Students taught through passive approaches follow and memorize methods instead of learning to inquire, ask questions, and solve problems. Jo Boaler, What’s Math Got to Do With It?
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The past 15-20 years have seen huge shifts in math instruction. New standards deemphasize rote memorization of procedures and outline an approach to teaching math that balances procedural fluency, conceptual understanding, and problem-solving. That is in large part due to the fact that the way we use mathematics has changed in the past 50 years. Our mobile phones now have the power to do calculations that previously were either done manually or using room-sized computers. That’s not to say that procedural fluency is no longer important, it’s just not the only thing that’s important.
Now think about the traditional model for teaching math; I Do, We Do, You Do. This model is also called the gradual release of responsibility. Look back at Jo Boaler’s quote at the beginning of this post, and do you see that this traditional approach is very passive? Students are basically just memorizing and mimicking a procedure modeled by the teacher. Yet this is still the predominant instructional model in math classrooms. The lessons in most math textbooks are structured based on the model. Unfortunately, this model does little to address problem solving or conceptual understanding.
But what if we flipped the script? Now the model becomes You Do, We Do, I do.
So now we have a more student-centered model that incorporates problem-solving. It’s much less scripted. Let me illustrate with an example.
Say, for example, that I want to introduce all the combinations for a number, in this case 5, to a Kindergarten class. I could present a very scripted lesson, such as the one shown below. Recognize that this is very passive learning for students. They are merely mimicking the teacher’s actions. And the teacher is doing all the explaining.
Contrast that with this approach. This time, I’m going to give pairs of students two plates and 5 counters. Then I’m going to pose the following problem: Stephan has 5 cookies he wants to put on two plates. Use your counters and paper plates to show how he might place the cookies. Can you think of more than one way?
After giving students a few minutes to work on the problem (you do), I’ll solicit the combinations they discovered and record them on the board or chart paper. I can question them about their process and we can discuss any patterns we see (we do). To extend the activity, I might ask, Huh, I wonder if we found all the ways to make 5? Then we could discuss different ways to organize our data to help us determine if we found all the combinations. Finally, I’ll consolidate the learning (I do), asking students to reflect on what they learned and stating my teaching point: There are many different ways to make numbers and we call them combinations.
Notice that with this lesson, students are actively involved. They are working on the problem with a partner, which encourages great mathematical conversations. They are making their own discoveries, and that helps them take ownership of the learning. And then the lesson is tied up neatly with a bow!
Change can be hard! The I Do, We Do, You Do model has been around for a very long time. Let’s break that mold and put students in charge of their learning!