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.

I find it very interesting that you looked at the articles from a mathematical, rather than a scientific, perspective. I too wondered while reading if the modeling methods described would be too complex to present to younger students, even though they gave some examples using elementary schoolers. I think that for younger students, the focus of the teacher is on teaching them what the concept of modeling entails, rather than modeling specific concepts for the class. This probably would help students handle future modeling exercises better.

ReplyDeleteI enjoyed your mathematical applications to these papers. I think it was Da Vinci who said "Math is the language God used to write the world." Thinking about this from a chemistry perspective, how can we use math as a model to make chemistry make sense? One application off the top of my head might be having students explore the effect on boiling point when you add salts to a solvent. Another possible application to this would be giving students a first hand experience in determining one of the many possible uses of math, which may significantly change a student's attitude toward either subject.

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