Active learning strategies for an effective mathematics teaching and learning

Isabel Vale 1 2, Ana Barbosa 1 2 *
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1 Instituto Politécnico de Viana do Castelo, Viana do Castelo, PORTUGAL
2 Research Center on Child Studies, University of Minho, Braga, PORTUGAL
* Corresponding Author
EUR J SCI MATH ED, Volume 11, Issue 3, pp. 573-588.
Published Online: 30 March 2023, Published: 01 July 2023
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Learning is an active enterprise, where three dimensions stand out, cognitive, social, and physical, and, in addition, not all students learn in the same way. Grounded on these ideas, this article reports a study that aims to understand and characterize the performance of pre-service teachers when experiencing active learning strategies during their mathematics classes. The participants were 48 future teachers of primary education (3-12 years old) that experienced paper folding, a gallery walk, and a math trail as active learning strategies. We followed a qualitative methodology, collecting data though observations, written productions, and photographic records. The analysis involved a qualitative and inductive approach resorting to content analysis. The results of the study show that the participants valued these experiences, due to their potential in the development of a diversity of mathematical concepts and abilities, and throughout them showed traits of cognitive, social, and physical engagement. Active learning provided collaborative work and mathematical communication enabling the emergence of different strategies to solve the proposed tasks. The participants were able to reflect and be aware of their ideas, mistakes, and difficulties, as well as of others, in a non-threatening environment, where movement was highlighted for not being a popular dimension in mathematics classes. Although more research is needed, the results encourage the use of active learning strategies as a valuable approach to teaching and learning.


Vale, I., & Barbosa, A. (2023). Active learning strategies for an effective mathematics teaching and learning. European Journal of Science and Mathematics Education, 11(3), 573-588.


  • Barbosa, A., & Vale, I. (2018). Math Trails: a resource for teaching and learning. In V. Gitirana, T. Miyakawa, T., M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the Re(s)sources 2018 international conference (pp. 183-186). ENS de Lyon.
  • Barbour, B. (2014). Introducing qualitative research: A student’s guide. SAGE.
  • Blanco, T., Godino, J., Sequeiros, P., & Mantecón, J. (2019). Skill levels on visualization and spatial reasoning in pre-service primary teachers. Universal Journal of Educational Research, 7, 2647-2661.
  • Boakes, N. (2009). Origami instruction in the middle school mathematics classroom: Its impact on spatial visualization and geometry knowledge of students. Research in Middle Level Education Online, 32(7), 1-12.
  • Borromeo-Ferri, R. (2012). Mathematical thinking styles and their influence on teaching and learning mathematics [Paper presentation]. The 12th International Congress on Mathematical Education.
  • Braun, B., Bremser, P., Duval, A., Lockwood, E., & White, D. (2017). What does active learning mean for mathematicians? American Mathematical Society, 64(2), 124-129.
  • Cahyono, A. N., & Ludwig, M. (2019). Teaching and learning mathematics around the city supported by the use of digital technology. EURASIA Journal of Mathematics, Science and Technology Education, 15(1), 1-8.
  • CCR. (2015). Four-dimensional education: the competencies learners need to succeed. Center for Curriculum Redesign.
  • Clements, D. H., & McMillen, S. (1996). Rethinking concrete manipulatives. Teaching Children Mathematics, 2, 270-279.
  • Cross, R. (1997). Developing maths trails. Mathematics Teaching, 158, 38-39.
  • DeYoung, M. J. (2009). Math in the box. Mathematics Teaching in the Middle School, 15(3), 134-141.
  • Edwards, S. (2015). Active learning in the middle grades. Middle School Journal, 46, 26-32.
  • Edwards, S., Kemp, A., & Page, C. (2014). The middle school philosophy: Do we practice what we preach, or do we preach something different? Current Issues in Middle Level Education, 19(1), 13-19.
  • Erickson, F. (1986). Qualitative methods in research on teaching. In M. C. Wittrock (Ed.), Handbook of research on teaching (pp. 119-161). Macmillan.
  • Fosnot, C., & Jacob, B. (2010). Young mathematicians at work: Constructing algebra. Heinemann.
  • Francek, M. (2006). Promoting discussion in the science classroom using gallery walks. Journal of College Science Teaching, 36(1), 27-31.
  • Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. Basic Books.
  • Hannaford, C. (2005). Smart moves: Why learning is not all in your head. Great River Books.
  • Hannula, M. (2001). The metalevel of emotion-cognition interaction. In M. Ahtee, O. Björkqvist, E. Pehkonen, & V. Vatanen (Eds.), Research on mathematics and science education: From beliefs to cognition, from problem solving to understanding (pp. 55-65). University of Jyväskylä, Institute for Educational Research.
  • Jensen, E. (2005). Teaching with the brain in mind. Association for Supervision and Curriculum Development.
  • Kenderov, P., Rejali, A., Bartolini Bussi, M., Pandelieva, V., Richter, K., Maschietto, M., Kadijevich, D., & Taylor, P. (2009). Challenges beyond the classroom–sources and organizational issues. In E. Barbeau, & P. Taylor (Eds.), Challenging mathematics in and beyond the classroom–New ICMI study series 12 (pp. 53-96). Springer.
  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. University of Chicago Press.
  • Leikin, R. (2016). Interplay between creativity and expertise in teaching and learning of mathematics. In C. Csíkos, A. Rausch, & J. Szitányi (Eds.), Proceedings of the 40th Conference of the International (pp. 19-34). PME.
  • Lucke, T., Dunn, P. K., & Christie, M. (2017). Activating learning in engineering education using ICT and the concept of ‘flipping the classroom’. European Journal of Engineering Education, 42, 45-57.
  • Ludwig, M., & Jablonski, S. (2021). Step by step: Simplifying and mathematizing the real world with MathCityMap. Quadrante, 30, 242-268.
  • Meyers, C., & Jones, T. (1993). Promoting active learning: Strategies for the college classroom. Jossey-Bass Publishers.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis. SAGE.
  • NAEYC. (2009). Developmentally appropriate practice in early childhood programs: Serving children from birth through age 8. National Association for the Education of Young Children.
  • NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
  • NCTM. (2014). Principles to actions: Ensuring mathematical success for all. National Council of Teachers of Mathematics.
  • Nesin, G. (2012). Active learning. In AMLE (Ed.), This we believe in action: Implementing successful middle level schools (pp. 17-27). Association for Middle Level Education.
  • OME. (2016). Capacity building series: Communication in the mathematics classroom. Ontario Ministry of Education, Queen’s Printer for Ontario.
  • Prince, M. (2004). Does active learning work? A review of the research. Journal of Engineering Education, 93, 223-231.
  • Ratey, J. S. (2008). The revolutionary new science of exercise and the brain. Little Brown.
  • Richardson, K. (2004). Designing math trails for the elementary school. Teaching Children Mathematics, 11, 8-14.
  • Shoval, E. (2011). Using mindful movement in cooperative learning while learning about angles. Instructional Science, 39(4), 453-466.
  • Stein, M., & Smith, M. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268-275.
  • Vale, I., & Barbosa, A. (2015). Mathematics creativity in elementary teacher training. Journal of the European Teacher Education Network, 10, 101-109.
  • Vale, I., & Barbosa, A. (2019). Gallery walk a collaborative strategy to discuss problem solving. Quaderni di Ricerca in Didattica (Mathematics), 2, 151-156.
  • Vale, I., & Barbosa, A. (2020a). Gallery Walk: Uma estratégia ativa para resolver problemas com múltiplas soluções [Gallery Walk: An active strategy to solve problems with multiple solutions]. Revista da Sociedade Brasileira de Educação Matemática, 17, 1-19.
  • Vale, I., & Barbosa, A. (2020b). Mathematics & movement: The gallery walk strategy. In G. S. Carvalho & P. Palhares, F., Azevedo, & C. Parente (Eds.), Improving children’s learning and well-being (pp. 7-22). Centro de Investigação em Estudos da Criança/Instituto de Educação.
  • Vale, I., & Barbosa, A. (2021). Promoting mathematical knowledge and skills in a mathematical classroom using a Gallery Walk. International Journal of Research in Education and Science, 7, 1211-1225.
  • Vale, I., Barbosa, A., & Cabrita, I. (2019). Mathematics outside the classroom: Examples with pre-service teachers. Quaderni di Ricerca in Didattica (Mathematics), 2, 137-142.
  • Vale, I., Barbosa, A., & Cabrita, I. (2020). Paper folding for an active learning of mathematics: An experience with preservice teachers. Quaderni di Ricerca in Didattica (Mathematics), 7, 53-59.
  • Vygotsky, L. S. (1996). A formação social da mente [The social formation of mind]. Martins Fontes.
  • Webster, C. A., Russ, L., Vazou, S., Goh, L., & Erwin, H. (2015). Integrating movement in academic classrooms: Understanding, applying and advancing the knowledge base. Obesity Reviews, 16, 691-701.
  • WEF. (2016). New vision for education: Fostering social and emotional learning through technology. World Economic Forum.