# Pedagogy

## A Test Dilemma: Do As You’re Told, or Do What’s Right?

(A new question of the week) Some questions we get, while small, raise interesting issues. In a question we got last month, there are several little issues pertaining to how the final answer should be chosen; as is too often the case, it seems that a diligent student who cares about accuracy might be penalized. …

## How to Ask a Good Question

As many schools get into a new semester, this may be a good time to take a look at ways to use our service as effectively as possible.

## Place Value: Whole Numbers

We’ll be looking at various aspects of place value, starting here with the basic concepts. As soon as you learn to write numbers beyond 10, you have to start understanding this concept; so we have to begin at a concrete level and move gradually to something more abstract.

## John Conway on Thinking and Teaching

(An archive question of the week) When I heard Thursday that the great mathematician John Conway had died (see the New York Times obituary here), I recalled not only his books I have read, but his involvement in Ask Dr. Math‘s early days. In addition to a couple dozen quotes from him, there were several …

## The Art of Proving Trig Identities

(A new question of the week) Last week we looked at a recent question about basic trigonometric equations. That discussion continued into the subject of identities, which we’ll look at here. We’ll be sitting in on an extended chat about many important aspects of this kind of work. It’s still very long, even after extensive …

## What It Takes to Be a Math Doctor

In the Ask Dr. Math service, new volunteers went through a period of training (“internship”), first demonstrating their ability to write effectively about math with some example problems, and then answering actual questions under supervision, discussing their answers with a mentor online before they were actually sent out. Once our reliability was confirmed, we were …

## Do Curved Surfaces Have Faces, Edges, and Vertices?

Having discussed how to count faces, edges, and vertices of polyhedra, and then looked at Euler’s formula that relates them (not only in polyhedra but in graphs on planes and other surfaces), we need to consider a question we have received at least 100 times: Are these terms even defined (or defined correctly) for cylinders, …

## Studying Math: Get Motivated!

As fall approaches, and the beginning of a new school year for many, let’s take a look at some of our past discussions of how to study math. We’ll start with some perspectives on being motivated to study, since you are not likely to do well if you hate math (as so many students tell …

## What is Multiplication? How (Not) to Teach It

Last time we looked at the roles of multiplier and multiplicand from several perspectives. This time, I want to focus on one extended discussion about how children should be taught to think of multiplication.

## Who Moved My Postulate?

Last time we looked at the question of why we have to have postulates, which are not proved, rather than being able to prove everything. Often, this question is mixed together with a different question: Why do different texts give different lists of postulates, so that what one calls a postulate, another calls a theorem? …