Effects of the Enactive, Iconic, Symbolic (EIS) Intervention on Student Math Skills in Primary School
Abstract
Abstract
«Enactive, Iconic, Symbolic» (EIS) is a recently developed program modeled after instructional methodologies used in the Singapore math approach. The intervention emphasizes sequential mastery of math concepts, problem solving, and the use of the Concrete to Pictorial to Abstract approach (CPA). This quasi-experimental study evaluates the impact of EIS program on student math performance to explore the applicability of the Singapore approach in the Italian context and define the most appropriate methods for future large-scale evaluations. Eleven third- through fifth-grade treatment classes were matched comparison classes using propensity score matching, with mathematics performance measured before and after the intervention. A two-level random intercept hierarchical linear model was used to estimate treatment impact. We found no statistical significance effects of EIS after 16-20 weeks, ranging between 0.12 to 0.35 standard deviation units. The findings suggest the need for further investigations through largescale evaluations.
Keywords
Full Text:
PDFReferences
Anthony, G., & Walshaw, M. (2009). Characteristics of effective teaching of mathematics: A view from the West. Journal of Mathematics Education, 2(2), 147-164.
Bartolini Bussi, M.G., Sun, X., & Ramploud, A. (2013). A dialogue between cultures about task design for primary school. In C. Margolinas (Ed.), Proceedings of ICMI Study 22: Task Design in Mathematics Education (pp. 551-560). Oxford: ICMI.
Bruner, J.S. (1966). Toward a Theory of Instruction. Cambridge, MA: Belknap Press of Harvard University.
Chang, S.H., Lee, N.H., & Koay, P.L. (2017). Teaching and learning with concrete-pictorial-abstract sequence: A proposed model. The Mathematics Educator, 17(1), 1-28.
Cheung, A.C., & Slavin, R.E. (2016). How methodological features affect effect sizes in education. Educational Researcher, 45(5), 283-292.
https://doi.org/10.3102/0013189X16656615
Di Martino, V. (2015). Encouraging the success of foreign students in schools: Reinforcing problem solving in mathematics. In C. Coggi (Ed.), Enhancing school success: The Fenix program (pp. 159-185). Lecce: Pensa Multimedia.
Doane, D.P., & Seward, L.E. (2011). Measuring skewness: A forgotten statistic? Journal of Statistics Education, 19(2).
https://doi.org/10.1080/10691898.2011.11889611
Durlak, J.A., & Dupre, E.P. (2008). Implementation matters: A review of research on the influence of implementation on program outcomes and the factors affecting implementation. American Journal of Community Psychology, 41(3-4), 327-350.
https://doi.org/10.1007/s10464-008-9165-0
PMid:18322790
Educational Research Institute of America (2010). A study of the Singapore Math Program, Math in Focus, state test results (Report 404). Boston, MA: Houghton Mifflin Harcourt.
Educational Research Institute of America (2013). A study of the instructional effectiveness of Math in Focus (Report 466). Boston, MA: Houghton Mifflin Harcourt.
Gallucci, M. (2020). GAMLj suite for Jamovi.
https://github.com/gamlj/gamlj
Gertler, P.J., Martinez, S., Premand, P., Rawlings, L.B., & Vermeersch, C.M. (2016). Impact evaluation in practice. Washington, DC: World Bank Publications.
https://doi.org/10.18235/0006529
https://openknowledge.worldbank.org/handle/10986/25030
Harrison, B.A., & Mayo-Wilson, E. (2014). Trial registration: Understanding and preventing reporting bias in social work research. Research on Social Work Practice, 24(3), 372-376.
https://doi.org/10.1177/1049731513512374
Hedges, L.V., Tipton, E., Zejnullahi, R., & Diaz, K.G. (2023). Effect sizes in ANCOVA and difference‐in‐differences designs. British Journal of Mathematical and Statistical Psychology, 76(2), 259-282.
https://doi.org/10.1111/bmsp.12296
PMid:36594164
Hill, C.J., Scher, L., Haimson, J., & Granito, K. (2023). Conducting implementation research in impact studies of education interventions: A guide for researchers (NCEE 2023-005). Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance (NCEE).
http://ies.ed.gov/ncee
Ho, D.E., Imai, K., King, G., & Stuart, E.A. (2011). MatchIt: Nonparametric preprocessing for parametric causal inference. Journal of Statistical Software, 42(8).
https://doi.org/10.18637/jss.v042.i08
INVALSI (2024). Rapporto INVALSI 2024.
Jaciw, A.P., Hegseth, W.M., Lin, L., Toby, M., Newman, D., Ma, B., & Zacamy, J. (2016). Assessing impacts of Math in Focus, a «Singapore Math» program. Journal of Research on Educational Effectiveness, 9(4), 473-502.
https://doi.org/10.1080/19345747.2016.1164777
Jerrim, J., & Vignoles, A. (2016). The link between East Asian «mastery» teaching methods and English children's mathematics skills. Economics of Education Review, 50, 29-44.
https://doi.org/10.1016/j.econedurev.2015.11.003
Kapur, M. (2016). Examining productive failure, productive success, unproductive failure, and unproductive success in learning. Educational Psychologist, 51(2), 289-299.
https://doi.org/10.1080/00461520.2016.1155457
Kaur, B. (2019). The why, what and how of the «Model» method: A tool for representing and visualising relationships when solving whole number arithmetic word problems. ZDM Mathematics Education, 51(1), 151-168.
https://doi.org/10.1007/s11858-018-1000-y
Kaur, B. (2021). A look at Singapore mathematics education through the PISA and TIMSS lenses. In Singapore Math and science education innovation (pp. 61-73). Singapore: Springer.
https://doi.org/10.1007/978-981-16-1357-9_4
Lee, N.H., Lee, J., & Wong, Z.Y. (2021). Preparing students for the fourth industrial revolution through mathematical learning: The constructivist learning design. Journal of Educational Research in Mathematics, 31(3), 321-356.
https://doi.org/10.29275/jerm.2021.31.3.321
Lee, N.H., Seto, C., Rahim, R., & Soon, T. (Eds.). (2020). Mathematics teaching in Singapore, Vol. 1: Theory-informed practices. Singapore: Word Scientific.
https://doi.org/10.1142/11822
Lindorff, A.M., Hall, J., & Sammons, P. (2019). Investigating a Singapore-based mathematics textbook and teaching approach in classrooms in England. Frontiers in Education, 4, art. 37.
https://doi.org/10.3389/feduc.2019.00037
Lucangeli, D., Tressoldi, P.E., & Cendron, M. (2003). Test SPM - Abilità di soluzione dei problemi matematici. Abilità di soluzione dei problemi matematici. Trento: Erickson.
Montgomery, P., Grant, S., Mayo-Wilson, E., Macdonald, G., Michie, S., Hopewell, S., & Moher, D.; on behalf of the CONSORT-SPI Group (2018). Reporting randomised trials of social and psychological interventions: the CONSORT-SPI 2018 extension. Trials, 19, 407.
https://doi.org/10.1186/s13063-018-2733-1
PMid:30060754 PMCid:PMC6066921
Mullis, I.V.S., Martin, M.O., Foy, P., Kelly, D.L., & Fishbein, B. (2020). TIMSS 2019 international results in mathematics and science. Boston College, MA: TIMSS & PIRLS International Study Center.
https://timssandpirls.bc.edu/timss2019/international-results/
Ng, S.F., & Lee, K. (2009). The model method: Singapore children's tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282-313.
https://doi.org/10.5951/jresematheduc.40.3.0282
Nutley, S.M., Powell, A.E., & Davies, H.T.O. (2013). What counts as good evidence. London: Alliance for Useful Evidence.
http://hdl.handle.net/10023/3518
OECD - Organisation for Economic Co-operation and Development (2023). PISA 2022 results, Vol. 1: The state of learning and equity in education. Paris: OECD Publishing.
https://doi.org/10.1787/53f23881-en
Pellegrini, M., Lake, C., Neitzel, A., & Slavin, R.E. (2021). Effective programs in elementary mathematics: A meta-analysis. AERA Open, 7.
https://doi.org/10.1177/2332858420986211
Porta, M. (2008). A dictionary of epidemiology (5th ed.). New York: Oxford University Press.
Purwadi, I., Sudiarta, I., & Suparta, I.N. (2019). The effect of concrete-pictorial-abstract strategy toward students' mathematical conceptual understanding and mathematical representation on fractions. International Journal of Instruction, 12(1), 1113-1126.
https://doi.org/10.29333/iji.2019.12171a
Raudenbush, S.W., & Bryk, A.S. (2002). Hierarchical linear models: Applications and data analysis methods, Vol. 1. Newbury Park, CA: Sage.
Rubin, D.B. (2001). Using propensity scores to help design observational studies: Application to the tobacco litigation. Health Services and Outcomes Research Methodology, 2(3-4), 169-188.
https://doi.org/10.1023/A:1020363010465
Salingay, N., & Tan, D. (2018). Concrete-Pictorial-Abstract approach on students' attitude and performance in mathematics. International Journal of Scientific & Technology Research, 7(5), 90-111.
Schoenfeld, A.H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Journal of Education, 196(2), 1-38.
https://doi.org/10.1177/002205741619600202
Shadish, W.R., Cook, T.D., & Campbell, D.T. (2002). Experimental and quasi-experimental designs for generalized causal inference. Boston, MA: Houghton, Mifflin and Company.
Singapore Ministry of Education (2006). Mathematics Syllabus Primary.
https://libris.nie.edu.sg/sites/default/files/math2007a.pdf
Slavin, R.E. (2008). Response to comments. Evidence-based reform in education: Which evidence counts? Educational Researcher, 37(1), 47-50.
https://doi.org/10.3102/0013189X08315082
Spagnolo, F., & Di Paola, B. (2010). European and Chinese cognitive styles and their impact on teaching mathematics. Berlin: Springer.
https://doi.org/10.1007/978-3-642-11680-3
The Jamovi project (2022). Jamovi (version 2.3).
https://www.jamovi.org
Tipton, E., & Olsen, R.B. (2022). Enhancing the generalizability of impact studies in education (NCEE 2022-003). Washington, DC: U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance (NCEE).
http://ies.ed.gov/ncee
Toh, T.L., Chan, C.M.E., Tay, E.G., Leong, Y.H., Quek, K.S., Toh, P.C., …, & Dong, F. (2019). Problem solving in the Singapore school mathematics curriculum. In T.L. Toh, B. Kaur, & E.G. Tay (Eds.), Mathematics education in Singapore (pp. 141-164). Berlin: Springer.
https://doi.org/10.1007/978-981-13-3573-0_7
PMCid:PMC6528291
What Works Clearinghouse (2022). What Works Clearinghouse procedures and standards handbook, version 5.0. U.S. Washington, DC: Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance (NCEE).
https://ies.ed.gov/ncee/wwc/Handbooks
Wolf, B., & Harbatkin, E. (2023). Making sense of effect sizes: Systematic differences in intervention effect sizes by outcome measure type. Journal of Research on Educational Effectiveness, 16(1), 134-161.
https://doi.org/10.1080/19345747.2022.2071364
Zan, R. (2011). The crucial role of narrative thought in understanding story problems. Current State of Research on Mathematical Beliefs, XVI, 287-305.
Zan, R. (2016). I problemi di matematica. Difficoltà di comprensione e formulazione del testo. Roma: Carocci.
DOI: https://doi.org/10.7358/ecps-2025-031-pell
Copyright (©) 2025 Marta Pellegrini, Valeria Di Martino, Roberto Trinchero – Editorial format and Graphical layout: copyright (©) LED Edizioni Universitarie

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Journal of Educational, Cultural and Psychological Studies (ECPS)
Registered by Tribunale di Milano (19/05/2010 n. 278)
Online ISSN 2037-7924 - Print ISSN 2037-7932
Research Laboratory on Didactics and Evaluation - Department of Education - "Roma Tre" University
Executive Editor: Gaetano Domenici - Associate Executive Editor & Managing Editor: Valeria Biasci †
Editorial Board: Eleftheria Argyropoulou - Massimo Baldacci - Joao Barroso - Richard Bates - Christofer Bezzina - Pietro Boscolo - Sara Bubb - Giuseppina Castellana - Jean-Émile Charlier - Lucia Chiappetta Cajola - Jean-Louis Derouet - Peter Early - Giancarlo Fortino - Constance Katz - James Levin - Pietro Lucisano - Roberto Maragliano - Massimo Marcuccio - Arianna Lodovica Morini - Romuald Normand - Michael Osborne - Donatella Palomba - Nazarena Patrizi - Michele Pellerey - Vitaly V. Rubtzov - Jaap Scheerens - Noah W. Sobe - Francesco Susi - Giuseppe Spadafora - Pat Thomson - Roberto Trinchero - Ira Vannini
Editorial Staff: Fabio Alivernini - Guido Benvenuto - Anna Maria Ciraci - Massimiliano Fiorucci - Luca Mallia - Massimo Margottini - Giovanni Moretti - Carla Roverselli
Editorial Secretary: Conny De Vincenzo
© 2001 LED Edizioni Universitarie di Lettere Economia Diritto