Battle of the traditions…

A few days ago, this comic appeared in my Google Reader: http://spikedmath.com/339.html. OK, this is not too difficult when you know who Kenny Baker is (and who doesn’t?!). Click that previous link before you read further.

I then did the calculations by hand, as seen in the first picture (yes, it looks horrible, just like mathematical work should).

I figured I should check my answer, and brought out my TI-89. Not a tool I use too often, as wxMaxima and GeoGebra fulfill all my needs, but it was “nice” to see it again.

Punching in the exercise I got the correct answer there too, shown in the calculator shot.

Now, first of all, nice going on making this exercise Spiked math! Finding proper integration limits so that integrating C-3P0 turns into R2-D2 is not trivial.

Second, it struck me how different even straight forward exercises like these are when using two different means of solving. One can argue using a calculator is less work for the brain, but I can’t recall one instance in the handwritten version, where I actually had to stop to think. It was all memorized rules of calculus and algebra, rote work.

Using a CAS like the TI-89 (now replaced by the TI Titanium, and later the TI n-spire), there was still not much work for the brain involved. The only parts where you (or rather, I) would stop to think was wether the syntax of the input line was “expression, variable, lower limit, upper limit” or “expresseion, lower limit, upper limit, variable”. Logically enough, you should tell someone (anyone!) what dummy variable is involved in the calculations before applying the limits of integration.

Either way, solving the problem felt good because it was Star Wars related. The one who learned anything at all from this, was the one who devised the problem in the first place.

And perhaps Kenny Baker got a giggle out of it, too.

Let Live Search Do Your Algebra

Great idea from Lifehacker.com : Let Live Search do your algebra. I guess most of you are familiar with the fact that google search (even the search bar in Firefox) can do simple calculations and unit conversions. Microsoft’s latest effort goes to eleven though. It is capable of solving simple algebra problems. With symbols. So it’s one point for microsoft. Firefox and Google had thousands of points from before, but this means they are catching up 🙂

GeoGebra

This computer program has now become extremely popular in Europe. This software package makes it easy to draw geometrical shapes (in 2D) and stretch and turn them around afterwards. That is, it’s a DGS (Dynamic geometry system/software). If you have tried Cabri, you should be no stranger to this.

In addition, you get a function drawing program, were you equally easy can draw most function you will ever need (in 2D). This is all done in the same coordinate system, making it easier to see connections between functions and geometry.

You can also do calculations of many sorts in this software. You can calculate with variables like line segments and function values, and they are (of course) automatically altered and updated when you change your drawing or graphs. You can’t do CAS calculations though.

I have tried a few softwares like this earlier, like Cabri and the newer stuff from Texas Instruments, but nothing comes close to GeoGebra in terms of ease and usability.

You can make dynamic documents and send them off to students. You can use a web version or software version of the program and they are completely identical. You can save stuff as pictures, documents or java applets, and embed them in your website, blog or LMS. What’s not to like?

The software is originally made (I think) as a Ph.D. project in Austria by Markus Hohenwarter. And best of all – it’s completely free and lots of resources exist in all kinds of school levels.

I have held a couple of courses, lectures and workshops around the country, where we have started using this program among others. So far I have been to Molde, Kristiansand S, Oslo, Bergen, Stavanger and Levanger. There’s a bunch of exercises and activities at this site, but the little text there is, is in Norwegian.

I will also give a talk at a conference at NTNU in september where I will talk about a practical pedagogy for GeoGebra. My intentions are to focus on the gap between the teacher and learner, and we go about forcing ourselves to take the learner aspect into our lesson planning.