Mathematical Language Errors and Academic Performance in Preservice Calculus Teachers
Relationship and Lived Experiences
Abstract
This study explores the impact of mathematical language errors (MLE) on the academic achievement of preservice calculus teachers, addressing the critical issue of how these errors impede mathematical understanding and performance. Conducted within the context of South Africa's education system, where effective mathematics instruction is vital for educational and economic development, this study aims to identify common mathematical language pitfalls, analyze their consequences, and propose strategies to mitigate these errors. An exploratory sequential mixed-methods design was employed, combining qualitative and quantitative approaches to understand the issue comprehensively. The study involved 120 preservice teachers divided into first and second-year cohorts. Data collection included qualitative analysis of student responses through thematic coding and quantitative analysis of assessment results using descriptive statistics, chi-square test, and ANOVA. Significant findings identified two major MLE types: incorrect terminology and ambiguous language errors, which were prevalent and significantly impacted academic performance. First-year students exhibited higher frequencies of these errors, correlating with lower academic scores than second-year students. Statistical analyses confirmed significant differences in error distribution and their impact on performance, highlighting the need for early and targeted interventions. The study contributes to the literature on mathematics education by highlighting the importance of mathematical language in education and provides evidence-based strategies for improving mathematical instruction. By addressing mathematical language errors through explicit instruction, interactive activities, and peer feedback, mathematics educators can enhance students' understanding and performance, ultimately fostering a more effective and inclusive learning environment.
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References
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Sapkota, Bima, and Amanda Huffman Hayes. 2024. “Preservice Teachers’ Mathematical Knowledge for Teaching: Focus on Lesson Planning and Reflection.” School Science and Mathematics. https://doi.org/10.1111/ssm.12644.
Tachie, Simon Adjei. 2020. “Teachers’ Attitudes towards Lesson Study as a Viable Strategy to Improve the Teaching and Learning of Mathematics.” Universal Journal of Educational Research 8 (6). https://doi.org/10.13189/ujer.2020.080616.
Taylor, Nick. 2021. “The Dream of Sisyphus: Mathematics Education in South Africa.” South African Journal of Childhood Education 11 (1). https://doi.org/10.4102/sajce.v11i1.911.
Venkat, Hamsa, and Mike Askew. 2021. “Development in South African Primary Mathematics Teacher Educators’ Work with In-Service Teachers.” International Journal of Science and Mathematics Education 19. https://doi.org/10.1007/s10763-021-10161-6.
??????, ?.?. 2023. “For the Purity of Mathematical Language.” Management of Education, no. 1(59). https://doi.org/10.25726/m2832-1698-0025-w.
Baidoo, J., Adane, M., & Luneta, K. 2020. “Solving Algebraic Fractions in High Schools: An Error Analysis.” Journal of Educational Studies 19 (2).
Baidoo, J. 2019. “Dealing With Grade 10 Learners’ Misconceptions and Errors When Simplifying Algebraic Fractions ’.” Journal of Emerging Trends in Educational Research and Policy Studies 10 (1).
Essien, A . 2021. “Rethinking Exemplification in Mathematics Teacher Education Multilingual Classrooms.” Exploring New Ways to Connect.
Essien, A. 2010. “Investigating Proficiency in the Language of Instruction as Means of Improving Mathematical Proficiency in a Multilingual Classroom.” Education as Change 14 (2). https://doi.org/10.1080/16823206.2010.518006.
Essien, A. 2021. “Understanding the Choice and Use of Examples in Mathematics Teacher Education Multilingual Classrooms.” ZDM - Mathematics Education 53 (2). https://doi.org/10.1007/s11858-021-01241-6.
Fetters, Michael D., and Chihiro Tajima. 2022. “Joint Displays of Integrated Data Collection in Mixed Methods Research.” International Journal of Qualitative Methods 21. https://doi.org/10.1177/16094069221104564.
Hill, Heather C., Deborah Loewenberg Ball, and Stephen G. Schilling. 2008. “Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-Specific Knowledge of Students.” Journal for Research in Mathematics Education 39 (4). https://doi.org/10.5951/jresematheduc.39.4.0372.
Hill, Heather C., Brian Rowan, and Deborah Loewenberg Ball. 2005. “Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement.” American Educational Research Journal 42 (2). https://doi.org/10.3102/00028312042002371.
Hirose, Mariko, and John W. Creswell. 2023. “Applying Core Quality Criteria of Mixed Methods Research to an Empirical Study.” Journal of Mixed Methods Research 17 (1). https://doi.org/10.1177/15586898221086346.
Ili, La. 2022. “Analysis of Students’ Misconceptions in Solving Mathematics Problems on Flat Construction Materials.” Eduvest - Journal Of Universal Studies 2 (3). https://doi.org/10.36418/edv.v2i3.388.
Johnson, Marysia. 2022. “8. Vygotsky’s Sociocultural Theory and Second Language Learning.” In A Philosophy of Second Language Acquisition. https://doi.org/10.12987/9780300129410-010.
Johnson, R. Burke, and Anthony J. Onwuegbuzie. 2007. “Toward a Definition of Mixed Methods Research.” Journal of Mixed Methods Research 1 (2). https://doi.org/10.1177/1558689806298224.
Jojo, Zingiswa. 2020. “Mathematics Education System in South Africa.” In Education Systems Around the World. https://doi.org/10.5772/intechopen.85325.
Joubert, Jody, Ronel Callaghan, and Johann Engelbrecht. 2020. “Lesson Study in a Blended Approach to Support Isolated Teachers in Teaching with Technology.” ZDM - Mathematics Education 52 (5). https://doi.org/10.1007/s11858-020-01161-x.
Khalo, Xolani, Emmanuel Olusola Adu, and Babawande Emmanuel Olawale. 2022a. “Language Difficulty as a Factor Related to Learner Errors in Financial Mathematics.” Eurasia Journal of Mathematics, Science and Technology Education 18 (10). https://doi.org/10.29333/ejmste/12407.
———. 2022b. “Language Difficulty as a Factor Related to Learner Errors in Financial Mathematics.” Eurasia Journal of Mathematics, Science and Technology Education 18 (10). https://doi.org/10.29333/ejmste/12407.
Ko, Inah, Vilma Mesa, Irene Duranczyk, Patricio Herbst, Nidhi Kohli, April Ström, and Laura Watkins. 2024. “Understanding the Characteristics of Mathematical Knowledge for Teaching Algebra in High Schools and Community Colleges.” International Journal of Mathematical Education in Science and Technology 55 (3). https://doi.org/10.1080/0020739X.2021.2006348.
Mahlaba, Sfiso Cebolenkosi. 2020. “The State of South African Mathematics Education: Situating the Hidden Promise of Multiple-Solution Tasks.” Eurasia Journal of Mathematics, Science and Technology Education 16 (12). https://doi.org/10.29333/ejmste/9279.
Makonye, J. P., and O. Matuku. 2016. “Exploring Learner Errors in Solving Quadratic Equations.” International Journal of Educational Sciences 12 (1). https://doi.org/10.1080/09751122.2016.11890407.
Makonye, Judah P., and Nageshwari Pam Moodley. 2023. “Connecting Mathematics to STEM Education: Interdisciplinary Teaching and Learning Facilitation.” ZDM - Mathematics Education 55 (7). https://doi.org/10.1007/s11858-023-01522-2.
Makonye, Judah Paul. 2012. “Learner Errors on Calculus Tasks in the NSC Examinations: Towards an Analytical Protocol for Learner Perturbable Concepts in Introductory Differentiation.” International Journal of Learning 18 (6). https://doi.org/10.18848/1447-9494/cgp/v18i06/47634.
McLachlan, Kathryn, and Anthony A. Essien. 2022. “Language and Multilingualism in the Teaching and Learning of Mathematics in South Africa: A Review of Literature in Pythagoras from 1994 to 2021.” Pythagoras 43 (1). https://doi.org/10.4102/pythagoras.v43i1.669.
Mooij, Susanne M.M. de, Iroise Dumontheil, Natasha Z. Kirkham, Maartje E.J. Raijmakers, and Han L.J. van der Maas. 2022. “Post-Error Slowing: Large Scale Study in an Online Learning Environment for Practising Mathematics and Language.” Developmental Science 25 (2). https://doi.org/10.1111/desc.13174.
Morales López, Ana Isabel, and Paula Tuzón Marco. 2022. “Misconceptions, Knowledge, and Attitudes Towards the Phenomenon of Radioactivity.” Science and Education 31 (2). https://doi.org/10.1007/s11191-021-00251-w.
Naidoo, Jayaluxmi. 2022. “Technology-Based Pedagogy for Mathematics Education in South Africa: Sustainable Development of Mathematics Education Post COVID-19.” Sustainability (Switzerland) 14 (17). https://doi.org/10.3390/su141710735.
Nugraha, Trisna, and Sufyani Prabawanto. 2021. “The Enhancement of Students’ Mathematical Conceptual Understanding Through RADEC Learning Model.” Eduma?: Mathematics Education Learning and Teaching 10 (2). https://doi.org/10.24235/eduma.v10i2.9073.
Oliveira, Gisela. 2023. “Developing a Codebook for Qualitative Data Analysis: Insights from a Study on Learning Transfer between University and the Workplace.” International Journal of Research and Method in Education 46 (3). https://doi.org/10.1080/1743727X.2022.2128745.
Prince, Robert, and Vera Frith. 2020. “An Investigation of the Relationship between Academic Numeracy of University Students in South Africa and Their Mathematical and Language Ability.” ZDM - Mathematics Education 52 (3). https://doi.org/10.1007/s11858-019-01063-7.
Prinsloo, C. H., and J. C. Harvey. 2020. “The Differing Effect of Language Factors on Science and Mathematics Achievement Using TIMSS 2015 Data: South Africa.” Research in Science Education 50 (6). https://doi.org/10.1007/s11165-018-9769-9.
Sapire, Ingrid, and Anthony A. Essien. 2021. “Multiple Monolingualism Versus Multilingualism? Early Grade Mathematics Teachers’ and Students’ Language Use in Multilingual Classes in South Africa.” In. https://doi.org/10.1007/978-3-030-72009-4_5.
Sapkota, Bima, and Amanda Huffman Hayes. 2024. “Preservice Teachers’ Mathematical Knowledge for Teaching: Focus on Lesson Planning and Reflection.” School Science and Mathematics. https://doi.org/10.1111/ssm.12644.
Tachie, Simon Adjei. 2020. “Teachers’ Attitudes towards Lesson Study as a Viable Strategy to Improve the Teaching and Learning of Mathematics.” Universal Journal of Educational Research 8 (6). https://doi.org/10.13189/ujer.2020.080616.
Taylor, Nick. 2021. “The Dream of Sisyphus: Mathematics Education in South Africa.” South African Journal of Childhood Education 11 (1). https://doi.org/10.4102/sajce.v11i1.911.
Venkat, Hamsa, and Mike Askew. 2021. “Development in South African Primary Mathematics Teacher Educators’ Work with In-Service Teachers.” International Journal of Science and Mathematics Education 19. https://doi.org/10.1007/s10763-021-10161-6.
??????, ?.?. 2023. “For the Purity of Mathematical Language.” Management of Education, no. 1(59). https://doi.org/10.25726/m2832-1698-0025-w.
Published
2025-01-06
How to Cite
BAIDOO, Joseph.
Mathematical Language Errors and Academic Performance in Preservice Calculus Teachers.
Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, [S.l.], v. 9, n. 1, p. 118-133, jan. 2025.
ISSN 2549-5070.
Available at: <https://e-journal.ivet.ac.id/index.php/matematika/article/view/3318>. Date accessed: 15 july 2025.
doi: https://doi.org/10.31331/medivesveteran.v9i1.3318.
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