Analyzing the Impact of a Mathematical Competency-Based Curriculum
The Innovamat Case
Abstract
This study examines the impact of Innovamat: a curricular teaching and learning program that aims to foster the students' mathematical competence. To do so, this research considers the acquisition of mathematical competence in two different samples of 4th grade Mexican primary school students. Both samples belong to private schools with similar socio-economic backgrounds, their HDI (Human Development Index) being between 0.7 and 0.9. The first sample, called intervention group, consists of 28 private schools (912 students) that have used Innovamat for a year. The second sample, called control group, consists of 27 schools (1.111 students) that use textbooks publishers from widely known in Mexico. Our results indicate a correlation between the use of this programme—Innovamat—and a better performance on an adapted version of the TIMSS test (Trends in International Mathematics and Science Study), both in terms of content and in cognitive domains that characterise mathematical competence. However, it is not possible to conclude that the implementation of this programme improves student mathematical competence, since this study does not allow us to establish its causal effect.
Downloads
-
Abstract134
-
PDF (Español (España))260
-
PDF260
References
Alsina, Á. P. (2012). Más allá de los contenidos, los procesos matemáticos en Educación Infantil. Edma 0-6: Educación Matemática en la Infancia, 1(1), 1-14. https://doi.org/10.24197/edmain.1.2012.1-14
Alsina, Á. P. (2019). Itinerarios didácticos para la enseñanza de las matemáticas (6-12 años). Editorial Graó.
Arcavi, A. (1999). ...Y en matemáticas, los que instruimos ¿qué construimos? Números. Revista de didáctica de las matemáticas, 38, 39-56. Extraído de: https://dialnet.unirioja.es/servlet/articulo?codigo=2343631
Backhoff, E. y Solano-Flores, G. (2003). Tercer estudio internacional de Mathematics and Natural sciences (TIMSS): resultados de México en 1995 and 2000. No. 4. Instituto Nacional para la Evaluación de la Educación.
Bakker, A., Cai, J. y Zenger, L. (2023). Temas futuros de la investigación en educación matemática: una encuesta internacional antes y durante la pandemia. Educación Matemática, 35(2), 9-46. https://doi.org/10.24844/EM3502.01
Ball, D. L., Thames, M. H. y Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
Banchi, H. y Bell, R. (2008). The many levels of inquiry. Science and children, 46(2), 26. https://hal.science/hal-00692073v1
Barroso, C., Ganley, C. M., McGraw, A. L., Geer, E. A., Hart, S. A. y Daucourt, M. C. (2021). A Meta-Analysis of the Relation Between Math Anxiety and Math Achievement. Psychological Bulletin, 147(2), 134-168. https://doi.org/10.1037/bul0000307
Bay-Williams, J. M. y SanGiovanni, J. J. (23 de abril de 2022). Accessing fluency through routine and opportunity [presentación]. NCTM Annual Meeting 2022, Los Ángeles, CA.
Booth, T. y Ainscow, M. (2002). Index for Inclusion. Developing learning and participation in schools. Center for Studies on Inclusive Learning (CSIE).
Bouck, E. C., Satsangi, R. y Park, J. (2018). The Concrete–Representational–Abstract Approach for Students With Learning Disabilities: An Evidence-Based Practice Synthesis. Remedial and Special Education, 39(4), 211-228. https://doi.org/10.1177/0741932517721712
Bruner, J. S. (1977). The process of education. Harvard University Press.
Casey, K. y Sturgis, C. (2018). Levers and Logic Models: A Framework to Guide Research and Design of High-Quality Competency-Based Education Systems. iNACOL. Extraído de: https://bit.ly/3w0QeE9
Castillo-Sánchez, M., Gamboa-Araya, R. y Hidalgo-Mora, R. (2020). Factores que influyen en la deserción y reprobación de estudiantes de un curso universitario de matemáticas. Uniciencia, 34(1), 219-245. https://doi.org/10.15359/ru.34-1.13
Clements, D. H. y Sarama, J. (2020). Learning and teaching early math: The learning trajectories approach. Routledge.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed). L. Erlbaum Associates. https://doi.org/10.4324/9780203771587
Connolly, P., Keenan, C. y Urbanska, K. (2018). The trials of evidence-based practice in education: a systematic review of randomised controlled trials in education research 1980–2016. Educational Research, 60(3), 276–291. https://doi.org/10.1080/00131881.2018.1493353
Darling-Hammond, L. y Adamson, F. (2014). Beyond the Bubble Test: How Performance Assessments Support 21st Century Learning. John Wiley & Sons. https://doi.org/10.1002/9781119210863
Freudenthal, H. (1973). Mathematics as an educational task. Kluwer Academic Publishers.
Hattie, J. (2008). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge. https://doi.org/10.4324/9780203887332
Howard, J. (2007). Curriculum development. Center for the Advancement of Teaching and Learning. Elon University.
Innovamat Education S.L. (3 de diciembre de 2024). Libro blanco: El aprendizaje de las matemáticas. Fundamentos teóricos de la propuesta de Innovamat. https://www.innovamat.com/wp-content/uploads/2025/04/Libro-blanco-aprendizaje-matematicas-Innovamat.pdf
Kolomitro, K., Inglese, J. y Idzikowski, M. (2017). Curriculum Design Handbook. Centre for Teaching and Learning. Queen's University. http://www.dgma.donetsk.ua/docs/kafedry/avp/metod/Kolomitro%20-%20Curriculum%20Design%20Handbook%20-%202017.pdf
Kraft, M. A. (2020). Interpreting Effect Sizes of Education Interventions. Educational Researcher, 49(4), 241–253. https://doi.org/10.3102/0013189X20912798
Laski, E. V., Jordan, J. R., Daoust, C. J. y Murray, A. (2015). What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education. SAGE Open, 5(2), 1-8. https://doi.org/10.1177/2158244015589588
Leong, Y. H., Ho, W. K. y Cheng, L. P. (2015). Concrete-Pictorial-Abstract: Surveying its origins and charting its future. The Mathematics Educator, 16(1), 1-18. https://hdl.handle.net/10497/18889
López-Chao, V., Mato-Vázquez, D. y Chao-Fernández, R. (2020). Análisis confirmatorio de la estructura factorial de la ansiedad hacia las matemáticas. Revista de Investigación Educativa, 38(1), 221-237. https://doi.org/10.6018/rie.359991
Liljedahl, P. (2020). Building Thinking Classrooms. Corwin.
Martins, L. G. y Martinho, M. H. (2024). Tipologia de tarefas nos manuais escolares de Matemática: um estudo com manuais portugueses de 10. º e 11. º ano. Educación matemática, 36(1), 66-91. https://doi.org/10.24844/EM3601.03
Mayer, R. E. (2002). Rote Versus Meaningful Learning. Theory Into Practice, 41(4), 226–232. https://doi.org/10.1207/s15430421tip4104_4
Meyer, A., Gordon, D. y Rose, D. H. (2014). Universal Design for Learning: Theory and Practice. CAST Professional Publishing.
Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L. y Fishbein, B. (2020). TIMSS 2019 International results in mathematics and science. Boston College, TIMSS & PIRLS International Study Center: https://timssandpirls.bc.edu/timss2019/international-results/
National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. NCTM.
https://hdl.handle.net/20.500.12365/17719
National Governors Association Center for Best Practices (NGACBP) & Council of Chief State School Officers (CCSSO). (2010). Common Core State Standards for Mathematics. NGACBP & CCSSO Authors.
Niss, M. y Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102, 9-28. https://doi.org/10.1007/s10649-019-09903-9
Organisation for Economic Co-operation and Development (OECD). (2017). Marco de Evaluación y de Análisis de PISA para el Desarrollo: Lectura, matemáticas y ciencias. OECD Publishing.
Piggott, J. (2011). Mathematics enrichment: What is it and who is it for? NRICH - Millennium Mathematics Project. Cambridge University. https://nrich.maths.org/5737
Pólya, G. (1945). How to solve it. Princeton University Press.
Programa de las Naciones Unidas para el Desarrollo (PNUD). (2020). Informe sobre Desarrollo Humano 2020. La próxima frontera: El desarrollo humano y el Antropoceno. PNUD.
Purwadi, I., Sudiarta, I. y Suparta, I. N. (2019). The Effect of Concrete-PictorialAbstract 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
Santos-Trigo, M. (2024). Problem solving in mathematics education: tracing its foundations and current research-practice trends. ZDM–Mathematics Education, 56(2), 211-222. https://doi.org/10.1007/s11858-024-01578-8
Schleicher, A. (2019). PISA 2018: Insights and Interpretations. OECD Publishing.
Schoenfeld, A. H. (2014). Mathematical Problem Solving. Elsevier.
Shuxratovna, R. N. (2024). Pedagogical possibilities of implementing the CPA (Concrete-Pictorial-Abstract) approach. International Journal of Pedagogics, 4(2), 68–76. https://doi.org/10.37547/ijp/volume04issue02-13
Silver, E. A., Kilpatrick, J. y Schlesinger, B. (1990). Thinking through mathematics. College Board Publications.
Skemp, R. R. (1976). Relational Understanding and Instrumental Understanding. Mathematics Teaching, 77, 20–26. https://ci.nii.ac.jp/naid/10010963202
Slavin, R. E., Lake, C., Davis, S. y Madden, N. A. (2011). Effective programs for struggling readers: A best-evidence synthesis. Educational Research Review, 6(1), 1–26. https://doi.org/10.1016/j.edurev.2010.07.002
Solomon, T., Dupuis, A., O’Hara, A., Hockenberry, M. -N., Lam, J., Goco, G., Ferguson, B. y Tannock, R. (2019). A cluster-randomized controlled trial of the effectiveness of the JUMP Math program of math instruction for improving elementary math achievement. PLoS ONE, 14(10), e0223049. https://doi.org/10.1371/journal.pone.0223049
Stanton, E. A. (2007). The Human Development Index: A History. Political Economy Research Institute (PERI) Working Papers Series Nr.127. University of Massachusetts Amherst. https://doi.org/10.7275/1282621
Stephan, M. y Akyuz, D. (2022). Semiotics from a social constructivist perspective. International Journal of Science and Mathematics Education, 20, 1499-1519. https://doi.org/10.1007/s10763-021-10212-y
Stigler, J. W. y Hiebert, J. (1999). The Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the Classroom. The Free Press.
Suárez-Pellicioni, M., Núñez-Peña, M. I. y Colomé, À. (2016). Math anxiety: A review of its cognitive consequences, psychophysiological correlates, and brain bases. Cognitive, Affective, & Behavioral Neuroscience, 16(1), 3-22. https://doi.org/10.3758/s13415-015-0370-7
Tashtoush, M. A., Wardat, Y., Aloufi, F. y Taani, O. (2022). The effect of a training program based on TIMSS to developing the levels of habits of mind and mathematical reasoning skills among pre-service mathematics teachers. Eurasia Journal of Mathematics, Science and Technology Education, 18(11), em2182. https://doi.org/10.29333/ejmste/12557
Teig, N., Scherer, R. y Olsen, R. V. (2022). A systematic review of studies investigating science teaching and learning: over two decades of TIMSS and PISA. International Journal of Science Education, 44(12), 2035-2058. https://doi.org/10.1080/09500693.2022.2109075
Thiyagu, K. (2013). Effectiveness of Singapore math strategies in learning mathematics among fourth standard students. Vetric Education, 1, 1-14.
Vilalta, A. (2021). Un proyecto para desarrollar la competencia matemática en el aula de primaria. Uno: Revista de Didáctica de las Matemáticas, 92, 73-79.
Valencia Álvarez, A. B. y Valenzuela González, J. R. (2017). ¿A qué tipo de problemas matemáticos están expuestos los estudiantes de Cálculo? Un análisis de libros de texto. Educación matemática, 29(3), 51-78. https://doi.org/10.24844/em2903.02
Welch, B. L. (1947). The generalization of ‘Student’s’ problem when several different population variances are involved. Biometrika, 34(1–2), 28–35. https://doi.org/10.1093/biomet/34.1-2.28
Copyright (c) 2025 Revista de Investigación Educativa
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The articles and scientific documents published in RIE abide the following conditions:
1. The Servicio de Publicaciones de la Universidad de Murcia (the publisher) has the property rights (copyright) of all the documents published and allows the reuse under the user’s license indicated in point 2.
2. All documents are published in the digital edition of RIE under a Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (legal document) license. These documents can be copied, used, distributed, communicated and explained publicly if: i) the author(s) and its original source of publishing (magazine, publisher and URL of the document) are cited; ii) it is not used for commercial purpose; iii) the existence and the specifications about this license are mentioned.
3. Auto-archive’s conditions. The authors are allowed and encouraged to digitally distribute the pre-print versions (a version before evaluation) and/or post-print (a version that it is already evaluated and accepted to its publication). This promotes circulation and distribution earlier and can increase the citations and significance within the academic community.
