This post is an interactive exploration of the chain rule from calculus. It’s a continuation of previous posts on calculus and layouts. I hope it gives some visual intuition for why the rule works. I’ve worked on the color scheme a bit. Don’t forget to mouse over the blue background formulas to see the mapping between the formulas and the model.
This post is the next iteration in my process to build a strategy for explaining complex mathematical problems, proofs and ideas. My first attempt can be found here. The basic idea is to break my explanation down into three parts: the high level ideas, a picture of the model, and symbolic reasoning. The explanation should present all three parts in an integrated way. It should make sure the main ideas do not get lost in the details and it should help the reader map the symbolic statements to their meaning in the model.
For me, a mathematical explanation has three parts: the high level ideas, a picture of the model, and symbolic reasoning. Following the symbolic reasoning in proofs and explanations requires effort and focus. When we are done, we may believe the derived statement is true, but we’ve forgotten what it actually means in relation to the model. I’m trying to develop a strategy for explaining complex mathematical ideas that allows folks to maintain the mapping between the notational statements and their meaning along the way.
The USA Mathematical Talent Search USAMTS is a unique mathematical competition for middle school and high school students. Previous competitions contain a treasure trove of challenging, thought provoking and remarkably accessible problems. I’m writing some interactive apps for a few these problems so that it’s easier for more people to get to the heart of each problem. This problem is part of the 2019-2020 year problems, but it was in the first problem set and was due back in October 2019. So it’s too late for a submission and fair game for discussion. This is the second problem I’ve presented. You can find the previous USAMTS problem here.
The USA Mathematical Talent Search USAMTS is a unique mathematical competition for middle school and high school students. Previous competitions contain a treasure trove of challenging, thought provoking and remarkably accessible problems. I’m going to write some interactive apps for a few these problems so that it’s easier for more people to get to the heart of each problem. Here’s the first problem.