Solution Fluency: The Cambridge Card Trick Challenge

“This is very stressful!” “We don’t have enough information!” “This is heartbreaking!” “This sucks; I wanna know so bad!”

These were the sounds that filled the classroom the day I introduced a lesson on solution fluency. The problem they were being asked to solve was to determine how I did a card trick. Before we began though, we brainstormed on the board examples of problems they had faced in the past and overcome(learning to tie my shoes, building a catapult in my backyard, passing my driving test, etc.) and what strategies they used to overcome said problem (got help from someone, kept trying and trying, studied and practiced). Armed with the successes of the past, I split them into pairs and gave each pair a deck of cards. They were given 20-25 minutes to solve the problem. While they worked (I informed them that I would not be giving them assistance), I walked around observing and recording. I noticed some roadblocks that prevented some students from preserving through problem solving:

1) Perceived predisposed weakness. When I told students that this card trick was taught to me by a Cambridge math professor, and that there was a math equation that showed how it worked, one girl said with dismay, “Oh, Math! I’m out!” She believed that because she wasn’t a “math person”, she wouldn’t be able to succeed. (yet interestingly enough, she was the first of all my students to solve the trick!).

2) Lack of creativity.  Since the first part of the trick involves flipping cards over face up, when I saw one student flipping cards over face down, I intervened and reminded him that the trick won’t work if he flips the cards over that way. He stopped and stared at me incredulously, arguing, “But how else can I flip them? There’s no other way!” The inability to see something in a new light prevented him from moving forward. This reminded me of how linked all the fluencies are (creativity fluency, where are you? We need you now!) Strategies attempted were very limited and mostly involved guessing the card at random over and over again and puzzling over why it wasn’t working. On the flip side though, I did hear a few choruses of “Let’s try it again and see”, while students tried one different strategy after another such as “thinking about the trick backward” “look on YouTube”or “find a pattern”.

3) Other people’s success. Often when one pair/student was successful at solving the problem, it led to a general decline in other students’ willingness to keep trying. Many pairs just quit completely at that point. One student wrote on the follow up survey to this experience that the most frustrating part of the whole thing was “not getting the answer when other people were”. Rather then seeing their peers’ success as an invigorating indicator that the task was indeed achievable, students tended to view it with a “game over” mentality, as in a video game where one player wins and ends the game for everyone else.

Overall, this experience reaffirmed what I already knew: students need more practice solving problems in an environment where it is okay to fail and try again. An environment where the teacher doesn’t rush in to “help” all the time but patiently let’s them squirm till they find their way out of an uncomfortable yet productive place of uncertainty and into a solution they found, rather than one we delivered to them.