ATMOPAV Mathematics & Technology Conference, Fall 2011
Suzanne Alejandre, The Math Forum @ Drexel University, Philadelphia, PA
Saturday, October 22, 2011
Session 3: 1:15 to 2:15 pm
Middle School (grades 6-8)
The goal of the Math Forum’s problem-solving process is not to be over and done. It is to think, express, reflect, and revise. Leave with problems to try with students.
I. Introductions
II. The Math Forum’s Problem Solving Process — let’s experience a short version together!
III. Debrief that experience
- what did you notice?
- what are you wondering?
- CCSS Mathematical Practices
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
IV. More
Measuring Melons (photos)
Sports Weigh-in (photos on blog post with student comments)
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V. Resources:
- Problem Solving and Communication Activity Series [pdf]
- Max’s Blog: Mastering the Common Core Mathematical Practices [webpage]
- Problem Solving–It Has to Begin with Noticing and Wondering [pdf]
- The Math Forum @ Drexel: Free Online Resources [pdf]
- Making Effective Use of Math Forum Resources [webpage]
- Samples of the Problems of the Week [webpage with PDFs links]
- Technology Problems of the Week [webpage]
VI. Links to other Math Forum ATMOPAV talks:
Annie Fetter: Using Technology to Increase Conceptual Understanding in Algebra and Geometry
Steve Weimar and Max Ray: The Mathematical Practices and Understanding Key Concepts: The Case of Fractions
Annie Fetter and Valerie Klein: Online Tools for Building Crucial Elementary Math Concepts
Max Ray: I Tweet Therefore I Learn [link coming soon]
Some things that we noticed [while wearing our teacher hats] after Noticing and Wondering about the Measuring Melons picture:
There’s a lot to talk about! Would kids talk about as many things? Maybe, but maybe different things.
When you say it out loud, you can notice and wonder more, rather than if you’re writing it.
Important to group heterogeneously, because there might be kids who don’t have as many ideas.
It looked like an algebraic problem, but it might be that doing it algebraically could be harder. What if you focus on the pictures?
Some things Suzanne noticed when we were working on the Eating Grapes problem:
Most of us were writing symbols, not prose. Kids without algebra skills can’t write prose either. Maybe one kid talks and one writes?
We didn’t have a problem with the fact that she read Eating Grapes, then made us think about Measuring Melons, and then came back to Eating Grapes. Kids won’t have problems with it either.
The problem solving revelation I had this week was as a teacher I have complained in the past that kids give up on word problems so quickly and even found myself “giving up” on teaching them and focused on skills instead. Well, a few years ago when my relationship with the Math Forum began it became my new passion (more like obsession) to find a way for kids to be successful problem solvers. I have to admit I thought it would be a quick fix at first. Again, like kids it isn’t about being an easy or quick “answer” but instead a process. Well this process has been slow but the AHAs are really rolling in now. I have successfully transformed my classroom into a problem centered classroom where I pose PoWs and give specific feedback (noticing and wondering) and then encourage them to resubmit (revise).
It took me several years to get here but just like mulling over a difficult problem the pleasure you get from solving “the impossible” is unbelievable. I have started to instill that intrinsic drive in my students and I can’t wait to read more solutions…it is an addiction!!!
My advice to teachers is just when you think..”Why do I keep giving them questions they won’t try or don’t “get”?” Don’t give up….they will get there.
I do religiously use the Math Forum problem solving strategies. I started the year by only letting my students notice and wonder (and answer other open ended observations-relationships, counting, etc). After a few weeks of this I let me students choose one of the previous PoWs and solve it. My students have needed a lot of nudging to explain their reasoning but they are improving daily. (Mine do all of this on the computer and that is a motivator in itself.)
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