

Makhubele, Y., & Luneta, K. (2014). Factors attributed to poor performance in grade 9 mathematics learners’ secondary analysis of Annual National Assessments (ANA). In ISTE International Conference on Mathematics, Science and Technology Education (pp. 56–69).

Martin, A. J., & Evans, P. (2018). Load reduction instruction: Exploring a framework that assesses explicit instruction through to independent learning. Teaching and Teacher Education, 73, 203–214.

Mazana, Y. M., Suero Montero, C., & Olifage, C. R. (2019). Investigating students' attitude towards learning mathematics.

Mbewe, T. L. (2013). Misconceptions and errors in Algebra at Grade 11 level (Doctoral dissertation, Masters dissertation. University of Lusaka, Zambia).

Meng, Y., Qasem, S. N., & Shokri, M. (2020). Dimension reduction of machine learning-based forecasting models employing Principal Component Analysis. Mathematics, 8(8), 1233.

Metsapelto, R. L., Zimmermann, F., Pakarinen, E., Poikkeus, A. M., & Lerkkanen, M.K. (2020). School grades as predictors of self-esteem and changes in internalizing problems: A longitudinal study from fourth through seventh grade. Learning and Individual Differences, 77, 101807.

Michael, I. (2015). Factors Leading to Poor Performance in Mathematics Subject in Kibaha Secondary Schools (Doctoral dissertation, The Open University of Tanzania).

Mutodi, P. & Ngirande, H. (2014). The influence of students’ perceptions on Mathematics performance. A case of a selected high school in South Africa. Mediterranean Journal of Social Sciences, 5(3), 431.

Mutsvangwa, S. B. (2016). The influence of using a scientific calculator in learning fractions: a case study of one school in Gauteng Province (Doctoral dissertation).

Ncube, M. (2016). Analysis of errors made by learners in simplifying algebraic expressions at grade 9 level (Doctoral dissertation, University of South Africa).

Nett, U. E., Goetz, T., & Daniels, L. M. (2010). What to do when feeling bored? Students' strategies for coping with boredom. Learning and Individual Differences, 20(6), 626638.

Nerantzi, C. (2020). The use of peer instruction and flipped learning to support flexible blended learning during and after the COVID-19 Pandemic. International Journal of Management and Applied Research, 7(2), 184–195. http://ijmar.org/v7n2/20-013.html.

Novrian, Milda. & Surya, Edy. (2017). "Analysis of Student Difficulties in Mathematics Problem Solving Ability at MTs SWASTA IRA Medan". International 158 Journal of Basic Sciences and Applied Research (IJSBAR). 33 (3): 63–75.

Nugroho, K. Y. (2017). Constructivist learning paradigm as the basis on learning model development. Journal of Education and Learning, 11(4), 410415.

Ntow, F. D., & Hissan, Y. (2021). The impact of concept-based instruction on senior high school students’ achievement in circle theorems. African Journal of Educational Studies in Mathematics and Sciences, 17(1), 113–132.

Ojaleye, O., & Awofala, A. O. (2018). Blended Learning and Problem-Based Learning Instructional Strategies as Determinants of Senior Secondary School Students' Achievement in Algebra. International Journal of Research in Education and Science, 4(2), 486–501.

Omoniyi, A. A. (2016). Impact of constructivist instructional approach on grade12 learner's understanding of stationary points in differential calculus (Doctoral dissertation).

Ornstein, P. A., Shapiro, L. R., Clubb, P. A., Follmer, A., & Baker-Ward, L. (2018). The influence of prior knowledge on children’s memory for salient medical experiences. In Memory for everyday and emotional events (pp. 83–111). Routledge.

Owusu, J. (2015). The Impact of Constructivist-based Teaching Method: On Secondary School Learners' Errors in Algebra (Doctoral dissertation, University of South Africa).

Özreçberoğlu, N., & Çağanağa, Ç. K. (2018). Making it count: Strategies for improving problem-solving skills in mathematics for students and teachers’ classroom management. Eurasia Journal of Mathematics, Science and Technology Education, 14(4), 1253–1261.

Rahman, S., & Md Hassan, N. (2017). Problem solving skills, metacognitive awareness, and mathematics achievement: A mediation model. The New Educational Review, 49, 201-212.

Rameli, M. R. M., & Kosnin, A. M. (2016). Challenges in mathematics learning: a study from school students' perspective. Universiti Teknologi Malaysia.

Reddy, V., Winnaar, L., Arends, F., Juan, A., Harvey, J., Hannan, S., & Isdale, K. (2022). The South African TIMSS 2019 Grade 9 Results: Building Achievement and Bridging Achievement Gaps. HSRC Press, Cape Town. http://hdl.handle.net/20.500.11910/19286.

Rittle-Johnson, B., & Schneider, M. (2015). Developing conceptual and procedural knowledge of mathematics. Oxford handbook of numerical cognition, 1118–1134.

Roling, L. T., Choksi, T. S., & Abild-Pedersen, F. (2019). A coordination-based model for transition metal alloy nanoparticles. Nanoscale, 11(10), 4438–4452.

Ross, J. G., & Myers, S. M. (2017). The current use of social media in undergraduate nursing education: A review of the literature. CIN: Computers, Informatics, Nursing, 35(7), 338–344.

Saez-Lopez, J. M., Sevillano-García, M. L., & Vazquez-Cano, E. (2019). The effect of programming on primary school students’ mathematical and scientific understanding: Educational use of mBot. Educational Technology Research and Development, 67(6), 1405–1425.

Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 22-26.

Semilarski, H., Laius, A., & Rannikmäe, M. (2019). Development of Estonian Upper Secondary School Students' Biological Conceptual Understanding and Competences. Journal of Baltic Science Education, 18(6), 955–970.

Simonsmeier, B. A., Flaig, M., Deiglmayr, A., Schalk, L., & Schneider, M. (2018). Domain-specific prior knowledge and learning: A meta-analysis. Research Synthesis 2018, Trier, Germany.

Singha, K. G., Goswami, M., & Bharali, R. K. (2012). Study of various problems faced by the students and teachers in learning & teaching mathematics and their suggestive measures. International Journal of Advanced Research in Management and Social Sciences, 1(2), 195–201.

Sullivan, P., & McDonough, A. (2007). Eliciting positive student motivation for learning mathematics. Mathematics: Essential Research, Essential Practice, 2, 698–707.

Swanson, J. A. (2020). Assessing the effectiveness of the use of mobile technology in a collegiate course: A case study in M-learning. Technology, Knowledge and Learning, 25(2), 389–408.

Taley, I. B., & Ndamenenu, D. K. (2022). The Phobia and Contentment for Mathematics. What Context Factors Can Do?. Open Access Library Journal, 9(4), 1–21.

Thompson, P. W. (2020). Constructivism in mathematics education. In Encyclopedia of mathematics education (pp. 127–134). Cham: Springer International Publishing.

Watling, C. J., & Ginsburg, S. (2019). Assessment, feedback and the alchemy of learning. Medical Education, 53(1), 76-85.

Watson, G.A. (2007). Robust counterparts of errors-in-variables problems. Computational Statistics & Data Analysis, 52(2), 1080–1089.

Widyastuti, R., Anggoro, B. S., Negara, H. S., Yuliani, M. D., & Utami, T. N. (2020, February). Understanding mathematical concept: The effect of savi learning model with probing-prompting techniques viewed from self-concept. Journal of Physics: Conference Series (Vol. 1467, No. 1, p. 012060). IOP Publishing.

Yang, D. C., & Sianturi, I. A. J. (2021). Sixth grade students’ performance, misconception, and confidence on a three-tier number sense test. International Journal of Science and Mathematics Education, 19(2), 355–375. doi:10.1007/s10763-020-10051-3

Yasmin, M., Sohail, A., Sarkar, M., & Hafeez, R. (2017). Creative methods in transforming education using human resources. Creativity Studies, 10(2), 145158.

Yong, S.T., Gates, P., & Chan, A.T.Y. (2018). A gaming perspective on mathematics education. International Journal of Information and Communication Technology Education (IJICTE), 14(4), 85–98.

Yurekli, B., Stein, M. K., Correnti, R., & Kisa, Z. (2020). Teaching mathematics for conceptual understanding: Teachers’ beliefs and practices and the role of constraints. Journal for Research in Mathematics Education, 51(2), 234–247.

Zain, S.F.H.S., Rasidi, F.E.M., & Abidin, I.I.Z. (2012). Student-centred learning in mathematics-constructivism in the classroom. Journal of International Education Research, 8(4), 319.