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# Powerful Ideas Related to Measurement

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"OK, boys and girls, I want you to line up across the front of the room from the tallest to the shortest," said Mrs. Kelly, the prekindergarten teacher. When Shandra asked her if she could have a drink of water, Mrs. Kelly said that breaktime would be in five more minutes. After a half-hour nap time in the afternoon, Mrs. Kelly asked the children to raise their hands if they were the youngest child in their family. She gave these children an announcement from the school principal to take home to their parents.

Meanwhile, Mrs. Kelly's friend, Ms. Washington, was meeting with her math class of high school seniors. "...and so, the standard deviation is essentially an average. It is an average distance from a middle score," she was saying.

Across the hall from Ms. Washington, Mr. Stuzman was reviewing with his physics class. "Now the mean velocity of these particles is 1.2 times 10 to the fourteenth...."

The middle school students in Mr. Jacobs' social studies class were working on their economics project. "Mr. Jacobs, should we be giving the trade balances using American dollars or the currency of country we're studying? We're having a hard time comparing the countries when their currencies are all different, but we don't know for sure how to convert them all to dollars."

The students in Mrs. Shoemaker's room were browsing through their new book, A Connecticut Yankee in King Arthur's Court. "This was Mark Twain's tenth book. He completed it in 1889 when he was 54 years old," said Mrs. Shoemaker, the teacher of American Literature. "Although our edition has only 336 pages, the original version had 575 pages and about 220 illustrations."

## Overview of Measurement Topics

In the following articles, you will explore the tremendously practical and wide-ranging topic of measurement. You will be taken on an adventure that may surprise you by how long and wide and high and deep it stretches. There is very little in our modern world that is not touched in many ways by the concept of measurement. If it has been years since you have given any thought to what measurement is, you will be invited to do so now. What you find may impress you. We rely on measurement more than most people realize.

As a result of your studies with our resources:

• You will not only come to appreciate the meaning of measurement, but you will also gain skill in several different areas of using measurements.

• You will be able to explain how it is that nonstandard units can be used for measurement, and you will be able to explain why we have developed standard units.

• You will be able to recount some historical tidbits related to the development of some of the common measurements that we use.

• You will be able to describe the difference between linear measurement and area measurement.

• You will be able to highlight the significant issues for understanding measurement of volume, weight, and time.

• You will be able to describe some benefits of the metric system as a measurement system.

• You will be able to explain why it is that measurement is always an estimate, and you will be able to describe what we mean when we discuss precision in measurement.

• You will have opportunities to see the relevance of composition, decomposition, representation, relationship, and context. In the case of measurement, context, composition, and decomposition are by far the most relevant of the powerful ideas, as you will see.

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Elementary Mathematics: Pedagogical Content Knowledge, by James E. Schwartz, is designed to sharpen pre-service and in-service teachers' mathematics pedagogical content knowledge. The five "powerful ideas" (composition, decomposition, relationships, representation, and context) provide an organizing framework and highlight the interconnections between mathematics topics. In addition, the text thoroughly integrates discussion of the five NCTM process strands.

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