This week we focus on modeling real-world phenomena. That is a short sentence summarizing what I think is really a very complex concept, that being using some type of representation as a stand-in to explain real-world phenomena.
Jackson, Dukerich & Hestenes (2008) detail Modeling Instruction (capital M, capital I), which is a program equipping teachers with the tools to apply a rigously planned teaching method utilizing modeling and feedback from students themselves. Lehrer & Schauble (2010) discuss what constitutes a model, and the difficulties a novice may have recognizing a model. Finally, Lehrer, Schauble and Petrosino investigated the interactions students had with modeling experiments.
I mentioned the beauty and complexity of mathematics in our first Sci Lit class back in August. In its most applicable (and maybe purest as well) form, math describes the phenomena and nature of reality, sometimes with err but many times with incredible accuracy (and precision, etc.). I think this property of math is what drew me into it so profoundly as a high schooler—just as so many chemical and biological phenomena fit together so perfectly, so does mathmatics fit together so perfectly with itself. So although each of these readings discuss the use of modeling primarily outside the realm of mathematics, I paid closer attention to place where the authors mentioned mathematics and its particular qualities/difficulties/shortcomings. In Jackson, Dukerich and Hestenes, mathematical models are referenced in the Modeling Cycle Example which is presented on page 3. Upon observation of vehicles moving at constant speed, the teacher directs development of a model, lab investigation, and post-lab discussion, all using a mathmatical model designed in the first step. They do not really discuss much the use of the model itself or the concept of math as a model—it seems to be assumed to be know that math is used as a means to model physics. My question is during this process, does the teacher articulate that the mathematics is simply a model, and what that entails?
The 2010 piece from Lehrer and Schauble more directly discusses math as a model. On page 12, we read “Mathematics is a powerful language of modeling, and as these examples suggest, we regard mathematics as an essential resource for pursuing modeling investigations and explanations in science.” They reference the difficulty of the quantitative nature of math—they also reference the common preference towards ‘qualitative over quantitative analysis’, but the real challenge and expertise comes in the recognition of math’s ability to demonstrate an accurate, holistic analysis of scientific phenomena.
I just wonder if this is all too complex to present to students early on; that is, explicitly defining math as not a chore of numbers but rather a beautiful describing tool for the real world. This is an incredible insight--I would hope all students would be blessed with this insight as well.