Less is More
Dan Meyer has been talking recently about how "You can always add. You can't subtract." Usually a mediocre math task or even a good math task can be made much better by removing some of the information. For example, in this task called Styrofoam Cups by Andrew Stadel, rather than presenting students will all of the information they need to solve the problem (how many cups will stack to reach the height of the door), Andrew Stadel asks students "What information would be useful to know here and how would you get it?" Since we're not in Andrew's classroom and can't actually measure the height of the door and the height of the cup, he provides us with links to pictures of that information which can be given to students when they request it. By leaving that information off to begin with, students are given the opportunity to think about the problem and why that information would be useful.
I find that sometimes when students are given a problem that gives them every piece of information they need, they have a hard time then knowing how to process the information. In contrast, when I allow students to think about and request information, they have a much better idea of what to do with it because they've thought about why the information would be important and how it relates to the situation.
Processing the Information
Choosing the Model
Let the students choose the model! That is one of my biggest take-aways from Kara Imm's presentation last weekend. During first term, I always focus on connecting multiple representations of functions (picture, words, equation, graph, table). When I presented the Styrofoam Cups task to my three honors classes two weeks ago, I gave them this multiple representations form that I created (see document at right) to use in solving the problem. I was so concerned about their fluency in determining independent/dependent variables, slope, y-intercept and creating multiple representations, that I took away their opportunity to choose the model that made the most sense to them. I didn't let them choose a model - I made them use all of them! Coming back to the classroom this week, I could hear Kara Imm telling me "Less is More" and Dan Meyer telling me "You can always add. You can't always subtract." So that's what I did. I broke this lesson into two days for my accelerated class. On the first day, after we discussed all the important information, I had them choose any strategy they wanted to solve the problem and record their strategy in their math journal. On the second day, I asked them to describe their thinking and wrote them out on the board. The strategies ranged from guess and check, to writing an equation, to drawing a diagram. After we had discussed all of their strategies, I gave them the multiple representations form. This seemed like a good compromise between letting my students begin by choosing their own model and then later making certain that they are able to move fluently between models.
A Final Thought
My students have tool baskets at their tables, in which I vary the tools that are available depending on the activity. When I run the Styrofoam Cups lesson with my regular ed math classes in a week or two, I'm going to include some cups of varying sizes. If students struggle to identify the information that they need to solve the problem, I will give them some time to experiment with stacking the cups in their tool baskets, if they choose to do so. Just another testament to the power of online collaboration and the #MTBoS! Thanks Mr. Schwartz! I would have never thought of that without you!