Thursday I did the Dan Meyer Stacking Cups activity with my Algebra 2 classes. My intention was to give some motivation to linear functions, plus it's a fun activity and it would get them thinking. Or so I thought.
My first two classes did a nice job with the activity. Of course there was some playing around with cups and what not, but the pairs came up with good guesses and we had a nice discussion about them afterwards. I specifically told my 1st two classes to not tell the answer to my later classes and my first class honored that rather well. By the time I got to my last class, I knew something had to be up since there were about 4 pairs that had an answer rather quickly. The activity went rather poorly since they seemed to think they had a correct answer (which some did and some didn't) so they weren't engaged with the activity at all.
In the discussion phase, it did come out that two of my 2nd class students had told the answer to another student in the last class. They had blatantly volunteered the answer without even being asked about what we did. It totally ruined the activity. I wasn't in school Friday to talk to the two students about this and I was still trying to figure out what I wanted to say to them. The two students are both 9th graders - they took Algebra 1 in 8th grade but did not take the advanced class (I can't remember if it was because they weren't recommended or that they just chose not to). Both young people are pretty bright. Not having talked to them, I would guess that they were just being smart-aleky freshmen boys and trying to be better than the teacher.
After reading this post by @hillby258 at "Math is a Shovel" - it really clicked in my head why what they did ruined the activity. These students robbed my last period class of having the experience of figuring it out for themselves, of having the satisfaction of coming up with the correct answer on their own. But then I asked myself, how is my providing students the answers to their practice problems any different? If I am giving them the answers to the problems at the beginning - what's different than those two students giving the answer to the Stacking Cups problem? At the moment, I think it's different because it's in a different situation - I am giving them the answers so they can make sure they are practicing the problems correctly, whereas Thursday students were given the answers to a singular problem they were to figure out on their own with little information (but enough) provided.
And I'm also asking myself how can I continue to try these types of activities with my classes to provide context to the mathematics? There are students who are volunteering the easy way out to others and robbing them of the journey to get there. I have students who have little desire to go on the journey. How do I proceed with a similar task for my classes? I really felt it went well with one of my classes, okay with another one, and not well at all for the other class. I don't want to rob my students of the experiences of seeing the mathematics in a different context - not in the "here's the math - do the problems" structure of class. I thought I had made clear to my earlier classes in the day why it was important to not share the answer - and it was followed by all by two students, who wrecked the activity for my last class. How do I keep that from happening again? Or better yet, how do I adapt so that I deal better with it if it does happen again?