I worked hard on today’s calculus lesson and I’m so pleased with how it went!
This weekend I gathered (what I found to be) interesting statistics from Statista.com and then worked with regressions to make equations that matched the stats. This was no easy task, but I wanted the numbers we found in class to be accurate, or at least close to reality.
I made nine different scenarios and put the kids in groups of four: two kids to work with the physical model and two kids to work on the calculations.
The idea of average value is (1) find the integral (area under the curve for positive functions). The kids did this with peas:
Then (2) create a rectangle with the same area (so use the same peas) and same base. Your new height is the average value of that function:
The kids made approximations in that first step and then the calculus/calculations came in the next two steps.
I had all the groups put their findings on the board so we could discuss.
One of my favorite moments was talking about that last stat. “Who has the reported violent crimes stat? Hold up your graph.”
“What do you all notice!”
One class started applauding.
I almost started crying.
“That’s right. Don’t you believe for one second that this world is getting worse. We have mathematical proof that, on the whole, we are progressing and moving forward.”
The world is being restored. And if I didn’t believe that, why on earth would I invest this much in the future?
I loved this lesson because it was your classic low entry, high ceiling. We got to see some scenarios that are unsolvable without calculus. And my kinesthetic learners got to control the lesson today.
I love when I see growth in myself.
It’s a marathon–not a sprint–isn’t it, friends?