I have been struggling with how to engage students in my future math classrooms. Some teachable subject areas, such as social studies and english, seem to have more freedom to explore topics with an inquiry based approach to actively engage students in the prescribed content. I haven’t, yet, discovered an inquiry approach to link the heavy content curriculum of secondary mathematics, but I have found an approach that might secure engagement in the classroom. Peter Liljedahl, of Simon Fraser University, introduced his use of card trick in the classroom in the paper “Card Tricks, Discovery Learning and Flow in Mathematics Teacher Education”.

He begins by acknowledging that mathematics instruction often follows the pattern of direct instruction, teacher led exemplification, followed by the assignment of homework. As such, our future teachers of math have been through this instruction and generally fall into two categories: secondary teachers from those few who thrive in this system (guilty) and elementary teacher from the many who do not. We talk about this internal debate in our mathematics methods classes: I’m sitting in these classes because I did truly thrive in the high school mathematics environment, but pedagogically I understand that mathematics and problem solving can be taught so much better. 

Dr. Liljedahl is primarily an instructor in mathematics teacher education, therefore, he is instructing the future of mathematics instruction. One way that he tries to break the structured mold of mathematics instruction is by allowing teacher candidates to rediscover mathematics on their own, and often through card tricks.

Questions to accompany this video could be:

  1. How did he do this?
  2. Could you reproduce this trick?
  3. What would change if we omitted the face cards?

Peter Liljedahl has posted nearly 20 videos of mathematics based card tricks to his website (http://www.peterliljedahl.com/teachers/card-tricks) for teachers to use in their classrooms. But there’s one catch – He doesn’t post the mathematics underlaying the trick. As with many of his resources, he believes that teachers can and should learn alongside their students. As we have recently learned in Psychology, when it comes to vicarious learning a coping model will likely be more beneficial than a mastery model. This way, the teacher is either required to produce and understand the solution prior to sharing with their students, or they can work it out with the class and, therefore, demonstrate an element of authenticity in problem solving.

The video formatting of these trick are beneficial, compared to a live play-by-play demonstration of the trick, in that you can pause the video in order to keep track of the inner working of the cards. Dr.Liljedahl does not demonstrate any card tricks on his website that require fancy skills or slight of hand performances, rather they are all mathematical and logic based puzzles that fit well into the classroom.