Connecting with Mathematics

What is Mathematical Investigation?
Dissections and Area
Linearity and Proportional Reasoning
Pythagoras and Cousins
Pascal's Revenge: Combinatorial Algebra
Games and Number Theory

What is Mathematical Investigation?

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The power of mathematics is derived, in part, from the facts, formulas, and techniques it provides to the sciences. But what makes it of value even to those who will someday forget the facts and formulas is that it highlights, extends, and refines the kinds of thinking - including investigation, pattern-seeking, and proof - that people do in all domains. In What is mathematical investigation, participants will take a mathematical investigation from start to finish - from exploratory stages through reporting logically connected results - learning strategies that they can use with their students to develop their investigative skills. In the final sesssion, teachers will try another form of mathematical investigation by examining statistical concepts. New mathematical facts and relationships may well be encountered, but the real purpose of this module is to investigate investigation.

Some of the questions participants will explore - and expand on - are:

  • Which counting numbers are the result of adding at least two consecutive counting numbers?
  • What happens if the consecutive counting numbers are even or odd or perfect squares or . . . ?
  • Which numbers are the sum of unit fractions with consecutive denominators?
  • If your postmaster only sells stamps worth 7 and 9 cents, what amounts of postage can be purchased?
  • Measures of center: how they can help you and how they can get you into trouble? Why it's important to look at the entire distribution.
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