“I wonder…..”: Promoting curiosity in the mathematics classroom

I recently came across an article published in the neuroscience journal, Neuron that caught my attention. The article, by Gruber, Gelman and Ranganath (2014), describes a scientific investigation that explored how curiosity influences memory. The authors found a “link between the mechanisms supporting extrinsic reward motivation and intrinsic curiosity and highlight the importance of stimulating curiosity to create more effective learning experiences” (p. 486). In other words, students will learn more about topics they are interested in – something we’ve known along in the education world, but now we have scientific evidence!

Gruber et al. (2014) claim high curiosity results not only in the learning of interesting information but also incidental material. They also discuss how most of the events a person experiences in a day will be forgotten. If we translate this to children and their classroom experiences, can we expect that they won’t remember much of what happens during the average school day? This certainly presents a strong argument against the use of traditional approaches to teaching and learning, particularly the use of textbooks. How can we expect children to get excited and curious about mathematics from a worksheet? We need to ensure we find ways to ‘hook’ students into mathematics and provide opportunities for them to experience the joy of mathematical exploration and discovery.

So what kind of mathematics tasks and activities could be used in the primary classroom to promote curiosity? We know that the teacher is the biggest influence on student engagement with mathematics, and I firmly believe that curiosity is something that must be modeled by the teacher. There are many types of activities that would assist in promoting curiosity amongst students. For example, mathematical magic tricks, or ‘mathemagic’ is a great place to start.

Here’s one (it’s a favourite of mine) that uses three dice:

This trick is based on a simple mathematical fact: Each pair of opposite faces on a six-sided die always adds up to seven. All you need for this trick is three six-sided dice and basic multiplication, addition and subtraction skills! If you’ve got that, you’re ready for the trick.

Instructions:

  • Hand a student the three dice and ask he or she to stack them together so that they form a column
  • Turn your back to the student while he/she silently adds up the numbers on the five hidden dice faces. Tell your student to memorise the sum and keep it a secret.
  • When three dice are stacked together there are five faces that you can’t see: the bottom and top faces of the lowest die, the top and bottom faces of the middle die and the bottom face of the top die. Altogether you get five hidden faces.
  • When your student is ready and has figured out the sum of the numbers on the five hidden faces, you can turn around. Tell him/her that you will use your magical powers to name the sum of the five hidden faces, without looking.
  • Look at the top face of the stacked column, and subtract the number from 21 (For example, if the top number is 3, subtract three from 21) “Abracadabra, the sum is 18!”

When students (and most adults) first see this trick performed, they are amazed. Perform it a couple of times to prove that you are, indeed, magical, before asking them to explore how the trick works. Non-threatening, engaging activities such as this not only spark curiosity, they provide opportunities for mathematical discussion, reasoning, and generalising. An added bonus is that when students ‘get’ the trick, they feel empowered because they can go home and trick their families and friends!

Other activities that promote curiosity include explorations of magic squares, investigating number patterns, which can be as simple as using ten-point circles to explore the patterns with the multiplication tables or simply asking questions that begin with “I wonder …” about some of the day to day contexts that students find themselves in.

There are endless ways that teachers can arouse mathematical curiosity in their students and many resources, educational and otherwise, that could be used. Consider using picture books, non-fiction books such as the Guinness Book of Records, puzzles, video clips, and the list goes on. Anything that gets children interested in mathematics and encourages them to continue with and be successful in the study of mathematics has to be a good thing!

Gruber, M. J., Gelman, B. d., & Ranganath, C. (2014) States of curiosity modulate hippocampus-dependent learning via the dopaminergic circuit. Neuron, 84(2), 486-496.

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