I have been experimenting a lot this year. I have felt strong enough with the content this year to start to get exotic with our approaches to different subjects. Those of you who are new teachers and are finally coming up for air will get there soon, I promise. Pre Cal especially has become a bit of a playground for me just because of the flexibility offered by the structure of the course. I cut out a lot of topics, approached others more thoroughly, and tried to take advantage of the block days in our schedule for as many involved tasks as possible. One activity I had seen floating around forever was building 3D graphs out of index cards from the fabulous @mythagon.
I found myself with some days to kill between the end of production of our class films and the start of senior activities so I thought it would be a perfect experiment. I gave two classes a crack at it while the third had a go with the planets. After a little fiddling I picked a function that would show a lot of change over a very small z-interval.
I grabbed a couple index cards and developed an idea for a finished product. The function has a range of 0
Reality though, can be harsh. Organization is such a HUGE part of this process. Your average teenager who has no idea what you have in mind for the finished project is not going to know how to organize themselves for something like this. Especially if they are having a hard time visualizing what's going on in the first place. Knowing this in advance, I tried to be as explicit about organization as possible. We built the blocks first. Then we made 4 piles of 9 for the 4 component x-sections of each slice. Then we looked at the equation. We itemized the list of z-values needed and how that equated to a difference slice. I tried to set a lot of milestones along the way so that no particular group would get behind.
After some extremely lengthy explanations about what exactly was going on, we hit a good production groove. Kids understood what to produce, how many slices needed to be made, and how to prepare them for mounting. They dutifully set about the business of crafting what slowly became a massive effort. Bonus fact: use of desmos had become so routine, that I spent 0 seconds troubleshooting iPad problems.
Right around Day 4 (we've invested about 3.5 hours with this thing so far), the problems became all too apparent. Some groups didn't label the tops of the curves and thus cut the wrong section of the cards. Most groups were not very diligent in recreating the curves, ruining any structure to the function. Markers make index cards curl up and flop over. Some groups didn't label the z value for a particular slice and had no idea what was what after a while. After cutting all the material out of the cards, there was hardly any substance left to allow it to stand up, even if the flopping problem wasn't there. Some groups managed to waste a lot of time even getting the simplest infrastructure bits going.
After absorbing all of this, I stopped them. Any group that was close to finished was told to lay their curves out and let me see what they had. The problems I outlined are pretty apparent. Try to tell if these slices have anything to do with one another.
And yet, amid the flaming wreckage of this project, there was one group who not only spent the time to accurately represent the curves, but knew which one was which and was able to produce the desired effect. The cards were still too limp to be mounted vertically, but the pattern was there. The pattern was there!
A lot of teachers are scared of unknown, expensive (timewise) endeavors because potential failure means the concept flops and you now have several days less than you did before. But if you want to improve, failure is something you should embrace. There are a ton of misconceptions and issues hidden in this project that I would've known nothing about if I didn't have 60 kids pilot the idea for me. I could have ironed out the construction issues if I spent the time to build an example, but I lack the visual miconceptions and organizational problems that slammed into them. For instance, I discovered that a 10 minute discussion about 3D printers cleared the whole thing up for a lot of them, and yet I didn't bring it up until we were done.
So what would you do? Throw this idea in the trash? Use it as confirmation that time-expensive projects are risky? No way. This project will be in the regular rotation next year and I found a least a dozen little items that will improve it and get closer to the intended results. Most importantly, I made a point of gathering all the students around and discussing the issues we had and why it didn't work out. You are allowed to tell them you're conducting an experiment and you have no idea what will happen. If anything it serves as an example to them that trying the unknown is the only way to learn.
We closed with some videos about 3D printing, to many oooohs and aaaaahs, and went about our business preparing for the final.