Some of the most valuable courses I took while I was in school were so because, in addition to learning a specific body of content (and having it taught well), I picked up something extra along the way that turned out to be just as cool or valuable as the course material itself. Examples:

- I was a psychology major at the beginning of my undergraduate years and made it into the senior-level experiment design course as a sophomore. In that course I learned how to use SPSS (on an Apple IIe!). That was an “extra” that I really enjoyed, perhaps moreso than the experiment I designed. (I wish I still knew how to use it.)
- In my graduate school differential geometry class (I think that was in 1995), we used Mathematica to plot torus knots and study their curvature and torsion. Learning Mathematica and how to use it for mathematical investigations were the “something extra” that I took from the course. Sadly, the extras have outlived my knowledge of differential geometry. (Sorry, Dr. Ratcliffe.)
- In the second semester of my graduate school intro abstract algebra class, my prof gave us an assignment to write a computer program to calculate information about certain kinds of rings. This was a small assignment in a class full of big ideas, but I had to go back and re-learn my Pascal in order to write the program, and the idea of writing computer programs to do algebra was a great “extra” that again has stuck with me.

Today I really like to build in an “extra”, usually having something to do with technology, into every course I teach. In calculus, my students learn Winplot, Excel, and Wolfram|Alpha as part of the course. In linear algebra this year I am introducing just enough MATLAB to be dangerous. I use Geometers Sketchpad in my upper-level geometry class, and one former student became so enamored with the software that he started using it for everything, and is now considered the go-to technology person in the school where he teaches. In an independent study I am doing with one of my students on finite fields, I’m having him learn SAGE and do some programming with it. These “extras” often provide an element of fun and applicability to the material, which might be considered dry or monotonous if it’s the only thing you do in the class.

What kinds of “extras” were standouts for you in your coursework? If you’re a teacher, what kinds of “extras” are you using, or would you like to use, in your classes?

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Filed under Abstract algebra, Calculus, Computer algebra systems, Education, Geometers Sketchpad, Geometry, Linear algebra, Math, MATLAB, Sage, Teaching, Technology, Wolfram|Alpha

Tagged as Math, Mathematica, mathematics, Teaching, Technology, Wolfram Alpha

One of the more fascinating extras I got out of engineering school was simply the crunching of complex numbers on my then new HP42 calculator. To this day I am a huge fan of RPN and the 42 specifically because I have never since come across a newer calc that could handle complex numbers so easily and intuitively as the 42. Because of my enthusiasm for calculators I now have a collection of 50 or so of them, the latest being the nSpire CAS, for better or worse. The whole pedagogical, as well as professional, mix has been complicated by the advent of PDA and iPhone apps that do the same kind of thing as dedicated hardware. Also there are now all thePC platforms out there. And I have heard discussions about the diminishing returns of dedicated calculators, but I still find that math is still hugely facilitated by being able to graph a function on the fly on the lunchroom table while simultaneously talking or texting or surfing on the iPhone as a separate device.

I only wish that there had been that “extra” element of formal instruction back then on how to use calculators more effectively. I think in the 60’s you could take whole classes on the use of the slide rule. Rather , what I got was a course in Fortran or Basic done, in my case on an LN120 DEC line printer talking to an HP2000. Try putting that in you hip pocket! But after that I did everything on the programmable calc. I got caught in a transition perhaps (late 70’s).

So right now it is merely a hobby of mine but if I ever get a change to return to grqad school I hope to have all my tools in place and can expect good formal instruction in the use of these tools whether as a separate workshop, course, or integration into courses.

I am teaching my abstract algebra students how to use LaTeX. I am in the middle of grading our first homework assignment, and I am thrilled whenever a get to grade a TeXed assignment. It is much easier to read.

They also get unlimited chances to redo some of their homework, so they will benefit when they just need to edit a computer file rather than completely rewrite a proof by hand.

How are you phasing in LaTex and what methods, tutorials, software, etc are you going to teach to? I wish to learn it myself but there are so many confusing materials out there.

Will, I’m planning on blogging about that very topic later this week. I’ll try to see if I can get that post out tomorrow.

In Calculus … Jing, Wolfram Alpha, and MathType are probably the biggies.

In MathET … presentation design, blogging, how to build a webpage, building online mindmaps, and how to teach without lecturing