Assessing the added value of a history-based activity for students with low mathematics skills

Thomas De Vittori 1 * , Gaëlle Louaked 2, Marie-Pierre Visentin 3
More Detail
1 Laboratoire de Mathématiques de Lens, Faculté des Sciences Jean Perrin, Université d’Artois, Arras, FRANCE
2 Laboratoire Paul Painlevé, Université de Lille, Lille, FRANCE
3 Primary School Henri-Matisse, Saint Sulpice, FRANCE
* Corresponding Author
EUR J SCI MATH ED, Volume 12, Issue 1, pp. 112-127. https://doi.org/10.30935/scimath/13868
Published Online: 05 November 2023, Published: 01 January 2024
OPEN ACCESS   567 Views   358 Downloads
Download Full Text (PDF)

ABSTRACT

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed. Based on the data of a pre-test and a post-test surrounding an activity on an ancient Chinese numeration system, a statistical analysis using Rasch modeling shows a specific added value of the history of mathematics for students with low abilities in mathematics. For these students, a significant increase in observed abilities of +0.67 logit in mean is measured with a large effect size (Cliff delta +0.52). This effect is then weighted by considering the regression to the mean (RTM) effect, leading to a value around +0.14 logit in mean and a negligible effect size (Cliff delta +0.10). So, this pilot study shows the important effect of RTM, which suggests a very strong rebalancing of students’ results. In the last part of the paper, we discuss how RTM can nonetheless be positively interpreted in this specific context where students’ disorientation is one of the purposes of history in mathematics education.
Keywords: history of mathematics, number system, sixth grade, Rasch model, regression to the mean

CITATION

De Vittori, T., Louaked, G., & Visentin, M.-P. (2024). Assessing the added value of a history-based activity for students with low mathematics skills. European Journal of Science and Mathematics Education, 12(1), 112-127. https://doi.org/10.30935/scimath/13868

REFERENCES

  • Anicotte, R. (2019). Le livre sur les calculs effectués avec des bâtonnets: Un manuscrit du -IIe siècle excavé à Zhangjiashan [The book of calculations made with sticks: A 2nd-century manuscript excavated in Zhangjiashan]. Presses de l’Inalco. https://doi.org/10.4000/books.pressesinalco.18815
  • Barbin, E., Guillemette, D., & Tzanakis, C. (2020). History of mathematics and education. In S. Lerman (Ed.), Encyclopedia of mathematics education. Springer. https://doi.org/10.1007/978-94-007-4978-8_69
  • Barnett, A. G., van der Pols, J. C., & Dobson, A. J. (2004). Regression to the mean: What it is and how to deal with it. International Journal of Epidemiology, 34(1), 215-220. https://doi.org/10.1093/ije/dyh299
  • Barr, D. C. (1978). A comparison of three methods of introducing two-digit numeration. Journal for Research in Mathematics Education, 9(1), 33-43. https://doi.org/10.2307/748958
  • Bartolini Bussi, M. G., & Sun, X. H. (2018). Building the foundation: Whole numbers in the primary grades. The 23rd ICMI study. Springer. https://doi.org/10.1007/978-3-319-63555-2
  • Baturo, A. (2000). Construction of a numeration model: A theoretical analysis. In J. Bana, & A. Chapman (Eds.), In Proceedings of the 23rd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 95-103). https://merga.net.au/Public/Publications/Annual_Conference_Proceedings/2000_MERGA_CP.aspx
  • Bednarz, N., & Janvier, B. (1982). The understanding of numeration in primary school. Educational Studies in Mathematics, 13(1), 33-57. https://doi.org/10.1007/BF00305497
  • Bråting, K., & Pejlare, J. (2015). On the relations between historical epistemology and students’ conceptual developments in mathematics. Educational Studies in Mathematics, 89(2), 251-265. https://doi.org/10.1007/s10649-015-9600-8
  • Butuner, S. O. (2015). Impact of using history of mathematics on students mathematics attitude: A meta-analysis study. European Journal of Science and Mathematics Education, 3(4), 337-349. https://doi.org/10.30935/scimath/9442
  • Chambris, C., & Tempier, F. (2017). Dealing with large numbers: What is important for students and teachers to know? In T. Dooley, & G. Gueudet (Eds.), Proceedings of the 10th Congress of the European Society for Research in Mathematics Education (pp. 245-252). DCU Institute of Education and ERME. https://hal.science/CERME10
  • Chesné, J.-F., & Fischer, J.-P. (2015). Les acquis des élèves dans le domaine des nombres et du calcul à l’école primaire. Rapport pour la conférence de consensus nombres et opérations: Premiers apprentissages à l’école primaire [Students’ achievements in the area of numbers and calculation in primary school. Report for the consensus conference numbers and operations: First learning in primary school]. CNESCO. https://www.cnesco.fr/wp-content/uploads/2015/11/Acquis-des-élèves.pdf
  • Clark, C., Kjeldsen, T. H., Schorcht, S., Tzanakis, C., & Wang, X. (2016). History of mathematics in mathematics education: Recent developments. In L. Radford, F. Furinghetti, & T. Hausberger (Eds.), Proceedings of the 2016 ICME Satellite Meeting–HPM 2016 (pp. 135-179). IREM de Montpelier.
  • Clark, K. M., Kjeldsen, T. H., Schorcht, S., & Tzanakis, C. (2018). Mathematics, education and history: Towards a harmonious partnership. Springer. https://doi.org/10.1007/978-3-319-73924-3
  • CNESCO. (2015). Conférence de consensus. Nombres et opérations: Premiers apprentissages à l’école primaire. Recommandations du jury [Consensus conference. Numbers and operations: First learning in primary school. Jury recommendations]. https://www.cnesco.fr/wp-content/uploads/2015/11/Recommandations-du-jury.pdf
  • De Vittori, T. (2018). Analyzing the use of history in mathematics education: Issues and challenges around Balacheff’s cKȼ model. Educational Studies in Mathematics, 99(2), 125-136. https://doi.org/10.1007/s10649-018-9831-6
  • De Vittori, T. (2022). Relevance of a history-based activity for mathematics learnings. Discover Education, 1(1). https://doi.org/10.1007/s44217-022-00010-1
  • De Vittori, T. (2023). Regression to the mean (RTM) effect calculation by random data permutations. Zenodo. https://doi.org/10.5281/zenodo.8344700
  • Eberhard-Bréard, A. (2008). Mathematics in China. In H. Selin (Ed.), Encyclopedia of the history of science, technology, and medicine in non-Western cultures. Springer. https://doi.org/10.1007/978-1-4020-4425-0
  • Fauvel, J., & Van Maanen, J. (2000). History in mathematics education. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47220-1
  • Fried, M. N., Guillemette, D., & Jahnke, H. N. (2016). Theoretical and/or conceptual frameworks for integrating history in mathematics education. In L. Radford, F. Furinghetti, & T. Hausberger (Eds.), Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics (pp. 211-230). IREM de Montpellier. https://hal.science/HPM2016/public/hpm2016_eproceedings_final.pdf
  • Furrow, R. E. (2019). Regression to the mean in pre-post testing: Using simulations and permutations to develop null expectations. CBE–Life Sciences Education, 18(2), le2. https://doi.org/10.1187/cbe.19-02-0034
  • Guillemette, D. (2018). History of mathematics and teachers’ education: On otherness and empathy. In K. Clark, T. Kjeldsen, S. Schorcht, & C. Tzanakis (Eds.), Mathematics, education and history. ICME-13 monographs. Springer. https://doi.org/10.1007/978-3-319-73924-3
  • Houdement, C., & Tempier, F. (2019). Understanding place value with numeration units. ZDM Mathematics Education, 51(1), 25-37. https://doi.org/10.1007/s11858-018-0985-6
  • Ifrah, G. (2000). The universal history of numbers. Wiley.
  • Jahnke, H. N. (2014). History in mathematics education. A hermeneutic approach. In M. Fried, & T. Dreyfus (Eds.), Mathematics & mathematics education: Searching for common ground. Advances in mathematics education. Springer. https://doi.org/10.1007/978-94-007-7473-5_6
  • Kelly, C., & Price, T. D. (2005). Correcting for regression to the mean in behavior and ecology. The American Naturalist, 166, 700-707. https://doi.org/10.1086/497402
  • Lambert, K., & Moeller, K. (2019). Place-value computation in children with mathematics difficulties. Journal of Experimental Child Psychology, 178, 214-225. https://doi.org/10.1016/j.jecp.2018.09.008
  • Lim, S. Y., & Chapman, E. (2015). Effects of using history as a tool to teach mathematics on students’ attitudes, anxiety, motivation and achievement in grade 11 classrooms. Educational Studies in Mathematics, 90(2), 189-212. https://doi.org/10.1007/s10649-015-9620-4
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum. https://doi.org/10.4324/9781410602589
  • Nurul Hafizah, A., Zamalia, M., & Adzhar, R. (2020). Rasch rating scale item estimates using maximum likelihood approach: Effects of sample size on the accuracy and bias of the estimates. International Journal of Advanced Science and Technology, 29(4s), 2526-2531.
  • OECD. (2009). PISA data analysis manual: SAS. OECD Publishing. https://doi.org/10.1787/9789264056251-en
  • R Core Team. (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/
  • Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Danemarks Paedogogiske Institut.
  • Revelle, W. (2021). psych: Procedures for personality and psychological research. https://cran.r-project.org/package=psych
  • Rizopoulos, D. (2006). ltm: An R package for latent variable modelling and item response theory analyses. Journal of Statistical Software, 17(5), 1-25. https://doi.org/10.18637/jss.v017.i05
  • Slepkov, A. D., Van Bussel, M. L., Fitze, K. M., & Burr, W. S. (2021). A baseline for multiple-choice testing in the university classroom. SAGE Open, 11(2). https://doi.org/10.1177/21582440211016838
  • Thanheiser, E. (2012). Understanding multidigit whole numbers: The role of knowledge components, connections, and context in understanding regrouping 3+- digit numbers. The Journal of Mathematical Behavior, 31(2), 220-234. https://doi.org/10.1016/j.jmathb.2011.12.007
  • Thomas, N. (2004). The development of structure in the number system. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (pp. 305-312). Bergen University College Press. https://files.eric.ed.gov/fulltext/ED489178.pdf
  • Torchiano, M. (2020). effsize: Efficient effect size computation. Zenodo. https://doi.org/10.5281/zenodo.1480624
  • van der Linden, W. J. (1986). The changing conception of measurement in education and psychology. Applied Psychological Measurement, 10(4), 325-332. https://doi.org/10.1177/014662168601000401
  • Wright, B. D. (1993). Equitable test equating. Rasch Measurement Transactions, 7(2), 298-299.