Have you ever thought about the fact that “modeling” in the Common Core is not only in the Standards for Mathematical Practice, but also is a content standard? I have to admit that I hadn’t really thought much about it until a colleague asked me how the two things differed. I immediately started researching to see what the distinction was, or if one even exists.
The Standards for Mathematical Practice describe “habits of mind,” or productive ways of thinking that support the learning and application of formal mathematics, we want to develop in our students. Modeling here is defined by the Common Core as:
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another.
In the Mathematical Content Standards, modeling is defined as:
Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions.
Some obvious things here include:
1. The Mathematical Practice goes across all grade levels and involves applying mathematics students know to solve problems.
2. The Conceptual Category is a high school standard and goes across all mathematical content areas.
3. The conceptual category involves a modeling cycle that involves (a) identifying variables in the situation and selecting those that represent essential features, (b) formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables, (c) analyzing and performing operations on these relationships to draw conclusions, (d) interpreting the results of the mathematics in terms of the original situation, (e) validating the conclusions by comparing them with the situation, and then either improving the model or, if it is acceptable, (f) reporting on the conclusions and the reasoning behind them.
4. As emphasized in the diagram, choices, assumptions, and approximations are present throughout this modeling cycle.
I contacted another colleague of mine to see what his view of the differences was. His interpretation is that “the conceptual category is generally the same as the practice… only more so. It is more than a practice; it is also content that should be explicitly addressed.”
As we all engage teachers in a dialog around the Common Core, the question of modeling as a practice and as content should take place. It is obviously a focus of the Common Core, particularly at the high school level. I would love to hear your interpretation of this very important, but potentially confusing, distinction.