Engagement & Perseverance

           Why is it that some problems are more engaging than others? You know the kind I'm talking about...the kind where kids WANT to work through Recess..the kind where the kids CONTINUE to solve it while you're trying to 'move on'...the kind that has kids ASKING for more...the kind that has kids TALKING about it with their classmates. 

          The other day I stumbled upon one of these types of problems.  I subscribe to Marilyn Burns Math Blog as she is a math guru and seems to have wonderful ideas and practical resources regarding math. The actual post was titled "When Should or Shouldn't We Give Answers?" In the post she shares the "1 to 10 Card Investigation" (Read her original post about it here.) I was actually intrigued by the problem.  

          So during math class, I mentioned the post to my students.  I happened to say that I DID NOT know the answer to the Card Investigation myself.  This seemed to be a challenge they wanted to take on so I showed them Marilyn's video about how to set up the cards. When my homeroom students returned before lunch, their classmates mentioned the challenge to them.  I shared the video once again (quickly) before we headed to the cafeteria. I had no idea how it would take off.  The kids were abuzz about this problem.  (One student even made her own set of 1-10 from index cards!) 

Helping a classmate

          Upon returning from lunch many students started heading to the math center to find the playing cards. Some students paired up but many worked alone.  We didn't have much time as the class was headed to Phys. Ed.  But when they came back they REALLY wanted to try.  How could I say no? It's a math puzzle after all! So I let them work on it for about 15 minutes. The "awwwws" were audible when I told them they'd have to put their cards away so we could continue with our science (which is usually their fav!).

           To my surprise, students went home that evening and worked on the problem (without direction from me to do so).  A few came in with the problem solved while others were "soooo" close to the solution.  Really, the only direction I gave them was that they should be keeping track of their trials (as Marilyn Burns suggested). Again, the students wanted to work on this problem throughout the day.  Students who were successful got the extension activity that Marilyn had suggested.  

Recording each trial

           The students ALL agreed that the problem was difficult.  No one gave up! It was so fun to watch the smiles on the faces of those who figured it out.  It was heartwarming to see classmates helping each other solve without giving the solution away.  It was most amazing to hear students ask for extension after extension. (Several students are working on putting 4 cards under - this will make sense if you read the problem).  This was "perseverance" at it's best! This alone could have been the lesson!

            All of this is wonderful, but it makes me ask the question again, "Why is it some problems are more engaging than others?"  I asked my students why they loved this problem.  Some of the responses included "It's fun!" "It's challenging." "I like cards!" Could it be that they felt comfortable with the using smaller numbers? Or was it because they thought it was a "trick?" Or was it simply they like using the cards? 

             I would love to hear your ideas on what types of problems 'hook' your students and I'd love to learn how we find more of these types of problems that help our students learn?