(A new question of the week) In Monday’s post about fallacies in calculus, one of them used the definition of the derivative (or rather, misused it). Today we’ll look at a short question about applying that same definition, that came in last month.
(An archive question of the week) In searching for answers to include in Monday’s post on calculus fallacies, I ran across a long discussion that illustrates some important aspects of methods of integration. In particular, there are often multiple ways to find an integral (the best not necessarily being the one taught in your textbook); …
Integration: More Than One Way, More Than One Answer Read More »
“False Proofs”, where seemingly good logic leads to nonsensical conclusions, can be a good way to learn the boundaries of reality — what to look out for when you are doing real math. We have a FAQ on the subject; there we discuss several well-known fallacies based in algebra, and have links to others. Today, …
(A new problem of the week) We usually look here at problems or concepts that are relatively basic and generally applicable; that could give a wrong impression of the kinds of questions we get. Here I want to show a recent example of a discussion about a problem, related to a geometric figure called the …
(An archive question of the week) An interesting question came to us in 2016, where rather than using a well-known formula, it was necessary to work out both what data to use, and how to calculate the desired radius.
Students often wonder where the formula for the area of a circle comes from; and knowing something about that can help make it more memorable, as I discussed previously about other basic area formulas.
Sometime soon I will do a series of posts on word problems, which are a common point of difficulty with students. But here is one recent example from a high school student, where language was the main difficulty, but the algebra is worth discussing as well. We’ll look a little more deeply into the problem …
(An archive question of the week) Last time I discussed issues that arise in solving a simple algebraic equation. In researching that, I found a discussion of solving a formula for a variable (which in some countries is called “making x the subject”, that is, changing an equation involving x into the form “x = …
Questions about solving algebraic equations are common. Here I will bring together several answers where we discussed the basic principles for solving relatively simple equations, which are important to learn well before moving on to quadratic equations and beyond.
(A new question of the week) Having written last week about the definitions of trigonometric functions, I want to look at a question from a few months ago that illustrates a rather common mistake students make in applying those definitions. It also demonstrates the patience required to find out what is in a student’s mind, …