When I was in the process of publishing Math Makes Sense!: A Constructivist Approach to the Teaching and Learning of Mathematics!, my oldest daughter saw the cover the publisher had sent for my approval. “Dad”, she shrieked in disbelief, “that title doesn’t even make sense!” She was referring to the title “Maths Makes Sense” suggested by British publisher Imperial College Press. The graphic designer had changed “math” for “maths.” That gave me the opportunity to construct on her previous knowledge of similar issues between Latin American Spanish (in its several incarnations) and Spanish as spoken in certain regions of Spain. That’s what a constructivist approach is: we construct on students’ prior knowledge to make connections and anchor knowledge.

This PDF is an article Ana Quintero and I published in the British journal Creative Teaching & Learning. It furthers a constructivist approach to mathematics teaching and learning based on Freudenthals’ Realistic Mathematics Philosophy. Here’s an excerpt.

“When selecting problems for children to solve, we should remember that the ‘realistic’ concepts students bring to the classroom involve aliens flying across galaxies; wizards, gnomes and elves inhabiting enchanted forests; dragon-fighting knights rescuing princesses from mystical castles; superheroes saving the world; and much, much more! We can use these elements and concepts to create problems and puzzles that capture students’ attention and feed their imagination.”

Here’s another one.

“Yes, the learning of maths must follow children’s cognitive development, but this must take place in a community that promotes genuine interest in problem solving—in making conjectures, and in sharing, discussing and arguing those conjectures with their peers. This environment must be alive and support pupils’ participation in the process of using mathematics with understanding, in order to comprehend situations that are of interest and relevant to them. Only then will maths truly make sense.”

Here’s a picture of the cover, as published. My daughter was validated. 🙂

About the author: You may contact Hector Rosario at hr111@caa.columbia.edu.