Teaching Mathematics Via Learning CentersCharles Neatrour

Department of Elementary EducationMadison College

Harrisonburg, Virginia 22801

The learning center approach has made a definite impact uponeducational techniques in recent years. It is seen as a medium throughwhich classroom instruction can be individualized. Justification forits use is found in the emphasis currently placed on a system ofindividually guided education that provides for differences amongpupils with respect to rate of learning, learning style, and other needs.

Enjoying increasing popularity, the learning center not only providesinstruction and experience at various levels, but also allows the teachermore time with individual students. Through the use of a varietyof learning centers, mathematical concepts and skills can be developedusing physical materials, discovery patterns, and problem-solvingtechniques. Frequently the child will be motivated to explore mathon his own through this medium.The learning center represents a "pre-packaged" approach to

education. It should be used to increase interest, bolster self-confi-dence, and minimize failure. Centers are frequently designed so thatthey can be used for both individual and group learning. One canenvision these centers as a medium through which to challenge thegifted and to enrich the independent learning environment for slowlearners.

Types of Centers

Among the varied purposes for which learning centers in mathematicscan be used are pacing, parallel support, enrichment, and rein-forcement. The "pacing" center provides some activity for everystudent and allows each student to pursue the task at his own rate.The "parallel support" learning center is coordinated with currentclassroom activities. The "enrichment" center, on the other hand,functions without dependence upon classroom instruction. It intro-duces subject matter and experiences not currently included inclassroom routines. Enrichment centers serve to challenge the moregifted child. The "reinforcement" center, which is generally an integraltool of current classroom instruction, basically serves as a work centerin which students practice previously learned skills.

Criteria for Designing Learning CentersAmong the criteria to be considered when designing a learning center

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are the following:

(1) Each learning center should be designed with definite objectives in mind. Theseobjectives, preferably behavioral or performance in form, should specify clearlythe concepts and skills to be mastered.

(2) A learning center should provide experiences which relate to previously learnedconcepts and skills and, at the same time, develop new ones. If a child isto be prepared to use the center effectively, then "readiness" is an importantconsideration.

(3) Directions at a learning center should be clear and easy to follow. Two sensorystimuli (for example, reading and listening) should be used. When reading skillis required, it should be on level with the child’s development. The use ofan audiotape and recorder makes it possible for children experiencing readingdifficulties to be able to learn mathematical concepts on grade level.

(4) Active involvement�both physical and mental�should be provided at eachlearning center. When the work is so planned, the child will likely remain interestedthroughout the learning experience.

Evaluation of Centers

Evaluation is essential if the teacher is to know that the learningcenter is effectively fulfilling established objectives. An opportunityfor continuous evaluation of the child’s progress should be providedwithin the design. This can best be accomplished through worksheets,observations, discussions, and conferences.

Learning centers are generally non-graded; therefore, the evaluationprocess is directed more toward the effectiveness of the center inmeeting the needs of students and serving the purposes for whichit was designed. The teacher can best evaluate the usefulness ofthe center by judging the student’s reaction to the center, attentionspan, expressed interest, and success in completing the assigned tasks.

A Sample Learning Center

A learning center for mathematics should be enticing, attractive,and interesting enough that it lures the child to learn and enjoy hisexperiences. An example of such a center is "How to Measure."Using the multi-sensory approach, instructions for the activities atthis center have been prepared as an audio script. A grade one textbookprovided the basis from which the following learning center andaudiotape evolved.1 This center was designed for the purpose ofproviding parallel support for current classroom instruction.

1. Ernest R. Duncan, et al.. Modem School Mathematics: Structure and Use, Grade One, (Boston: 1967),pp. 207-10.

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MATH LEARNING CENTER-LINEAR MEASUREMENT (PRIMARY)

Tape Recorder

LINEAR MEASUREMENT

ReadinessThe child should:

(1) Be able to place objects in sets with like members(2) Know that a ruler can be used to measure linear distances(3) Know the difference between longer and shorter(4) Have used the 12-in ruler previously to measure to the nearest inch.

Behavioral ObjectivesThe child will be able to:

(1) Distinguish between the longer and shorter of two objects(2) Match objects of the same length(3) Measure the length of an object to the nearest inch.

AssignmentThe teacher will assign individual students to the center once the necessary readiness

has been attained.

EvaluationThe teacher will evaluate the learning center and a child’s progress at the center

through:(1) Checking the child’s work at the center after activities 1 and 2 have been

completed(2) Reviewing the child’s worksheets after activities 3,4 and 5 have been completed

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(3) Observing the child’s interest and success(4) Conferring with the child to determine if he has satisfactorily mastered the

behavioral objectives.

AUDIOTAPE(Use Cassette Tape Recorder)

Activity 1: Longer, Shorter, Same LengthFind cup A on the left side of the learning center board, (pause)Place the ten straws from cup A in front of you. (pause)Find the longest straw, (pause) Find the shortest straw, (pause)When we say that a straw is long or short, we are talking about the length of

the straw.Now find the pairs of straws with the same length, (pause)Place a rubber band around all the pairs of straws with the same length, (pause)Place those pairs in cup A. (pause)Place the remaining straws in paper bag B.

Activity 2; Longer, ShorterPlace the objects in cup C in front of you. (pause)Group them in sets of like things, (pause)Place the pencils in one set, the straws in one set, and the sticks in another set.

(pause)Find the shortest pencil in the set of pencils, the shortest straw in the set of straws,and the shortest stick in the set of sticks. Stop the tape recorder until you finish.

Place the shortest from each set in cup C. (pause)Now find the longest pencil, straw, and stick in these sets. Stop the tape recorder

until you finish.Place the longest from each set in cup D. (pause)Place the remaining objects in bag E.Now that you have completed Activities I and 2, please ask the teacher to come

to the learning center and check your work.

Activity 3: Length in InchesFind the rulers with the numerals 1 to 12 on them on the right side of the learning

center board. Take a ruler out of the loops and look at it carefully, (pause)Take a straw from the pocket and place it beside your ruler. Be sure that oneend of the straw is at the end where you see the numeral 1. Look at the diagramon the right side of the learning center board, (pause)

Look at the other end of the straw. What numeral do you see on the ruler belowthat end of the straw? (pause)

If you said, "S," you were right. The straw is 8 units long. Each unit on thisruler is called an inch. The straw is 8 inches long.

Find the worksheet marked Activity 3. (pause)Write the length of the straw on the worksheet, (pause)Now measure the pencil on the right side of the learning center board with your

ruler. Measure it the same way you did the straw, (pause)How long was the pencil? Write the length of the pencil on your worksheet, (pause)Measure the length of the crayon, (pause)Write the length of the crayon on your worksheet, (pause)Measure the long edge of your worksheet, (pause)Write the length of the long edge of your worksheet, (pause)Check your answers on the worksheet with the answer box.

Activity 4; Length in InchesThere are six pieces of colored string on the right side of the learning center board.

Find them.Measure the length of the red string, (pause)Find the worksheet marked with Activity 4. (pause)

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Write the length of the red string on the worksheet, (pause)Measure the length of the blue string, (pause)Write the length of the blue string on the worksheet, (pause)The red string is longer than the blue string. How many inches longer is it? (pause)

Write your answer on the worksheet, (pause)How many inches shorter is the blue string? (pause) Write your answer on the

worksheet, (pause)Now using your ruler measure the yellow, green, purple, and gold strings. Write

these measurements on the worksheets. Stop the tape recorder until you finish.Check your answers on the worksheet with the answer box.

Activity 5; Length to the Nearest InchOn the middle of the learning center board there are a screw, nail, chalk, screwdriver,and rubber band in pockets.

Find the worksheet marked with Activity 5. (pause)Measure each of the objects in pockets and write your answers on the worksheet.Let’s measure the nail first, (pause) We can see the nail is longer than 2 inches

but shorter than 3 inches, (pause)If we look closely, we can see that the nail is longer than 2 1 /2 inches and shorterthan 3 inches. What should we write down? (pause)

When a nail is longer than 2 1/2 inches and shorter than 3 inches, we say thatit is 3 inches when measured to the nearest inch. This means that the end ofthe nail is closer to 3 on the ruler than it is to 2.

Write 3 on your worksheet, (pause)Now see if you can measure the chalk to the nearest inch. Write the length of

the chalk on your worksheet. Stop the tape recorder until you finish this task.Did you write 2? Since the chalk is longer than 2 inches but shorter than 2 1/2

inches, we say that it is 2 inches when measured to the nearest inch.Now using your ruler, measure the length of the screw, screwdriver, and rubberband to the nearest inch. Stop the tape recorder until you finish writing themeasurements on the worksheet.

Check your answers on the worksheet with the answer box. Stop the tape recorderuntil you have finished.

Now that you have completed all five activities at this learning center, please takeyour worksheet to the teacher.

LINEAR MEASUREMENT WORKSHEETS^

Activity 3

The straw is _______ inches long.The pencil is ______ inches long.The crayon is ______ inches long.The paper is _______ inches long.

(see answer box)

Activity 4

The red string is -

The blue string isinches long.inches long.

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The red string is __________ inches longer than the blue string.The blue string is _________ inches shorter than the red string.The yellow string is ________ inches long.The green string is _________ inches long.The purple string is _______ inches long.The gold string is _________ inches long.The

��������� string is the shortest of all the strings.The

��������� string is the longest of all the strings.(see answer box)

Activity 5

The nail is about ______________ inches long.The chalk is about _____________ inches long.The screw is about _____________ inches long.The screw driver is about _________ inches long.The rubber band is about _________ inches long.

(see answer box)

*These worksheets should be placed on separate pages.

NUCLEAR SCIENTISTS MEASURE AIR QUALITY

Air quality�how are we going to maintain it? Government, industry, andcitizens groups throughout the nation are already trying to regulate or influenceone another as they seek to preserve the quality of the air we breathe.But what’s in the air we breathe? And when is it there, and for how

long? So far, the atmospheric sciences have collected little information onthe minute particulates in the air. Studies designed at Florida State Universityare gaining worldwide recognition as models of effective ways to identifyand measure the smallest nongaseous components of the air.Led by J. William Nelson, associate professor of physics, and J. W.

Winchester, chairman of FSU’s Department of Oceanography, some dozenor so nuclear scientists have for two years been applying skills and methodslearned in "pure" nuclear research to the problems of measuring the particulatematter in air. The U.S. Environmental Protection Agency last year provided$144,000 in support of their work. The outlook for funding for the currentyear is even better. Nelson expects that another six advanced students willbe added to the program, to complete or extend their doctoral training whilethey work toward the program’s goals of collecting and analyzing thenongaseous components of air. The program employs and trains undergraduatesand master’s degree candidates as well.