In the pre-calculus course I teach, two of the topics we cover are basic matrix operations (useful for solving systems of equations and later for determining the cross-product of two vectors) and linear programming (useful as a review of graphing linear inequalities, and then throwing a little something new on top).
The current masters course I'm taking is Discrete Optimization, and early on one of the things we've done is to describe linear programming problems with matrices. Wow, combining two of the things I teach into a single difficult problem, what could be more fun?!
I thought it might be interesting to show my students just how to use matrices to write the constraints of a linear programming problem, but after the "deer in the headlights" looks I was getting today when discussing linear programming without matrices I think I'll just keep that little bit of excitement to myself.
I'm pursuing this particular masters program, which will take me 5 years, rather than a 10 month generic masters in education from a diploma mill, because I want to learn more math and become a better math teacher. I've already moved forward towards both of those goals. The problem is that I get so excited about some of the things I learn that I want to share them with my students, who are nowhere near ready to hear or see that level of math. Even when it's appropriate to what we're doing in class, the background knowledge just isn't there to make the information accessible to students. I fear it might intimidate them unnecessarily and I have no interest in doing that.
So I get to enjoy those little connections all by myself. And sometimes I share them with other teachers.
6 comments:
Darren, in my teaching of 200-level Probability & Statistics at West Point, I don't hesitate to mention the complex problems you can solve with the basic concepts I am teaching. The key I've found is that you can't try and explain it so they understand. You have to mention it so the one kid who is interested gets their appetite whetted enough to wonder if this would be something to pursue later.
"Ever wonder how FEDEX decides where to position their hubs to get your package overnight from California to Maryland? It is just a complex matrix solved with linear algebra."
Kid who is interested in math will ponder that and maybe ask a question after class (It has happened to me). Kids that would glaze over don't have time to because I immediately move on after making the statement.
You're actually learning math instead of education theory? You da man!
If I were a parent in your school district, I would thank you for your concern for your craft (rather than merely your paycheck, as so many MEds seem to be).
And share them with us. I think it's cool ...
What Richard said.
Steve, that's good advice, thank you.
And when I get a chance I *will* share some of it. Right now I need to work on another lesson before heading off to work again for Back To School Night.
I found linear algebra was best used to explain Pandora's algorithm for picking the song you might like best:
Define a vector for each song, rating things like speed, genre, and such as different dimensions. Then use a weighted Euclidean inner product to define an angle [cos(theta) = /|u|*|v|] between songs, or a distance [d(u,v)=|u-v|] between songs. You give a song, and Pandora spits out "nearby" songs. You "like" songs, and we can define a subspace in the vector space of songs that you might like... Isn't it neat?
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