Life isn’t simple. From the time we wake up until the time we fall asleep there are always surprises each day. Just when I think I have a handle on what I’m doing for the day, something comes up and I adjust.
I wonder if we try too hard to present mathematics and, in particular, problem solving too simply to our students. Is that why we have a tendency to:
- bring closure to a problem during a class period rather than using a Take 5 Minutes approach and let time elapse between engagement with a problem?
- want to help too soon when students are struggling?
- want to confirm “yes, your answer is correct” instead of asking “why do you think that?” or some question that encourages explanation rather than right/wrong?
In October of 2011 I tried something during a workshop that I’d actually had slip back to the recesses of my mind … but … as I’ve been thinking more about helping teachers use more problem-solving activities in classrooms, it suddenly came forward again.
Here’s what a group of teachers in the workshop and I tried:
- Read-aloud scenario: Eating Grapes [Problem #4507]
- Look-at-the-picture scenario: Measuring Melons [Problem #5144]
- Look-at-the-picture-and-the-graphs scenario: Filling Glasses [Problem #5104]
We spent about 10 minutes on each first noticing and wondering orally and then taking a few minutes to individually write down some things that were noticed and wondered.
[NOTE: Some teachers encourage students to notice/wonder individually before anything is said aloud. Because my own classroom experiences were with struggling learners and I often work in classrooms now with teachers and students who are struggling, I tend to encourage a quick oral exercise of noticing and wondering before we ever get to the point of writing. So many of the students I've worked with would give up and think they can't participate if at first I asked them to write.]
After we had noticed and wondered on those three problems (not finding answers at all particularly because the scenarios didn’t include any questions!) we paused to reflect on the experience.
- Was it stressful?
- Were they on overload?
- Were they considering trying it in their classrooms?
They responded no, no, yes to these questions.
Thoughts?
If you try this, I’d love to hear stories!
Last Tweets
Hi Suzanne,
My initial response was one of concern. My wife reminds me that I like to compartmentalize many of my tasks. I do best when completing a task at a time so the thought of asking my adolescent students to do more that one problem at a time seemed scary. Therefore, I was initially concerned with this idea because I thought there’d be three questions instead of three scenarios. Thanks for clarifying as that made a huge difference.
I’m curious to eventually try out the idea of different scenarios with students, keeping in mind that the question for each hasn’t been posed yet. I like a couple things about this:
1) It allows students to potentially have choice in picking the problem they’re the most interested in.
2) If a student is an early finisher, they could possibly work on a second problem.
3) There’s something about multiple scenarios that allows students to prioritize the problems they encounter and that math class is not just a problem-a-day environment.
I also have some thoughts on rolling this out with students. I don’t think I’d recommend teachers (myself included) present multiple scenarios this with their students on the first go. Personally, I’d invest some time at the beginning of the year allowing students to get somewhat comfortable with problem-solving, using only one scenario (problem). When I feel the students have reached this comfort level, I’d introduce two scenarios for our problem-solving work together and eventually work my way up to three scenarios.
Thanks for sharing Suzanne.
I think you bring out a very good point, Andrew, in that this is not something to start with! Instead, it might be something to do once your students have some problem solving under their belts.
I’ve also just thought of another twist to this (again not something initial but later on). What if you combined this “Three Scenario” idea with focusing on a particular problem-solving strategy? So, for example, what if you presented three scenarios, did the initial noticing/wondering and the next day or the day after, gathered wonderings, decided on some questions and then stated — Let’s try to use Make a Table or Solve a Simpler Problem or Change the Representation or Work Backwards or …. to solve all three of these problems.
Have each group pick one of the three but all groups try using the same strategy. I think that could lead to some interesting discussion focused on the strategy and not as much on the problem itself.