Exploring trends in pre-service teachers’ additive reasoning: A quasi-longitudinal analysis of three-year cohorts
DOI:
https://doi.org/10.20853/40-1-6605Keywords:
Additive reasoning, Mathematical equivalence, design research, mathematics performance, equality, quasi-longitudinalAbstract
The study reported in this article examines the trends in pre-service teachers’ (PSTs) additive reasoning performance through a quasi-longitudinal analysis of three-year cohorts involving 498 PSTs. The findings indicate consistent improvement in additive reasoning performance across the cohorts. However, while PSTs excelled in simple missing addend tasks, they often struggled with tasks involving a deeper understanding of equivalence (such as equivalence tasks with two unknowns), as well as tasks requiring reasoning about structuring the numbers involved for efficient calculation and compensating for adding more or less than was intended. While these findings underscore the potential of targeted teaching interventions to shift PSTs performance across a variety of additive tasks, they also point to the need for more emphasis to be placed on developing PSTs reasoning about number structure and equivalence beyond simple missing addend problems. More generally, the findings highlight the need for continual assessment and tailored design instruction to address specific challenges in PSTs’ mathematical competencies in additive reasoning.
Downloads
References
Bowie, L., H. Venkat, and M. Askew. 2019. “Pre-service Primary Teachers’ Mathematical Content Knowledge: An Exploratory Study”. African Journal of Research in Mathematics, Science and Technology Education, 23(3), 286‒297. DOI: 10.1080/18117295.2019.1682777
Campbell, D. T., and J. C. Stanley. 1966. Experimental and quasi-experimental designs for research. Chicago: Rand-McNally
Capraro, R. M., M. M. Capraro, Z. E. Yetkiner, S. Özel, H. G. Kim, and A. R. Küçük. 2010. “An International Comparison of Grade 6 Students’ Understanding of the Equal Sign”. Psychological Reports, 106(1), 49‒53. https://doi.org/10.2466/PR0.106.1.49-53
Carpenter, T., L. Levi, M. Franke, and J. Zeringue. 2005. “Algebra in elementary school: Developing relational thinking”. ZDM, 37, 53–59. https://doi.org/10.1007/BF02655897
Davydov, V. V. 1998. “The Renewal of Education and the Mental Development of Schoolchildren”. Thinking: The Journal of Philosophy for Children, 13 (4):5‒7.
Donovan, A.M., A. Stephens, B. Alapala, et al. 2022. “Is a substitute the same? Learning from lessons centering different relational conceptions of the equal sign”. ZDM Mathematics Education 54, 1199–1213. https://doi.org/10.1007/s11858-022-01405-y
Essien, A. A., & Adler, J. 2016. Operationalising Wenger’s communities of practice theory for use in multilingual mathematics teacher education contexts. In A. Halai & P. Clarkson (eds), Teaching & learning mathematics in multilingual classrooms: Issues for policy, practice and teacher education (pp. 173–194). Rotterdam: Sense.
Essien, A & Setati, M. 2006. Revisiting the equal sign: Some Grade 8 and 9 learners' interpretations. African Journal of Research in Mathematics, Science and Technology Education, 10:1, 47-58, DOI: 10.1080/10288457.2006.10740593.
Essien, A. (2009). An analysis of the introduction of the equal sign in three Grade 1 textbooks. Pythagoras, 69, 28-35. doi:https://doi.org/10.4102/pythagoras.v0i69.43
Essien, A., Mathews, C., Tshesane, H., Weitz, M., Abdulhamid, L., Hoosen, T., & Lavans, L. 2023. Developing design principles to enhance pre-service teachers’ understanding of number structure and mathematical equivalence in early grade mathematics. African Journal of Research in Mathematics, Science and Technology Education, 27:3, 239-254, DOI: 10.1080/18117295.2023.2216608
Fleisch, B. 2008. Primary Education in a crisis: Why South African school children underachieve in Reading and Mathematics. Juta and Company Ltd.
Graven, M., 2016. “When systemic interventions get in the way of localized mathematics reform”. For the Learning of Mathematics, 36(1), 8–13
Hunter, J. 2007. “Relational or calculational thinking: Students solving open number equivalence problems”. Proceedings of the 30th annual conference of the mathematics education research group of Australasia, pp. 421‒429.
Jones, I., M. Inglis, C. Gilmore, and M. Dowens. 2012. “Substitution and sameness: Two components of a relational conception of the equals sign”. Journal of Experimental Child Psychology, 11, pp. 166‒176, 10.1016/j.jecp.2012.05.003
Kieran, C. 1981. “Concepts associated with the equality symbol”. Educational Studies in Mathematics, 12(3), 317– 326.
Kifer, E. 1975. “Relationships between academic achievement and personality characteristics: A quasi-longitudinal study”. American Educational Research Journal, 12(2), 191‒210.
Knuth, E., A. Stephens, N. McNeil, and M. Alibali. 2006. “Does understanding the equal sign matter? Evidence from solving equations”. Journal for Research in Mathematics Education, 36, pp.297‒312
Machaba, F. 2017. “Grade 9 learners’ structural and operational conceptions of the equal sign: A Case study of a secondary school in Soshanguve”. Eurasia Journal of Mathematics, Science and Technology Education, 13 2017, pp. 7243‒7255, 10.12973/ejmste/78017
Matthews, P., B. Rittle-Johnson, K. McEldoon, and R. Taylor. 2012. “Measure for measure: What combining diverse measures reveals about children’s understanding of the equal sign as an indicator of mathematical equality”. Journal for Research in Mathematics Education, 43(3), 316–350. https://doi.org/10.5951/jresematheduc.43.3. 0316
McNeil, N., C. Hornburg, H. Brletic-Shipley, and J. Matthews. 2019. “Improving children’s understanding of mathematical equivalence via an intervention that goes beyond nontraditional arithmetic practice”. Journal of Educational Psychology, 111, pp. 1023‒1044, 10.1037/edu0000337
Rathgeb-Schnierer, E. and M. Green. 2019. “Developing Flexibility in Mental Calculation”. Educação & Realidade, Porto Alegre, 44(2), e87078. http://dx.doi.org/10.1590/2175-623687078
Reddy V, M. Visser, L. Winnaar, F. Arends, A. Juan, C. Prinsloo, and K. Isdale. 2016. TIMSS 2015 highlights of mathematics and science achievement of grade 9 South African learners. Pretoria: HSRC
Reddy, V., L. Winnaar, F. Arends, A. Juan, J. Harvey, S. Hannan, and K. Isdale. 2022. The South African TIMSS 2019 Grade 9 Results: Building Achievement and Bridging Achievement Gaps. HSRC Press, Cape Town.
Reeves, T. 2006. “Design research from a technology perspective”. In J.V.D. Akker, K. Gravemeijer, S. McKenney and N. Nieveen (Eds.), Educational design research (pp. 52–66). New York: Routledge.
Reeves, T.C., S. McKenney, and J. Herrington. 2011. “Publishing and perishing: The critical importance of educational design research”. Australasian Journal of Educational Technology, 27(1). https://doi.org/10.14742/ ajet.982
Rittle-Johnson, B., P. Matthews, R. Taylor, and K. McEldoon. 2011. “Assessing knowledge of mathematical equivalence: A construct-modeling approach”. Journal of Educational Psychology, 103, pp. 85‒104, 10.1037/a0021334
Simsek, E., I. Jones, J. Hunter, and I. Xenidou-Dervou. 2021. “Mathematical equivalence assessment: measurement invariance across six countries”. Stud. Educ. Eval. 70, 101046. doi: 10.1016/j.stueduc.2021.101046
Skemp, R. R. 1976. “Relational understanding and instrumental understanding”. Mathematics teaching, 77(1), 20–26.
Spaull, N., and J. Kotze. 2015. “Starting behind and Staying behind in South Africa: The Case of Insurmountable Learning Deficits in Mathematics”. International Journal of Educational Development, 41, 13‒24.
Taylor, N., and S. Taylor. 2013. “Teacher knowledge and professional habitus, in Taylor, N., van der Berg,S., and Mabogoane, T. Creating effective schools”: Report of South Africa’s National Schools Effectiveness Study. Cape Town: Pearson.
Threlfall, J. “Strategies and flexibility in mental calculation”. ZDM Mathematics Education 41, 541–555 (2009). https://doi.org/10.1007/s11858-009-0195-3
Venkat, H. and N. Spaull. 2015. “What do we know about primary teachers’ mathematical content knowledge in South Africa? An analysis of SACMEQ 2007”. International Journal of Educational Development, 41, 121– 130. https://doi.org/10.1016/j.ijedudev.2015.02.002.
Venkat, H., and J. Adler. 2012. “Coherence and connections in teachers’ mathematical discourses in instruction”. Pythagoras, 33(3)http://doi.org/10.4102/pythagoras.v33i3.188.
Venkat, H., and M. Askew. 2018.” Mediating primary mathematics: Theory, concepts, and a framework for studying practice”. Educational Studies in Mathematics, 97(1), 71–92.
Venkat, H., and N. Roberts. 2022. “Children doing mathematics with confidence in the early grades by 2030: What will it take?” In H. Venkat and N. Roberts (Eds.), Early grade Mathematics in South Africa, (pp. 175‒192). Oxford University Press.
Vergnaud, G. 2020. “A classification of cognitive tasks and operations of thought involved in addition and subtraction problems.” In Addition and subtraction (pp. 39‒59). Routledge.
Vermeulen, C., and B. Meyer. 2017. “The Equal Sign: Teachers’ Knowledge and Students’ Misconceptions”. African Journal of Research in Mathematics, Science and Technology Education, 21(2), 136–147. https://doi.org/10.1080/18117295.2017.1321343
Weitz, M., and H. Venkat. 2017. “Using Assessments to Explore Early and Later Performance in Mathematics.” Improving Primary Mathematics Education, Teaching and Learning: Research for Development in Resource-Constrained Contexts, 27‒43.
Wilmot, E. M. 2018. “Effect of instruction on children’s strategies for solving addition problems”. African Journal of Educational Studies in Mathematics and Sciences, 14, 51‒69.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Sameera Hansa, Lawan Abdulhamid, Corin Mathews, Herman Tshesane, Anthony A Essien
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
This journal is an open access journal, and the authors and journal should be properly acknowledged, when works are cited.
Authors, copyright holders, may use the publishers version for teaching purposes, in books, theses, dissertations, conferences and conference papers.
A copy of the authors' publishers version may also be hosted on the following websites:
- Non-commercial personal homepage or blog.
- Institutional webpage.
- Authors Institutional Repository.
The following notice should accompany such a posting on the website: This is an electronic version of an article published in SAJHE, Volume XXX, number XXX, pages XXX “XXX", DOI. Authors should also supply a hyperlink to the original paper or indicate where the original paper (http://www.journals.ac.za/index.php/SAJHE) may be found.
Authors publishers version, affiliated with the Stellenbosch University will be automatically deposited in the University Institutional Repository SUNScholar.
Articles as a whole, may not be re-published with another journal.
The following license applies:
Attribution CC BY-NC-ND 4.0
