(A new question of the week) Since we’ve been doing a little trigonometry this week, let’s look at a recent set of questions from a student in the Philippines, all about compositions of trig and inverse trig functions. This is a topic with some interesting little surprises, and several of us answered, to give a …
(An archive question of the week) Last time we looked at various 2- and 3-set Venn diagram problems (and alternative methods). One discussion I found while collecting them deserved to be set aside for special examination, if only because it would scare the beginner. A mixture of tools will make the work easier. Here it …
Puzzles involving two or three properties of people or objects, commonly solved by Venn diagrams, are popular with teachers, and perhaps not so popular with students! Several have asked about them recently, leading me to catalog our past answers about them, to find the most useful examples to point to. Some of these are very …
(A new question of the week) Sometimes we give only minimal help on a question, to let a student puzzle over the problem and learn to figure it out herself. That may be enough, or we may go back and forth for some time, guiding her thinking until she finds the answer. In the latter …
(A new question of the week) A recent question about an old puzzle leads to multiple references to our archive.
Many students who write to us are involved in math competitions. They don’t always say that explicitly, but we can tell when the problems they ask about may be far beyond ordinary homework, requiring deeper problem-solving skills. The three questions I’ll look at today are from students asking how to prepare for these competitions, or …
(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 »
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 = …
(A new question of the week) Having discussed trigonometric identities on Monday, let’s make this Trig Week, by looking at a discussion from two months ago in which we were asked about alternative routes to a proof.