I’ve been developing a workshop on modeling as it is envisioned in the Common Core State Standards. A couple of ideas that I have gotten from my research are presenting quite a challenge:
• Modeling is not a recipe of what mathematics concepts to use and which strategy to follow to solve a particular problem or situation.
• Modeling is a process that allows students to make choices and to test assumptions.
The first statement reminds me of conversations I have had with my science colleagues. They were lamenting the fact that many science labs were laid out with such detailed step-by-step directions that it was no longer an “experiment” but a “recipe.” And all that students had to do was follow directions. They called these “labs” cookbook labs. The term stuck with me because it is so descriptive. Is the person who can follow a recipe for baking a cake really demonstrating that they are a “cook” or just that they are able to follow directions? I’m reminded of the typical algebra rate-of-work problems where an example is given and then students work several problems where they mimic the example. What do they do with those problems on a test or in the real world where they don’t have an example to follow?
The second statement is challenging in that it asks us to present tasks that allow students to make choices about what is the appropriate mathematics to use. Mathematics in the classroom is usually intended to teach a particular mathematical topic while mathematics in the real world is, in fact, having to choose what is appropriate for the situation. So how do we as teachers achieve the goal of teaching mathematical concepts while allowing choices that mirror the real world?
I interpret the Common Core to mean that the example may be more of a discussion than an example. The Common Core does mention that some choices may involve choosing whether to model a coin as a three-dimensional cylinder or a two-dimensional disk in a given situation. So this modeling idea has dimensions that I have never considered as a teacher. I always told my students which model of a coin was appropriate for the situation and which mathematics we were going to use on that day.
Just because I’ve always assumed the responsibility of choosing the model and the mathematics, does that mean that students cannot? If we assume that is true, then it follows that they cannot function in the real world. We’ve discussed a lot in mathematics education about what makes for a real world problem. We now need to spend time thinking about what constitutes real world modeling.
So is modeling as laid out in the Common Core a challenge or a mind shift? For most of us, it is probably both.