Power to the Students!

Most of this last week has been spent on technical issues, like how to record lectures to upload so that I can implement the flipped classroom.  Not exactly the type of thing that anyone wants to read about, kind of like learning how sausages are made. So I am left wondering what I can write about that more about the what of teaching as opposed to the how that I have been mired in.

As I was looking at the text for the summer I got my inspiration,

                                          EXPONENTS!

Teaching the rules of integer exponents in most texts drives me crazy. This was one of the places where, as a student, I was left feeling like it was magic. Or, as one of my mentors when I was an undergrad put it, like a bunch of mathematicians got together, got drunk, and decided it. Of course, that’s not the case, but how do we convey that to our students?

After introducing how to work integer exponents, what most texts (including the one I am using this summer) do is go straight to the “because” of a⁰ = 1.

What witchcraft is this?

A lot of texts will immediately follow that with a^-n = 1/aⁿ.

And by this point, if you ask students why the only response I have ever gotten is ,”Because that’s what they taught us.”

                                                              NO! NO! NO!

If we are really intending to teach our students mathematical thinking, then we need to pull back the curtain and teach them how we use the definition of exponents to build all of the rules we give them. Just like in Geometry where we start with postulates and build all of Plane Geometry, we build Algebra, and all mathematics, the same way. If we follow the original definition(s) where does that take us?

So, how can we do this with exponents?

Here is part of the worksheet that I will be giving to my students. This is how I used to do my lecture, and while I will do part of this in my videotaped lecture, I want to leave as much as I can for them to discover on their own.

This is known Experiential Learning. It is not surprising that research has shown that students have greater retention when involved in Experiential Learning than they do when taught in a regular lecture setting. I have talked in prior posts about the different needs of adult students, and this is one way to get them actively involved.

As always, feedback is welcome.