Kindergarten in the "Arithmetic Teacher": A decade of growth

Kindergarten in the "Arithmetic Teacher": A decade of growthAuthor(s): LAUREL NORMANSource: The Arithmetic Teacher, Vol. 18, No. 4 (APRIL 1971), pp. 253-256Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41186375 .

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Kindergarten in the Arithmetic Teacher: A decade of growth

LAUREL NORMAN

At the time of writing, Laurel Norman was a student in the New School of the University of North Dakota in Grand Forks. She is now teaching kindergarten in Cosmos Elementary School, Cosmos, Minnesota.

An this annotated bibliography an attempt has been made to include every article appearing in the Arithmetic Teacher during the sixties which had relevance to kindergarten teaching, even if an entire article was not about kindergarten. These articles constitute a good collection of read- ings for teaching mathematics at the kindergarten level. The January 1968 issue is particularly notable, containing five relevant articles.

In the first three years of the decade there were only seven relevant articles; in the last three years there were fifteen.

1960 Bjonerud, Corwin E. "Arithmetic Concepts Pos-

sessed by the Preschool Child." November: 347-50.

The writer conducted a study of twenty- seven kindergarten entrants and concluded that many entrants understand basic arithmetic concepts (e.g., simple fractional concepts, geometric figures, time on the full hour, recognition of common instruments used in measurement, etc.). Educational implications from his study were: (1) a planned arithmetic-readiness program at the kindergarten level, (2) a program of arithmetic in the first grade to reflect the readiness period carried out at the kindergarten level, and (3) an inventory of each child's number concepts and more emphasis on developing number understanding during the first part of the kindergarten year.

Clark, Caroline Hatton. "A One-handed Clock." March: 127.

The writer recommends the use of a one- handed clock for teaching children to tell the

time because it builds readiness for more pre- cise time telling.

1961

Heard, Ida Mae. "Developing Concepts of Time and Temperature." March: 124-26.

The writer suggests that daily experiences can give meaning to some phases of measurement. She suggests keeping a day-to-day cal- endar, reading the thermometer each day, and telling time as a class learning experience.

Suppes, Patrick, and Blair A. McKnight. "Sets and Numbers in Grade One, 1959-60." Oc- tober: 287-90.

The authors contend that operations on sets are concrete and, thus, more meaningful to students as they learn that a number is a property of a set. They also report the results of the workbook they devised for four first grades in California.

1962

Beard, Virginia. "Mathematics in Kindergarten." January: 22-25.

The kindergarten mathematics program should be "systematic, meaningful, sensible, functional, and incidental as well as planned."

The writer set up six objectives for her mathematics program and worked to accom- plish these through finger plays, songs, poems, dances, rhythms, and work-play activities. She had prepared a test of ten questions, which she presented to each of her pupils in the beginning of the year to measure their mathematical knowledge. She gave the test at the year's end to compare results.

Foster, James M. "Deductive Reasoning in the Primary-Arithmetic Program." January: 20-21.

The writer suggests several question games that can be used with primary children (e.g., "I'm thinking of two numbers that added to- gether make two. What are they?"). Questions

April 1971 253



can be asked that have multiple answers, and some that have no answer.

McDowell, Louise K. "Number Concepts and Preschool Children." December: 43 3-35.

The writer conducted a survey to investigate the number concepts of three-, four-, and five- year-old preschoolers. She compiled a list of ten questions that were intended to test important concepts such as rote counting, certain mathematical terms, the one-to-one relation- ship, and so on. She reports on the ten questions used and the number of correct responses to each.

1963

Andrews, E. E., and L. Doyal Nelson. "Begin- ning Number Experiences and Structured Ma- terials." October:330-33.

The authors warn that reliance on structured materials such as the Cuisenaire system may not help to build the abstract concept of number. Children must have varied experiences with numbers and the abstract concept to ensure understanding.

Burn, Margaret H. "Children Learning Mathe- matics." April: 179-82.

The writer concludes that there are three basic steps involved in the mathematics learning process: (1) the child must be able to explore through preconscious experiences those materials he will be working with; (2) the teaching skills should only occur when dis- covery by the child assures understanding; and (3) the child should be able to use the knowledge gained to solve problems in realistic sit- uations.

Dutton, Wilbur H. "Growth in Number Readi- ness in Kindergarten Children." May: 25 1-55.

The writer reports the results of the Metro- politan Readiness Tests given to 236 children upon kindergarten entrance and after one year in school. He stresses the necessity of entrance tests to determine the needs and abilities of the children and to guide the teacher in planning whole-group, small-group, and individual activities.

Kolson, Clifford J. "The Oral Arithmetic Vo- cabulary of Kindergarten Children." February: 81-83.

This 1960 study recorded the vocal* responses of children in free play at kindergarten, when stimulated by pictures, and at home. The researchers extracted 3,728 words that had to do with mathematics and categor- ized them according to arithmetic processes, time, measurement, quantity, geometric concepts, and finance. The article lists all the words and their frequency count.

Rice, Mary. "Clocks in Kindergarten." Novem- ber:455.

The teacher relates how a student-initiated interest in his watch grew to a class interest in making clocks, listing clocks they knew of, and playing games involving clocks.

1964

Deans, Edwina. "Ideas to Try with Primary Children." November: 502-5.

This writer proposes the idea of using sticks as a manipulative device for teaching addition. The sticks are to be placed in a tic-tac- toe pattern; and the children first count the horizontal sticks, then the vertical sticks, and finally they add them. This procedure is easily transferred to multiplication, where the children then count the touching places to find the product.

Fitzsimons, Lucille. "Kindergarten Mathematics." January: 33-35.

There are two approaches to an effective kindergarten mathematics program: (1) op- portune mathematics experience from everyday school living, and (2) planned programs to challenge the children's abilities and introduce important mathematical concepts. The author gives practical suggestions for implementing concepts in the program.

Korey, Ruth Anne. "Participation of Young Chil- dren in Mathematics." October: 42 1-22.

This teacher devised a system of introducing numbers to the children by working with one number at a time. By action learning (manipulative and tactile), the children had concrete experiences with abstract numbers. They would count a certain number of real things (depend- ing on which number they were working on) and draw that same number of things. The teacher would use that number in their rhythm band and physical-education activities.

1965

Bacon, Marjorie. "Operation Bottle Caps." Oc- tober: 466-68.

This teacher tells how bottle caps were used as a manipulative device to build sets. The children then told the stories the bottle caps showed and, eventually, recorded the equations. The children also built geometric forms and "stairs" to show the one-more-than and one- less-than properties.

Brace, Alec, and L. Doyal Nelson. "The Pre- school Child's Concept of Number." Feb- ruary: 126-33.

This is a report of a study done to determine the number knowledge of preschool children and to determine which factors influence early growth of number ideas. Several of the authors' conclusions were: (1) a child's ability to count is not a reliable indication of his true concept of number; (2) preschool children have limited knowledge of the nature of cardinal numbers; (3) environmental factors are important in the child's development of number concepts; and (4) age is an important factor in a child's concept of number, but sex is not.

Giddings, Marie. "Being Creative with Shapes." December : 645-46.

254 The Arithmetic Teacher



This teacher relates how a variety of shapes were used in her classroom to build toys and create pictures.

Josephina, Sister, CSJ. "Quantitative Thinking of Preschool Children." January: 54-55.

The preschool child possesses some quantitative ability, which suggests that much arith- metical knowledge is learned incidentally, since these children have not been formally taught. Teachers can build on this foundation in adding to children's knowledge.

Sueltz, Ben A. "The Mathematics of a Five- Year-Old Girl." March: 22 1-23.

Mr. Sueltz recorded fourteen examples of his daughter's use of mathematics and her curiosity about numbers. He indicates that a normal child's life before coming to school contains considerable experience with mathematical ideas and concepts.

Williams, Alfred H. "Mathematical Concepts, Skills, and Abilities of Kindergarten Entrants." April: 26 1-68.

In a study, a series of tests were given to 593 kindergarten entrants. Several implications from the results of those tests are: (1) assess- ment of kindergarten entrants' mathematical abilities should be made early in the year; (2) a planned, sequential mathematical program should be developed; (3) time devoted to mathematical readiness would also contribute to reading readiness; (4) the wide range of differences in mathematical ability suggests intraclass grouping of pupils by ability; (5) instruction should involve a wide variety of activities in use of numbers; (6) constant evaluation of the child's progress is necessary to ensure proper developmental activities; and (7) schools in different socioeconomic areas should adjust the beginning mathematics program to fit the needs of the pupils.

1966

Ashlock, Robert B. "Planning Mathematics In- struction for Four- and Five-Year-Olds." May: 397-400.

The curriculum task is that of finding appropriate mathematical experiences to reinforce the basic mathematical concepts. The teacher must plan carefully, but the activities chosen should be informal and fun. Ashlock lists several important basic concepts that should be included in the program: understanding of the one-to-one correspondence, cardinal and ordinal number ideas, ability to enumerate, geometry, sets, and the one-more-than concept. There should be a logical sequence of activities for any one concept, though activities associated with other concepts can in- tervene.

Deans, Edwina. "Games for the Early Grades." February: 140-41.

Edwina Deans suggests three games (Kitty- Cat, Tenpins, and Guessing How Many) that could be used to reinforce the mathematical experience in kindergarten or the early grades.

. "More Games for the Early Grades." March: 238-40.

The writer lists a few games that resulted from experiences in one classroom but that could transfer to other classrooms: Guessing and Checking (a measurement game), Shooting Rubber Bands (a number-target game), I'm Thinking of a Number, and so on.

Mastain, Richard K., and Bernice C. Nossoff. "Mathematics in the Kindergarten." January: 32-37.

The article states that the "purpose of mathematics in kindergarten is to develop further the understanding of quantity and relationships between quantities and to extend and enrich the vocabulary of comparisons." The authors include a list of content areas to cover in kindergarten (geometry, sets, numbers and operations, and measurement) learning experiences to reinforce those areas.

1967

Dutton, Wilbur H. "Teaching Time Concepts to Culturally Disadvantaged Primary-age Chil- dren." May: 358-64.

The results of a study done in Los Angeles suggest the necessity of a careful identification of the skills needed in telling time and in building a good concept of time. The curriculum materials and instructional practices must be adapted to the needs and interests of culturally disadvantaged children.

Killelea, Agnes Ryder. "Developing Number Ideas in the Kindergarten." May: 3 96-97.

The article suggests a game to help introduce the addition concept. The children are given a certain number of counters, which they ar- range in rows. The children then call off the number of counters in each row. The teacher records their numbers on the blackboard and asks how many counters they had to begin with, which would be the sum of the row numbers.

Muente, Grace. "Where Do I Start Teaching Numerals?" November: 575-76.

This teacher has had success with combining color words and numerals. She might draw a red "1" and then draw one red object. The children would then decide which color to associate with each successive numeral and would use the appropriate color when drawing pictures to illustrate that numeral.

Schlinsog, George W. "Mathematics in the Kindergarten?" April: 292-95.

The article begins with a brief discussion of teaching methods and then lists areas that should make up the content of the mathematical program for kindergarten: beginning quantitative concepts (size, quantity); beginning geometry (shapes); beginning set concepts; beginning number concepts; beginning concepts of basic operations (addition and sub- traction); beginning concepts of measurement (linear, volume, weight, fractional parts, time),

April 1971 255



positional relationships (under, on top of, etc.), and money.

1968

Heard, Ida Mae. "Making and Using Graphs in the Kindergarten Mathematics Program." Oc- tober: 504-6.

Dr. Heard tells of a Texas kindergarten experiment in which the children created a block graph depicting their birthdays and made observations about what the graph showed. They also graphed their height and weight.

Inskeep, James E., Jr. "Primary-Grade Instruc- tion in Geometry." May: 422-26.

Dr. Inskeep discusses three main reasons for implementing geometry in the primary grades: (1) primary-grade children's ability to learn geometry, (2) the existence of suc- cessful projects now being carried out in primary-grade geometry, and (3) the intrinsic worth of geometry. He then recommends some ways of getting a geometry program started, and suggests teaching techniques.

Lehew, Charmon. "The Performance of Four- and Five- Year-Old Children in Operation Head Start on Selected Arithmetic Abilities." January: 53-59.

This study gives a report of the performance of children according to earlier studies and reports the results of testing sixty-one Head Start children on counting, number recognition, and one-to-one correspondence. Many different questions were asked, and the exact wording used is reported.

McClintic, Joan. "The Kindergarten Child Measures Up." January: 26-29.

The author concludes from her experience that children of kindergarten age prefer a unit type of measurement (i.e., cubical blocks) to tapes or rods to indicate overall dimensions of an object.

Oberlin, Lynn, and Mary Jean Oberlin. "Mathe- matics for Four- Year-Olds." January: 10-12.

The article reviews many of the mathematical terms and concepts taught incidentally in songs, games, instructions, and so on.

Paschal, Billy J. "Readiness for Mathematics Learning." January: 5-6.

Dr. Paschal criticizes those teachers who are more concerned with product readiness (concepts, skills, abilities, and understanding children's needs in order to get correct answers) than process readiness (letting children experiment with data, make their own mis- takes, and learn from them).

Schlinsog, George W. "More about Mathematics in the Kindergarten." December: 70 1-5.

The mathematics taught in kindergarten should not concentrate on the mastery of specific facts but, rather, on concepts and ideas. Games, manipulative devices, and group experiences can be used to expose children to mathematical concepts. The article relates one such experience that the teacher capitalized

on to provide many sorts of mathematical experiences. (A child wanted to share with the class his pumpkin garden, so the children mapped their way to his house, watched for house numbers, counted the pumpkins, made a jack-o'-lantern and counted the seeds, planted their own pumpkins, etc.)

Swartz, Evelyn. "Interrelationships between Math- ematics and Art for the Kindergarten." May: 420-21.

Dr. Swartz notes similarities between art and mathematics instruction in the kindergarten, stressing objectives (helping children develop visual-perception skills), content (shape and size being basic concepts in the content of mathematics and art), and teaching procedures (use of multisensory learning devices).

Woods, Ruth L. "Preschool Arithmetic Is Im- portant." January: 7-9.

Important relationships (e.g., more than, less than, the same as, one-to-one correspondence) can be learned at home and are basic to the child's understanding of mathematical symbols used in school.

1969 Bachrach, Beatrice. "Do Your First Graders

Measure Up? (A Report of a Unit with Dis- advantaged Learners)." November: 537-38.

By introducing a ruler and the accompanying language for measurement, first graders in Chicago acquired interest and skill in measurement.

Patterson, Katherine. "A Picture Line Can Be Fun!" December:603-5.

This teacher used a walk-on picture line with movable pictures to teach order and sequence (left to right).

John, Are you tired of having only drill exercises in your math books? Look at some of the "Think" problems in ESM.

See Page 264.

256 The Arithmetic Teacher



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Kindergarten in the "Arithmetic Teacher": A decade of growth