# The Week in Review

## October 20, 2023

This week, I continued the differentiated instruction experiment. Wednesday, my classes were working on analyzing the first and second derivatives of functions to determine intervals of increase/decrease, local extrema, intervals of concavity, and inflection points. The differentiated instruction wasn't as successful for this topic. I think this was for a couple of reasons:

I put too many problems on the worksheet.

In retrospect, I could have put a few less problems on the worksheet considering that three of them required students to find all the previously mentioned features. Students struggled with doing the algebraic computations efficiently without a calculator. This was especially true when they were completing the sign chart parts of the questions. Their instinct was to worry about the value of the function at test points rather than using number sense to quickly determine the sign.

Students weren't as confident with the material as other lessons.

It turned out that most of the students started with A problems, so the class ended up operating more similarly to pre- differentiated instruction experiment than the past few days. All students prepared for class by either attending the lecture or watching the recording before class, which I was super happy with. Also, it was a little counterintuitive. I would've thought that giving students the opportunity to use class time to watch lectures would make them want to always use class time for watching lectures. However, this doesn't seem to be the case.

Students weren't able to progress past the A problems either like the past few days. Perhaps this indicates that the Pre-Recitation Prep could have scaffolded the problems better, or the problems need to be written fundamentally differently. I was in a rush to finish writing this lesson, and I got all problems straight from the textbook. I did this before with the highly successful logarithmic differentiation lesson, but in my opinion, those problems were much more interesting. On the other hand, this lesson's problems were kind of boring to be honest.

I wasn't able to continue with the differentiated instruction experiment today. The classes had to take their common quiz for the semester, and they didn't finish one of the curve sketching examples in their lecture notes, so we used the first 30 minutes of class to go over that problem before the quiz.