# Exponent Rules, Polynomials, and Adaptations

It’s the end of Spring Break, and I’m just finishing up my Algebra plans for the coming week. The backstory to this post is the week before break I began exponent rules with the Algebra classes and successfully confused lotsa kids. Woosh. I’ll take responsibility for some of it, and I think I know what went wrong.

First, I tried to use Smart Slides to guide the classes through the material. For those of you who pre-prepare your slides for class, you’re stronger planners than I. My pre-prepared Smart notes have some significant flaws. For example, I might introduce a new concept like negative exponents with $2^{-2}$, get some head nods and then run the train straight into a brick wall with the next slide: $\left(\dfrac{2x^3}{3x^3y^5}\right)^{-2}$. I’m not kidding. And the best part? I won’t know it’s coming either! Kids will just look at the slide and think: “I had it. Then I lost it.”

This sounds gnarly. My problem is not that I can’t plan, and normally the gaps aren’t that gross, but I’m trying to make a point here. What you think will flow smoothly on Sunday at the Coffee Shop doesn’t always flow smoothly on Monday in class. And you’ll have a much better sense of what should come next when you’re in class. So, wouldn’t it be nice to not be tied to the next slide?

Solution: Return to the whiteboard. I realize that lecturing is not the most progressive education strategy available, but many of us still present content this way. So we should at least do it well. There’s a reason that many professors who lecture for a living, even in Computer Science, still use a chalkboard. It puts a subtle break on the amount you write, it gives the audience time to follow you, and allows you to adjust on the fly without being tied to your next slide. I connect more with the class when the material is coming from me not from the surprise next slide I created a few days ago. I’m also giving students a little more processing time because I can’t reveal paragraphs with the click of a button. The white board also doesn’t change with a click so choosing carefully what you put up there helps students because they’ll have the reference for the rest of class. This is very hard to do well with any brand of Powerpoint/Smart/Keynote presentation.

Not that I want to present everything by lecture, but Exponent Rules and some brand new skills are worth presenting this way. There are many rules, they’re not so tricky, but they deserve clear names and a multitude of examples. So I outlined my notes, the examples I want to give, and I’ll have a printed copy to work off in class this week as we revisit the confusing stuff from last week, and jump into the void of new stuff.

Here are my notes.

Once kids have a decent grasp of the rules I’m going to give them a shot at two problems I like. There’s slight WCYDWT bend to the first problem.

What’s the largest open box you can fold from a sheet of paper?

If you want to run calculations on the fly for this problem, you might want to download Maxima (a great Computer Algebra System). I’ve made a little file that can crunch numbers for this problem given arbitrarily sized pieces of paper, and fold lengths.

Here are the resources for the boxfold problem.

The rest of the files I have for this unit are in the box.

# Update!

By way of David Cox if you want to do the Box Folding problem, consider incorporating this virtual manipulative it’s perfect.

1. Note the second option in the “Cell” menu in Maxima is “Evaluate All Cells” this will crunch the numbers initially, and you should do it again whenever you change any of the input…

### 6 Responses to “Exponent Rules, Polynomials, and Adaptations”

1. Riley March 29, 2010 at 8:13 am #

I ran into similar problems when I first started using powerpoint in my classes, but I dealt with them in two main ways:

1) I interspersed hecka practice problems after even the most simple introduction. For instance, after your 2^-2 example I would have had the kids practice on 5 or 6 problems (make it fun with k8nowak’s row games or whatever).

2) I started putting more slides in the deck. Your jump from 2^-2 to (2x^3y^2/sy*df7s934hvafjS)^-2 [which may be how some students actually read it] is much too big, as you said. If you had slides like 2^-2 -> 3^-2 -> 10^-2 -> -5^-2 -> x^-2 -> y^-2 -> (2x)^-2 -> (4x)^-2, etc, then you wouldn’t need to write on the board much. And if your kids are getting it (practice problems help tell you this) then you can burn through these slides quickly.

2. Riley March 29, 2010 at 8:18 am #

I have another comment! You said that writing things out on the board gives your audience time to follow you, but you can give them that time with a slide show too.

You’re absolutely right that slide shows lock down your flexibility, but I think the advantages in legibility, advanced planning & scaffolding, and error reduction are worth the cost. Many of the other problems you’re having sound like they stem from a lack of practice with slide shows, and I think they can be mitigated or even solved.

3. Jonathan April 1, 2010 at 7:00 am #

Not a big fan of the slide. Not as student. And I don’t use them as teacher.

It is true, the level of preparation is an impediment. But a far bigger obstacle, I want to model the work I am asking kids to do. And that is much much easier with chalk in hand. I pause at the right moments. I recite (or mumble) mnemonics, AS I COMPLETE THE STEP (which they can see, in action).

Hey, I make mistakes and correct mistakes.

And I am convinced that slides would make much of this work not as well.

They would look better…

4. Rhea S. April 2, 2010 at 4:10 pm #

I think you’re on the right track to incorporate both slides and boardwork into your classes. As a math teacher I have realized that there are just going to be certain lessons for which you cannot plan every detail. Sometimes our students are just going to surprise us by how quickly or slowly they grasp the material, and we need to be able to adapt accordingly. Solely using slides limits our ability to adapt on the spot. I’ve come to teach by the motto “Everything in moderation.”

5. David Cox April 12, 2010 at 3:10 pm #

I agree with Riley about the legibility/scaffolding/error reduction of slides but like that you can insert a slide with Smart. I don’t usually show the process with my slides, I do that with the students. The legibility is less, but I think it’s worth it when they can see the way I break down a process.

As for the box folding problem, have you seen this:

http://geogebrawiki.pbworks.com/Box-Folding-Problem

6. Nick April 20, 2010 at 5:27 pm #

David Thanks so much! That’s a great link to accompany the problem. Post updated.

Riley Sorry for the long delay. I read your comments and am weighing my options. At the moment, I think there’s been an improvement in understanding with the whiteboard, but I’m not lost on the utility of slide decks. I appreciate the feedback.