Month: December 2023

How to Think About the Chain Rule

Having recently helped some students (in person) with the rules of differentiation, I’m reminded to do so here, starting with the chain rule. It is easy to make this topic look harder than it really is; the two main ways to state the rule are often confusing, and different approaches fit different problems. We’ll try …

Finding an Unknown Angle: Trig or Geometry

I am always interested in problems that can be solved in different ways, particularly because this can give a student a chance to be creative, as well as learning from experience that you don’t have to do it “the teacher’s way”. Here we’ll use trigonometry, and two different ways to add lines to a figure …

Slow and Fast Ways to Solve a Probability Problem

Last week’s discussion reminded me of another question, from July, about a probability problem that was solved in a hard (but educational) way and an easy way. This instance is more extreme, and, due to its length, requires extreme editing in order to fit here.

Different Ways to Solve a Probability Problem

Sometimes there are several ways a problem could be solved, and we encourage students to pursue the path they’ve started on, rather than give them a method that may not be natural to them. (And we encourage them to start, if they haven’t yet, in part so we can see what might be most helpful …

Why Are There Different Definitions of Range?

A recent question about two interpretations of the range of a data set in statistics leads us into some older questions and some mysteries. Is “range” defined as the interval containing the data, or the difference between largest and smallest values, or 1 more than that? Yes! All three are used, and are useful.