In yesterday’s problem we took apart a poorly designed math homework. Essentially the math textbook asked the students to practice a highly sophisticated method of addition.
The strategy for breaking one number and adding it to the first to make a 10 then mentally adding the rest is great, but probably should come naturally as it occurs to students as opposed to being forced on them. The real problem is the students who need it the most probably wouldn’t come upon this strategy naturally. So what we have to do is teach this strategy to our students so they can add it to their arsenal of weapons to use when solving math problems. We want to do all of this without actually walking them through a step by step process.
Why not just teach a strategy straight out? Two reasons: First teaching a procedure doesn’t always lead to “ownership” of the procedure. Second, because that isn’t the hard part of math. The hard part is recognizing when it might be the best strategy to use. (Which I suppose is kind of the definition of ownership.)
So for homework (and I am really against homework, but if you insist on giving it at least make it painless and force the parents to be involved as more than a checker of correctness) I might take these same problems and then ask them to choose one and talk out a strategy. They could use a phone or iPad to record the strategy, or call my google voice number and leave a message, They could tell it to their parents, or in any number or methods. The one caveat might be, if they are leaving me a recording it has to be less than 15 second long. (Do you ever notice how much you ramble when you are unsure of yourself?), The next day I might ask two or three or even four students if I could play their recording or if they would like to explain their method. Then I could ask the rest of the class if they tried a similar or different method.
Another alternative, I could ask them to ask their parents to solve one of the problems in their head and teach them the steps they took. Then the student would have to do a different problem and explain the steps back to their parents.
A third alternative, I might ask the students to choose one problem and ask the them to solve it in 3 different ways. Explaining their work each time. I like to encourage a voice recording the when a procedure is new, because it is easier for the kids, I just want them to keep redoing it until it is short enough so that I can listen to 30 in less than a week.
Yes the textbook and I would like to teach the students all of the great strategies for addition, but I think they are going about it the wrong way. They are pulling each strategy out and teaching it explicitly, so instead of learning one way of “doing” addition students are forced to learn a plethora of ways to “do” addition. Completely missing the point of understanding the concept of addition and choosing the best strategy based on the situation.
By asking students to talk about how they solve a problem in their head, especially with others like parents, students are exposed to a variety of strategies for “doing” math. By choosing to have students explain a few different methods the teacher can then make sure each child is exposed to all the strategies she feels the students should know. Now instead of asking students to solve a problem by the “making tens” method we can ask students which method did they choose. Did you choose Bobby’s method, Sarah’s mom’s method, etc… and why did you choose that method?
The point is not to make students practice problems, but to give them an arsenal to choose from and the knowledge of which weapon works in which situation.