Measurement in the elementary school

Measurement in the elementary schoolAuthor(s): DONALD D. PAIGE and MARGARET JENNINGSSource: The Arithmetic Teacher, Vol. 14, No. 5 (MAY 1967), pp. 354-357Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41185601 .

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Measurement in the elementary school DONALD D. PAIGE and MARGARET JENNINGS Southern Illinois University, Carbondale, Illinois

Donald D. Paige is an assistant professor of elementary education and mathematics at Southern Illinois University, and Margaret Jennings is a member of the department of elementary education at the same university.

A his paper represents a survey of thirty- nine complete or partial series for elementary school as concerns their pres- entations of various areas of measurement. Some of the methods of teaching measurement will be discussed and evaluated. In addition, some suggestions for the im- provement of the teaching of measurement will be suggested.

Money Let us look first at the concept of money,

which is the beginning type of measurement a child meets in school. The first- grade level of most series presents the concepts of penny, nickel, and dime while a few series include the quarter and one includes the half-dollar and the dollar. Recognition of coins is augmented through the use of pictures to the extent that one series even shows the edge of various coins. It is suggested that actual coins be available for the students to examine and that whenever funds are collected in the classroom the coins are again mentioned. Naturally, some of the older books require extra explanation as they picture, for example, the old Liberty Head dime instead of the more common Roosevelt dime.

After coin recognition has been estab- lished, the children are taught the values of the various coins and they learn to count them to find the total value. Discus- sions are centered around the cost of

simple items with the students required to select the coins needed to pay for these items. Coin equivalencies are also covered, i.e., five pennies equal one nickel. A few series also introduce the idea of making change at the first-grade level.

Most of the first-grade books have a great deal of money experiences well scattered throughout the text, while a few have just one section devoted to this concept. A majority of the books include suggestions for classroom experiences such as "play store," where the students are given practice in counting and making change. Most teaching ideas presented in the first grade are continued in higher grades.

During the second grade most series have introduced all coins and the dollar. Concepts of cost and change are also extended to this level. Many texts use only the $1.00 notation while a few use $1.00, 100^, 1 dollar, and $1. Several of the series unrealistically picture only the silver dollar but most picture the paper dollar although they do not depict the actual size.

To this point little work has been done with the addition and subtraction of monies. The few computations that are included only cover cents less than one dollar and no regrouping. This, then, is the most important concept introduced during the third grade. Multiplication and division of monies by numbers is also intro- , duced during the third-grade year, which includes regrouping across the decimal

354 The Arithmetic Teacher



point. A few series introduce five- and ten- dollar bills at the third-grade level, but most leave these topics to be learned out- side the classroom.

Beginning some time during the third- grade year, and until interest is introduced in the sixth grade or in the junior high school, the concept of money as a measurement is excluded as a basic topic. In- stead, as a process is taught for whole numbers, examples are also included which deal with money. Interest, then, is the last concept of money which is covered in most elementary series, and it is introduced late in the sixth-grade year. Along with interest, some sixth-grade books also include topics such as keeping accounts, writing checks, and figuring commissions and discounts.

Time

The next area of measurement to be widely included in elementary school is that of time. When the child enters school, time suddenly becomes much more important than it has ever been before. He must get to school at a certain time, eat at a certain time, and leave for home at a certain time. For many reasons the child soon wants to learn to tell time. (And as all parents realize, he also wants to own a watch.)

Although most first-grade teachers begin teaching children how to tell time, only a little over half of the first-year arithmetic books include anything on the subject. These that do include this concept at the first-grade level cover telling time to the nearest half-hour. Development cen- ters around the times at which the child does various everyday acts, such as getting up, going to school, eating lunch, etc.

In addition to time-of-day, a few first- grade books introduce the calendar, a topic which most first-grade teachers cover whether it is in the text or not. Months, weeks, etc., are covered lightly in a few of the series.

The second-grade level finds all books including some work with time. A major-

ity of the books cover the telling of time to five-minute intervals, while a few also introduce the idea of passing-of-time, which includes simple addition of hours. Many books during the second and third grades introduce Roman numerals on the clock face. This is a practice of doubtful value, since few clocks with Roman numerals are encountered today; and if they are, the "four" on the clock is incorrectly written as IIII.

During the third- and fourth-grade years, the study of time is expanded in both directions to include seconds and to include years, decades, and centuries. The a.m. and p.m. notations are covered along with computation problems of addition and subtraction which include regrouping seconds to minutes and minutes to hours.

The fifth- and sixth-grade years find concepts such as b.c. and a.D., the twenty- four hour clock, time zones, and all types of computations. Many books have little or no specific instruction about time but cover the concepts in problem-solving situations.

Linear measure

Another important measure is that of linear measurement. In the first grade, about half of the books introduce the concept of an inch while a few also introduce a foot. This teaching is accompanied by many pictures of things for the children to measure and suggestions of classroom activities that involve measurement. Some books have poor diagrams showing scale drawings of inches, rather than the actual size representations found in most series. Only a few series introduce linear measurement with an unnamed unit of measure and develop the necessity of a standard unit of measure.

In the second grade practically all books reviewed have some work with linear measurement. Most of these cover concepts of yard and half-inch. Simple adding and subtracting are done without changing from one unit to another. Concepts are extended at the third-grade level to in-

May 1967 355



elude fourth-inch and mile. Most books during the third grade have some discus- sion of formal and informal measure and include the development of standard units of measure. Standard units are most often developed from a historical viewpoint, but how some series can include city block as a standard unit is doubtful.

Eighth-inch and sixteenth-inch are introduced in most fourth-grade texts, along with proper formats for the use of a ruler. At this level many texts introduce the metric system and perform basic operations on linear measures, including problems in which the student must change from one unit to another.

During the fifth- and sixth-grade year, most series extend the use of the metric system and stress its merits in relation to our system. Problems at this level deal more with the use of linear measures in relation to finding perimeters, etc.

Liquid measurement

The only other type of measure treated extensively in the first grade is liquid measure, and this is introduced in only about half of the texts examined. Those that do introduce this concept include mostly pint and quart. Cup is sometimes introduced, as is glass. Glass seems a poor idea, as it is hardly a standard unit of measure. Again, some series introduce units without names and stress the idea of a standard unit of measure.

In the second grade cup is found in most all texts, and the gallon is also introduced. A few books have interesting sections showing pictures of odd-shaped con- tainers with equal volumes.

Grade three begins operations with these units of measure. In addition, concepts such as teaspoon and tablespoon are generally introduced at this level, although many series do not introduce these measures at any level.

Fluid ounce is the only concept introduced in the last three years of most elementary series, except for the measures used with the metric system. Except for

new steps in operations and conversions, these grades merely reinforce and extend liquid measurement concepts which have already been taught.

Weight The measure of weight was found in

only one first-grade text, but was fairly common at the second-grade level. Gen- erally, the pound is introduced during the second grade and the ounce during the third grade. Computation with these measures follows the same patterns as estab- lished for other units of measure.

The last three years of elementary texts include both the long and short ton, while a few also include the hundredweight. As with other types of measures, the metric system standards are also introduced late in the series.

Miscellaneous measure

Many fourth-grade and fifth-grade books introduce the concept of dry measure. Units commonly discussed are the dry quart, the peck, and the bushel. Most of the books point out that because of wide variations, dry measures are now stand- ardized by weight for most commodities.

Area measurement is introduced in all but a few of the series reviewed. Some begin at the fourth- and fifth-grade level, but most introduce this concept during the sixth grade. Square units of measure in both our system and the metric system are rather quickly introduced, since the students are already familiar with the cor- responding linear units. Acre and section are also introduced but seldom used. Prob- lem situations center around finding the area of the region of rectangles, triangles, and, in some cases, circles.

Cubic measurement of volume is introduced in about a third of the sixth-grade texts. In these texts it is generally found as part of a unit on geometry. Standard units ordinarily found at this level are cubic inch, cubic foot, cubic yard, and, from the metric system, cubic meter and cubic centimenter. Most of the develop-

356 The Arithmetic Teacher



ments are such that the student could easily generalize to other cubic units, if they were needed for some specific pur- pose.

About half of the series reviewed include the measurement of temperature at some level. Introduction of the thermometer varies from first to fourth grade, while use of the word "Fahrenheit" varies from third grade to sixth grade. Four series also introduce centigrade - one at fourth-, one at fifth-, and two at sixth- grade level. Freezing, boiling, and below- zero temperatures are found in a few series, and a very few cover the reading of a medical thermometer.

Summary

First- and second-grade-level texts are very inconsistent on measurement concepts. Some texts do not mention measure- ments at all, while others have many topics scattered throughout the book. Unfortu- nately, many of these books have sections on measurement toward the back of the book, where they are seldom reached by the ordinary class.

Starting in the third grade, approxi- mately half of the books examined put measurement concepts in a separate chap-

ter. In these, there are few measurement problems found in the rest of the book. Also, in third grade most series begin introducing abbreviations for the names of units of measure.

Tables of measure are found in the back of most books used for the fourth grade. Problems at this level involve regrouping of measures and conversions from one system to another. By fifth grade most series have developed the idea of standard unit of measure and error of measurement. Many books introduce schedules, scale drawings, and maps at the fifth-grade level. The development of relationships between measures, such as d - r • t, is the last stage of measurement instruction in the elementary school, and many series introduce it at the sixth-grade level.

As can be seen from the previous discus- sion, there is much general agreement about the teaching of measurement in elementary school. What does seem to be missing, though, are exploratory experiences where students can create their own standard units of measurement. Also, more emphasis could be placed on practical applications, and more problems could be devised which physically require the students to do some measurement.

Tampa Meeting- October 19-21, 1967

The new Curtis Hixon Convention Hall in Tampa will be the site of an NCTM meeting October 19-21. Beginning with a social evening on Thurs- day, the meeting will conclude with Saturday's luncheon, featuring speaker James R. Cannon. Providing inspiration in between as general- session speakers will be Julius H. Hlavatý, Paul J. Kelly, Robert E. Eicholz, Vernon R. Hood, and Roy Dubisch. Phillip S. Jones will speak at the banquet on Friday evening.

Many other nationally-known leaders in mathematics education will be on hand for the elementary, junior high, senior high, junior college,

and general-interest section meetings. These speakers will cover topics ranging from the role of manipulative materials to mathematical induction and computers.

Situated on Florida's Gulf coast, the Tampa Bay area is easy to reach by car, train, bus, plane, or boat. Tours to Busch Gardens, Cape Kennedy, the Gulf beaches, Ybor City (Tampa's Spanish section), and other attractions will be available. The average high temperature in Tampa during October is 84° and the average low is 66°. Come on down!

May 1967 357



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Measurement in the elementary school