We’re missing a ton of students for the last two days before break, trips and etc, only a 1/3 of students. Frustrating. Anyway, my challenge for them was to make a map and color the map with the minimum amount of colors. Follow up? Can you make a map that requires 5 colors? A lot of fun creating maps, coloring maps, and then trying to break the 5 color examples. A lot of fun, truly.
I get pretty “traditional” when it comes to introducing the concept of derivatives coming from limits. I think the reason why is that there is so much great history to talk about, and while it is an easy enough topic to grasp for some students, some students struggle with the ideas and I want to make sure that they’re solid for as many students as possible.
Here’s an example of the notes that we had after a 20 minute conversation:
These were built up very slowly and they earned each and every part as a class. The only top down parts from the teacher were the setup of the function, the motivation of what we were trying to do, and finally the name of the variables. The students came up with the idea for approximating the tangent line with the secant line (informally first, and then they remembered the language from the circles unit of geometry). They came up with the slope of the secant line, the difference quotient, and how to make the approximation of the slope better. The limits work we did leading up helped with the concept of sending h to zero while not actually having to divide by zero itself. To nail home the concept of shrinking h to get a better approximation, I used this desmos sketch:
We worked on some more limits today in PreCalculus H. First we did some practice on a pretty great desmos activity builder from Elizabeth Pursel with looking at a graph and evaluating limits. Here’s a short video of some students working on a slide:
And then we did some practice on whiteboards:
We then we worked the other way around (they got to be creative):
Good stuff. And man o man do some students struggle with the concepts of limits. They eventually get there, but the rate of change (see what I did there?) is quite a bit different with each kid.
As a pre-assessment, I gave them this pear deck on limits. It’s interesting to see what they’re lacking (still) in function knowledge, and what they can infer from new notation. It turns out that they learn a bunch by trying to sense the patterns, they get far better at understanding this new notation just by seeing more examples, they never hear answers!
After this pre-assessment we do some more formal examples and I actually confirm answers.
Last week of the quarter, and it was busier yesterday. It’s a lot of extra work (and stress), but I find value in it. The conversations that spontaneously occur when I pass back the assessments in class are fantastic because they know that they’ll probably be able to fix their mistakes.
Things are coming along nicely. After looking at some paper assessments, they are learning just as much, if not more, then we would have with the traditional method. They are learning so many important things about object-orientated languages, class inheritance, object instances, passing parameters, global vs local variables, public vs private variables, static vs non-static methods. This knowledge came into play on their assessment.
Cool topics! There are about a third of students missing here because they are still deciding what topic to look into in more depth.