Math as Model

My elementary math education in must have been effective – to this day there are specific, although arguably obscure, things that I remember. Specific useful items such as multiplication tables – check. Addition, subtraction, division – check. A little on the obscure, but still useful side, the concepts of additive and multiplicative identity. Respectively, those two identities are, zero plus anything equals that same anything, unchanged, and one times anything equals that same anything, again, unchanged . So identities – check. Rote facts and concepts dutifully absorbed. But one key idea was missing. Why does math matter? What’s it good for? Just a little bit of mathematical philosophy would have gone a long way.

That key missing idea is actually pretty simple – it is that math serves as a model; a method to simplify and understand the world. Once modeled we have a means to comprehend, deal with and predict behaviors in the future.

These things are essential to problem solving – this is the basis for so much of our industry as humans.

This concept might seem obscure at first, but throughout my many years of practice as an aerospace engineer, I’ve learned that the concept serves as the foundation of understanding – models are key to our understanding of the world.

If someone had explained this to me as a child, in terms I could comprehend, which I think it easily realizable, I could have avoided substantial frustrations while learning math – years of math classes that took me all the way through five semester of college math.

Even though I survived my journey could have been much easier.

As a young boy growing up, I was surrounded by models as plaything. Building blocks, Legos, Lincoln Logs, Tinkertoys and even model airplanes. All of these things let me build models. Along the way I was asking , and answering questions that were important to me at the time. What would happen if I stacked the pieces this way, or that? Do I need attach wheels here to make it my creation balanced? What would my model look like if I changed this aspect or that?.

If I would have known that learning math was all about modeling the world, my understanding and ease in class would have been greatly facilitated. After all, for me, modeling was fun.

How much easier would my education have gone? Rather than just survive, I believe I would have thrived.

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2 Responses to “Math as Model”

  1. Eric says:

    I also fully believe that showing the real-world applications of math would have been very useful in encouraging students to become more interested in math. I had a differential equations class where half the textbook were the use of differential equations to solve real-world problems / explain real world occurances. We never covered those sections and I do feel sad that they were never part of the intended course material.

  2. B192 says:

    Thanks Eric; yes more real-world examples would help. DifEq, surprisingly, was one of the more accessible of my 5 semesters of math in college. As a kid, I was constantly building things with blocks, and lego’s, and even model airplanes from kits; all of these things are models. My entire trajectory through education would have been made more organic and practical if someone had taken the time to teach that math is the powerful language of modeling. I would have become “hooked on” math rather than being “hooked by” math. There is a world of difference between those two experiences.

    I appreciate your interest in my blog.