Last week, I had the pleasure of attending a workshop with Peter Liljedahl from Simon Fraser University. The session was on assessment, but he opened with his take on problem solving. I’m going to discuss the assessment stuff in a later post, but I really wanted to talk about his problem solving process while it was fresh in my mind.
Peter grouped us randomly by having us select cards, and then gave us the following problem.
1001 pennies are lined up in a row. Every second penny is replaced with a nickel. Then every third coin (might be a penny or a nickel) is replaced with a dime. Then every fourth coin is replaced with a quarter. What is the total value of the coins in the row?
He gave each group a whiteboard marker, and a window or small whiteboard to work on. We were to solve the problem on the space we were given. Peter circulated and encouraged us to look at what was written on the other windows if we were stuck. In the end, most of us were satisfied that we were right. Peter never told us the answer or revealed it in any way.
Here’s what interested me about Peter’s take on problem solving, which is very similar to what I have advocated as Learning Through Problem Solving.
- The problem wasn’t written down any where. He just told us the story, clarified, and put us to work. This isn’t a textbook problem.
- He grouped us randomly, rather than letting us sit with the people we came with. Throughout the day, he kept on re-grouping us. His feeling is that this frequent changing of the groups leads to more productive classes, and helps include all students. Kids are more willing to work with someone they don’t like when they know that it won’t be for long. This process helps include even the shy and “outcast” students in the classes. These students are included because the people working with them know that the groups will change again very soon, and so they can be patient for that long. Peter also has a way to assess group processes, which I will discuss in the subsequent post on his assessment material.
- Writing on non-permanent surfaces is critical to Peter’s process. He has observed that when kids work on paper, they take a long time to start. When they work on something like a window or a whiteboard, they start right away, because they know they can erase any mistakes easily. Groups that are stuck can step back and see what the other groups are doing as a way to help them get started. When finished, each group’s work is displayed prominently around the room so that students can share solutions with each other in a non-threatening way. Students could do a gallery walk and discuss the different solutions, or sit down and write down one that works for them individually.
- This is the third time I have had the pleasure of working with Peter. He has never once told us the right answer. This drives teachers nuts. I’ve tried it in classrooms, and it drives kids nuts. The message, though, is that they have to figure out the answer. The teacher isn’t going to let them off the hook. An even more important message is that the teacher is less concerned about the answer than she is about the process. These are two pretty nice messages.
Peter’s problem solving process fits really nicely with the Learning Through Problem Solving discussed frequently on this blog. There’s always a “yeah, but” when I share some of this with teachers. They have one whiteboard, no windows, and nothing else to write on in their classrooms. Let me solve that problem for you.
Superstore has $20 whiteboards that are just the right size. Staples has tons of different sizes available for less than $30 each. I’m confident you could get enough whiteboard space in your classroom for 15 groups to work for less than $300. Your principal will find that kind of money in a hurry, especially when you explain that you are going to use it to enhance mathematics instruction by engaging students in group processes that will lead to better problem solving skills. I’ll write you a letter if you need one.
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When I was in high school, I had a teacher who used something other than boring old “Name: __________” at the top of his tests. He’d put things like, “Hello, my name is: _______” or “_____________ is going to ace this test.”
When I started teaching, I did the same thing. The kids really liked it, and any time it left room for creativity, they did some neat stuff. Over the years, I acquired a pretty long list of them. Whenever I created a new test or handout, I would open up the document with all of them in it, and pick one. Sometimes I asked students to write their own. There is nothing pedagogically brilliant about this. It just amused me.
Here’s the document.
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Posted in Classroom Strategies, Engagement, Learning Through Problem Solving, Lesson Ideas, Math 10-3, tagged Classroom Strategies, Learning Through Problem Solving, Math 10-3, Student Engagement, Teaching on October 31, 2010|
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October’s issue of the NCTM Mathematics Teacher magazine included an excerpt from an interesting article in their Media Clips section. They used a Forbes article that dealt with tween earnings, and the portion they included is:
Hollywood’s 10 top-earning tweens collectively pulled down $107 million between June 1, 2007 and June 1, 2008. According to Alloy Media and Marketing, it’s a rabid and often indulgent fan base: America’s 20 million kids aged 8 to 12 spend $51 billion of their own money annually and influence $150 billion more in spending by their doting parents. Tied for the top spot: Hannah Montana star Miley Cyrus and Harry Potter lead Daniel Radcliffe. The young talents each banked a cool $25 million in the last year.
I love this article for the questions it could elicit. The problem with the Mathematics Teacher Magazine treatment of this is that it follows the article with 8 questions we are supposed to ask kids. Teachers might see this, and defer to the questions provided, thereby missing a great opportunity. I’d much rather show students the article, and have the kids decide what would be interesting to explore further. There are lots of potential rate and ratio questions that could come from student exploration here.
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