Yesterday, we designed an Algebra II lesson using 3D modeling to derive the factored formula for difference of cubes. As we began to finish up, Sheila (@mrssheilaorr), the math teacher sitting beside me made a passing reference to being frustrated trying to prove the sum of cubes formula. Me, being a geometry teacher by trade decided to give it a try perhaps hoping to offer a fresh perspective. I mean, I was curious. It looked like this:
On the surface, it didn’t seem unapproachable. I quickly became frustrated as well. Most frustrating was the mutual feeling that we were so stinkin’ close to cracking the missing piece. Finally, Luann, a math teaching veteran sat down beside us, commented on her consistently getting stuck in the same spot we were stuck and then, as the three of us talked about it, the final piece fell in and it all made sense (it’s always how you group the terms, isn’t it?)
Then this morning, it happened again. Writing a quiz for Calculus, I needed a related rates problem. Getting irritated with the lousy selection of choices online, I decided that I needed to try to create my own. And I wanted to go #3Act and after some preliminary brain storming with John Golden (@mathhombre) (Dan Meyer’s Taco Cart? Nah… rates of walkers not really related…) we found some potential in Ferris Wheel (also by Dan Meyer)! Between my curiosity and my morning got mathy in a hurry.
First I tried to design and solve the problem relating the rotational speed in Act 1 to the height of the red car. That process looked like this:
Meanwhile Dr. Golden found a video of a double Ferris wheel, which was pretty awesome. Seemed a little it out of my league, so kept plucking away at my original goal.
It clearly wasn’t out of Dr. Golden’s league, as he took to Geogebra and did things I didn’t know Geogebra was capable of. (You’re going to want to check that out.)
So, what is the product of all of this curiosity and random math problem-solving? As I see it, these past 48 hours have done two things: Reminded me of what makes me curious and reminded me what it’s like to be a learner.
I have a feeling my students will be the beneficiaries of both of those products. There’s a certain amount of refreshment that comes from never being too far removed from the stuff that drew us to math in the first place. The problem you want to solve just because you want to see what the answer looks like.
And this curiosity, the pursuit, it feeds itself. In the process of exploring that which you set out to explore, you get a taste of something else that you didn’t know you would be curious about until it fell down in front of you. (For example, Geogebra… have no idea what that program is capable of, which is a shame because it is loaded on all my students’ school-issued laptops…)
And this process breeds enthusiasm. Enthusiasm that comes with us into our classrooms and it spreads. I’m not trying to be cheesy, but much has been said about math functionality in the modern economy, how essential it is in college-readiness and the like with few tangible results. Let’s remember that there are kids who are moved by enthusiasm, who will respond to joy, who will pay attention better simply because the teacher is excited about what they are teaching. It won’t get them all, but neither will trying to convince them of any of the stuff on this poster.
Now, who’s going to teach me how to use Geogebra?