The Development of Time Concepts byKindergarten Children

Lois StephensPrincipal, McKinna Elementary School\ Oxnard, California

and

Wilbur H. DuttonProfessor, Elementary Education, University of California,

Los Angeles, California

Children who enter school at about five years of age have hadmany experiences with number which equip them for delving intonumerous aspects of mathematical thinking. Their physical andmental development is such that they are ready for many systematicmathematical learnings which would be of immediate and practicaluse to them.

Research studies [2] indicate that the five-year-old child alreadyknows many of the arithmetic concepts which are usually listed asbeing appropriate for the kindergarten program. Button found thatapproximately one-third of the beginning kindergarten childrenmight be ready for some organized sequential work in arithmeticbased upon data secured with the Metropolitan Readiness Tests [5].Other writers including Lambert [81 and Deane [4] point out thatit would be impossible to keep mathematics out of the kindergartenbecause the four- and five-year-old child needs these skills and con-cepts to carry on his small affairs. In spite of these research findings,little has been done to add mathematics to the kindergarten programin other than incidental or experimental situations.

PURPOSE OF THE STUDYThe purpose of this study was to determine the capacity of children

of kindergarten age of varying abilities to develop mathematicalconcepts related to telling time.

Significance of the Problem. Many investigators have attempted tomeasure children’s understanding of time concepts. Ames, in 1946,charted the development of a sense of time in various stages, andidentified "clocktime" stages for children of five, six, and sevenyears of age. [1].

Lovell evaluated children^ development of concepts of time andpointed out the importance of teaching all children to tell time. Henoted the fact that we do not as yet know the best means for helpingchildren to develop their concept of time [9J.Dutton found that environmental factors influence the culturally

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disadvantaged child’s concept and use of time. Irregular workinghours of parents, different school schedules, dependence of childrenupon parents and teachers for meeting time schedules, and no syste-matic or sequential plan for teaching time hindered children in theirlearning and use of time [6].The agreement on the importance of developing concepts of time

coupled with the lack of knowledge concerning how teachers canbest help children develop these concepts emphasizes the significanceof this study.

PROCEDURES

The Time Concept Test. The writers prepared a Time ConceptTest based upon preliminary work done by Springer in 1950 [10, 11].The test was divided into three parts.The first part of the test is an analysis of the child’s drawing of a

clock as he responds to the direction, "Draw me a clock." Analysisof the drawing was based upon the eight stages of development ob-served by Springer in her study. The second part of the test is com-posed of questions relating to times of the day which might befamiliar to a child and those relating to the operation of a clock. Partthree requires the child to tell the time shown on each of twelveclock faces, and to place the hands on another twelve clock faces atthe times indicated by the examiner.The test is administered individually, taking from three to ten

minutes per child, depending on the extent of the individual’s know-ledge and his general characteristics in attacking each question.The validity of the test was based on rational validity, all items

being related to the telling of time. The test was submitted to a panelof primary teachers to determine the appropriateness of content andstatement of test items.The reliability of the test was 0.88 determined by the Kuder-

Richardson formula 21. An item analysis of the post-test for all pupilsusing Davis’ charts [3] showed adequate discrimination on all items.The difficulty index ranged from 2 to 79 with many items clusteredat the more difficult levels.

Pupils. The 160 pupils used in this study were in the secondsemester of kindergarten in either Oxnard or Los Angeles SchoolDistricts. At the time of the post-test the ages ranged from 63months to 75 months with a mean chronological age of 69.9 months.Children’s intelligence was measured by using the Primary MentalAbilities Test, 5-7. Results of this testing showed the IQ range was78 to 142, with a mean of 109.2. The mean IQ for sub-groups was:108.69 for girls; 109.75 for boys; 109.44 for the training group;

The Development of Time Concepts 61

109.00 for the non-training group; 118.56 for the high IQ group;99.88 for the low IQ group.

Methods. During a period of approximately six weeks following theadministration of the Time Concept Test, a planned program ofinstruction in developing time concepts was presented to the traininggroup. Specific lesson plans were prepared and provided for eachteacher. Teachers also received instructional aids which included aJudy Clock, flannel board clock face, and a book, How to Tell Time[12].Following the period of instruction, the Time Concept Test was

again administered as a post-test to both the training and the non-training groups.

Statistical Analysis. The 160 kindergarten pupils (80 boys and 80girls) were divided into two equal groups. One group received in-struction in telling time in a specific, planned program in addition tothe incidental teaching which is typical of the kindergarten program.Of the 40 children in each of the groups of boys and girls, half werehigh IQ and the other half low IQ. In order to determine the sig-nificance of the differences which appeared in the post-test, a two-by-two-by-two analysis of covariance was computed. The first vari-able was sex, the second IQ, and the third was the type of instruction.

RESULTSThe range of scores on the pre-test was from 0 to 26, and on the

post-test from 1 to 37. The means for the various sub-groups on thepre-test and the post-test were computed as shown in Tables I, IIand III.Table I shows the differences between scores for boys and girls on

pre-tests and post-tests to be non-existent.

TABLE 1. MEAN SCORES ON PRE-TEST AND POST-TEST FOR GIRLS AND BOYS OF HIGH IQ AND LOW IQ

HighIQ

LowIQ

Girls

Pre-Test

5.9

4.4

Post-Test

11.1

7.8

Boys

Pre-Test

6.0

3.8

Post-Test

11.2

7.6

The differences between the pre-test scores of the training andnon-training groups were significant (Table II), thus making itnecessary to use an analysis of covariance to offset the initial effect

62School Science and Mathematics

of this difference. There appeared to be no consistent differencebetween boys and girls on the Time Concept Test.Table III shows considerable difference between the amount of

knowledge of time concepts possessed by children of high IQ andthose of low IQ. Pupils who received training showed markedlygreater gains in this knowledge than those who did not receivetraining.

TABLE II. MEAN SCORES ON PRE-TEST AND POST-TEST FORGIRLS AND BOYS OF TRAINING AND NON-TRAINING GROUPS

Training

Non-Training

Girls

Pre-Test

6.8

3.5

Post-Test

13.4

5.5

Boys

Pre-Test

6.3

3.4

Post-Test

12.5

6.3

TABLE III�MEAN SCORES ON PRE-TEST AND POST-TEST FOR PUPILSWITH HIGH IQ AND LOW IQ IN TRAINING AND NON-TRAINING GROUPS

Training

Non-Training

High IQ

Pre-Test

7.4

4.5

Post-Test

14.5

7.8

LowIQ

Pre-Test

5.7

2.4

Post-Test

11.3

4.0

CONCLUSIONS AND RECOMMENDATIONSConclusions. For children included in this study neither boys nor

girls learned significantly more than each other of the time conceptsas measured by the Time Concept Test. The children of high IQlearned significantly more about time concepts than those of low IQwhether the concepts were presented in a planned program or in anincidental approach alone. There was a significant gain in time con-cepts made by pupils whe received specific instruction in these con-cepts in addition to incidental teaching compared with those whoreceived incidental teaching alone, as measured by the Time ConceptTest.

Recommendations. This study showed that kindergarten childrencan develop more concepts of telling time when these concepts arepresented in a planned program of instruction in addition to theincidental teaching than when they are presented only incidentally.

The Development of Time Concepts 63

Because of the immediate, practical application of this knowledge oftelling time it is a worthwhile tool for the children, and is recom-mended to be included in the kindergarten program.

In learning the time concepts there are many related mathe-matical ideas which will be developed, and which will increase thechil(Ts general mathematical understanding. These concepts include:(1) recognition and writing of the numerals from 1 to 12; (2) rationalcounting to 12; (3) linear measurement (around the edge of theclock); (4) recognition and naming of the circle; (5) fractions-onehalf, one quarter, three quarters; (6) counting by fives to 60. Wordsadded to their vocabulary include: (1) ^long^ and ^short" in relationto the hands; (2) "clockwise" direction; (3) "slower" and "faster"in relation to the movement of the hands; (4) "center" (attachmentof the hands to the face); (5) "before" and "after". Although some ofthe concepts and words will be introduced through incidentalteaching, careful attention should be given to these factors in a

planned program of instruction.

BIBLIOGRAPHY[I] AMES, LOUISE BATES, "The Development of the Sense of Time in the Young

Child." Journal of Genetic Psychology, 69:97-125, March, 1946.[2] BROWNELL, WILLIAM A., Arithmetic in Grades I and II: A Critical Summary

of New and Previously Reported Research, Duke University Research Studiesin Education, No. 6, Durham, North Carolina: Duke University Press, 1941.

[3] DAVIS, FREDERICK B., Item-Analysis Data, Harvard Education Papers, No.2, Cambridge, Massachusetts: Graduate School of Education, 1949.

[4] DEANS, EDWINA, Arithmetic�Children Use It\ Washington, D. C.,: Asso-ciation for Childhood Education International, 1954.

[5] DUTTON, WILBUR H., "Growth in Number-Readiness in KindergartenChildren." The Arithmetic Teacher, May, 1963.

[6] DUTTON, WILBUR H., "Teaching Time Concepts to Culturally Disad-vantaged Children." The Arithmetic Teacher, May, 1967.

[7] FULLER, ELIZABETH MACHEM, What Research Says to the Teacher AboutKindergarten, Washington, D. C.,: National Education Association, 1961.

[8] LAMBERT, HAZEL M., Teaching the Kindergarten Child, New York: Har-court, Brace, 1958.

[9] LOVELL, KENNETH, The Growth of Basic Mathematical and Scientific Con-cepts in Children, Warwick Square, London: University of London Press,Ltd., 1961.

[10] SPRINGER, DORIS V., "Development of Concepts Related to the Clock asShown in Children’s Drawings." Journal of Genetic Psychology, 79:47-54,September, 1951.

[II] SPRINGER, DORIS V., "Development in Young Children of an Understandingof Time and the Clock." Journal of Genetic Psychology, 80:83-96, March,1952.

[12] WATSON, JANE WERNER, Bow to Tell Time, New York: Golden Press, 1957.