Engaging students: Computing inverse functions

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Derek Skipworth. His topic, from Algebra II: computing inverse functions.

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B. How can this topic be used in your students’ future courses in mathematics or science?

In essence, an inverse function is supposed to “undo” what the original function did to the original input.  Knowing how to properly create inverse functions gives you the ultimate tool for checking your work, something valuable for any math course.  Another example is Integrals in Calculus.  This is an example of an inverse operation on an existing derivative.  A stronger example of using actual inverse functions is directly applied to Abstract Algebra when inverse matrices are needed to be found.

 

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C. How has this topic appeared in high culture?

The idea of inverse functions can be found in many electronics.  My hobby is 2-channel stereo.  Everyone has stereos, but it is viewed as a “higher culture” hobby when you get into the depths that I have reached at this point.  One thing commonly found is Chinese electronics.  How does this correlate to my topic?  Well, the strength of the Chinese is that they are able to offer very similar products comparable to high-end, high-dollar products at a fraction of the costs.  While it is true that they do skimp on some parts, the biggest reason they are able to do this is because of their reverse engineering.  Through reverse engineering, they do not suffer the massive overhead of R&D that the “respectable” companies have.  Lower overhead means lower cost to the consumer.  Because of the idea of working in reverse, “better” products are available to the masses at cheaper prices, thus improving the opportunity for upgrades in 2-channel.

 

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E. How can technology be used to effectively engage students with this topic?

A few years ago, there was a game released on Xbox 360 arcade called Braid.  It was a commercial and critical success.  The gameplay was designed around a character who could reverse time.  The trick was that there were certain obstacles in each level that prevented the character from reversing certain actions.  To tie technology into a lesson plan, I would choose a slightly challenging level and have the class direct me through the level.  This would tie into a group activity where the students are required to calculate inverse functions to reverse their steps (like Braid) and eventually solve a “master” problem that would complete the activity.  This activity could be loosely based off a second level that could wrap up the class based off the results that each group produced from the activity.

http://braid-game.com/

 

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