Pedagogy

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. Place value for children Our first question …

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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 …

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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? …

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Mean, Median, Mode: Which is Best?

It seems common for teachers to ask students which “measure of central tendency” (average) is best. Sometimes they ask this in a particular context (say, to report the “average” salary at a company); other times there is no context (other than perhaps some unidentified data). In the latter case, we generally consider the question to …

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