Let's Just Call it What it is...

There has been plenty of talk about the increasingly popular Khan Academy. I am not here to say anything “new” but to demonstrate how it can be used or misused.  As you may know much in math education barely scratches the surface of the grandeur of mathematics (a fact that Vi Hart bemoans); this is clear to many of us, our students included.  Though they may not put as fine a point on it, their questions such as “When am I ever going to use this in the real world?” or even “This doesn’t make sense” shows that math, this wonder of logic and creativity, has been lost by many a struggling student.  I am not saying that math must be used in “the real world” (whatever that really means), but what I am saying is that if students have no grasp why they are doing any particular math, then it will continue to be an alien language incomprehensible by mere mortals. Khan Academy can help to alleviate this, but only if presented at the right moment.

The danger that I see in the KA approach is that he begins with the 'mathiest' part, right from the get-go! A good learning cycle generally looks like this:

1. Hook: This grabs students' attention, and usually poses a question.
2. Investigation: This is where students try out a concept on their own, assisted by teacher questioning.
3. Direct Instruction: This can be to fill in the holes, or to formalize what they have learned.
4. Practice: Try out the formalization.
5. Create: Going further by application.

Now this is not set in stone.  Project Based Learning flips this around a bit (or rather makes the creation the hook), but in general we want to have students in a state of ‘messing around with concepts’ before we formalize them, otherwise they have no anchor for the formalisations.  This is the reason KA cannot be a teacher replacement simply because students remain in steps 3 and 4 with Khan.  This is why when I teach exponents I start with Vi’s videos.  I can hook students on doodling in math class, and having them make Sierpinski triangles and Hydra Head Binary trees.  If I start my lesson with, “Graph this equation!,” I lose them. This is how I would teach this particular lesson:

1. Hook: Watch Vi Hart’s Video (full link at the bottom of the post), and pause right before she tries to get to the bottom of the page.  Challenge my class to do so.
2. Investigation: Students get frustrated that they can’t reach the bottom.  I ask them, “Why can’t they? What are some strategies to get further?”  Watch more of the video, ask them if they could do this (with a really small pencil), how many hydra heads would be at the bottom of the page?
   
   Here you let students, draw a T-Chart, here you let them look at the pattern.  Here you get them to draw a graph, and ask them, “Does that look linear?” but only after they make the realisation that, “We get MORE AND MORE EVERYTIME! ZOMG!”
   
   Here you can also talk to some students about going into negative exponents, “What does that do?”
3. Direct Instruction: Now we can talk about what they are graphing.  We term this as an exponential function (non-linear), we talk about our x-axes, and our y-axes. We have them try it with other functions (and maybe with a Sierpinski’s Triangle).
4. Practice: If you are into textbook work, they can do this.  If you want them to look at some more interesting examples of exponents have them do that. If you want them on Khan Academy, get them here now.
5. Create: Estimating Population, Bacteria growth, etc. etc. Have them apply what they have learned here!

That is a brief outline, but you can see the point.  KA just does not fit anywhere but in Direct Instruction and Practice, and this is not a bad thing.  It is only a bad thing when we try to force it where it does not belong, if we try to say it is engaging, when it really isn’t.  KA can fill a void, but it should fill the right void. It may be better than a textbook, and you know what, I am all right if it replaces my textbook, I can handle that, but if we expect KA to fill the gap of the same humdrum curriculum that poor Vi had to sit through when she was a kid, it just doesn’t measure up. I tried too many times last year to tell students “How to do math.”  Please just let them do math, and if Uncle Sal wants to let them in on some of the formalities, by all means let him, just make sure you are not making him Mr. Sal; he’s not the teacher in your classroom, you are.

Am I being unfair? Which video would you rather start off with? Here are the original videos in their entirety: