Teaching Mathematical Problem-Solving with the Brain in Mind: How can opening a closed problem help?

  • András Ambrus
Keywords: problem solving, brain based learning, working memory, open problems, representations, students’ activity


In the international literature, increasing numbers of articles and books are published about teaching and learning, with the brain in mind. For a long time, I have been sceptical about this question. However, seeing many unresolved issues in the teaching and learning of mathematics, I slowly started to study the relevant literature and have attempted to implement some ideas in my teaching. In this article, I will report on my experience with a selected mathematical problem in mathematics lessons and group study sessions; I will demonstrate how I modified the problem, based on my experience with the students, and I will reflect on my studies of brain-based mathematics teaching and learning.


Download data is not yet available.


Aschraft, M. H., & Radvansky, G. A. (2010). Cognition. New York: Pearson.

Baddeley, A., Eysenk, M. V., & Anderson M. C. (2009). Memory. New York: Psychology Press.

Banikowski, A. K. (1999). Strategies to enhance memory based on brain-research. In Focus on Exceptional Children. Vol.32. Issue 2.

Bender, W. N. (2009). Differentiating Math Instruction. California: Thousand Oaks.

Davidson, J. E., & Sternberg, R. J. (2003). The Psychology of Problem Solving. Cambridge: Cambridge University Press,

Della Sala, S., & Anderson, M. (2012). Neuroscience in Education. Oxford: Oxford University Press.

Eysenk, M. V. (2007). Fundamentals of Cognition. New York: Psychology Press.

Gasser, P. (2008). Neuropsychologische Grundlagen des Lehrens und Lernens. Bern: h e p Bildungsverlag.

Gasser, P. (2010). Gehirngerecht lernen. Bern: h e p Bildungsverlag.

Gathercole, S. E., & Alloway, T. P. (2009). Working memory and Learning. London: SAGE Publication.

Kahneman, D. (2011). Thinking, Fast and Slow. New York: Farrar Straus and Giroux.

Lakoff, G., & Nunez, R. (2000). Where mathematics comes from: how the embodied mind brings mathematics into being. New York: Basic Books.

Meltzer, L. (2007). Executive Function in Education. New York: The Guilford Press.

Nunez, R., & Freeman, W. J. (Eds.) (1999). Reclaiming Cognition. The primacy of action, intention and emotion. Thorverten, UK: Imprint Academic,

Pinker, S. (1999). How the Mind Works. New York: W. W. Norton Company,

Sammons, L. (2010). Guided Math. A Framework for Mathematics Instruction. Huntington Beach: Shell Education.

Small, M. (2012). Good Questions: Great Ways to Differentiate Mathematics Instruction. London: Teacher College Press.

Small, M., & Linn, A. (2010). More Good Questions. Great Ways to Differentiate Secondary Mathematics Instruction. New York: Teacher College Press,

Sousa, D. A. (2008). How the Brain Learns Mathematics. Thousand Oaks: Corwin Press.

Sternberg, R. J., & Ben-Zeev, T. (1996). The Nature of Mathematical Thinking. Malwah, N.J: Lawrence Erlbaum Associates.

Ronis, D. (2007). Brain-Compatible Mathematics. London: Corwin Press.