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Quantitative thinking of preschool children Author(s): SISTER JOSEPHINA Source: The Arithmetic Teacher, Vol. 12, No. 1 (JANUARY 1965), pp. 54-55 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41185083 . Accessed: 14/06/2014 18:40 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Arithmetic Teacher. http://www.jstor.org This content downloaded from 195.34.78.242 on Sat, 14 Jun 2014 18:41:00 PM All use subject to JSTOR Terms and Conditions

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Quantitative thinking of preschool childrenAuthor(s): SISTER JOSEPHINASource: The Arithmetic Teacher, Vol. 12, No. 1 (JANUARY 1965), pp. 54-55Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41185083 .

Accessed: 14/06/2014 18:40

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

http://www.jstor.org

This content downloaded from 195.34.78.242 on Sat, 14 Jun 2014 18:41:00 PMAll use subject to JSTOR Terms and Conditions

Page 2: Quantitative thinking of preschool children

Quantitative thinking of preschool children

SISTER JOSEPHINA C.S.J. Boston College, Chestnut Hill, Massachusetts

Sister Josephina is a Professor in the school of education at Boston College, where she has opened a modified Montessori class for children ages 8t 4, and ôt after having studied the method in nine European countries.

1 he kindergarten organization within the United States is in the second century of its establishment. Yet the program, more than any other segment of the school, has been characterized by diversity of prac- tice. With a steady increase of attendance in kindergartens (in 1960 the Bureau of Census reported 58.8 percent of all five- year-old children enrolled in public and private kindergartens) arise the problems of what should constitute the scholastic diet of these children and, more impor- tantly, how they should be educated.

Recent statements of objectives run the gamut of familiar terms from promoting the physical, mental, emotional, and social development of young children, to the more special aims of discovering the inter- est and aptitudes of young children, lay- ing the foundation for reading, writing, and number work, developing the crea- tivity abilities, and encouraging children to develop their ideas through a variety of media.1

With the renaissance of the Montessori method and its insistence upon specific, didactic materials, one looks for empirical data on which to base decisions regarding the kind of program best suited for the four- and five-year-old child. Conspicu- ously absent are any studies related to Montessori classes which have been de- rived from careful designs with statistical controls.

Research studies, though limited, indi- cate that young children show an early

interest in numbers. Schools, then, must be ready to handle these children, and must provide a carefully prepared environ- ment filled with enrichment, exploratory, and manipulative materials on a larger scale than ever before.

Pitcher castigates early education prac- tices and rightly so. She states that to some degree it is the fault of educators who have not been more articulate in their descriptions of how the young child learns the so-called "academics" in his own way. She further emphasizes that the time has come when schools for the young child must stand ready for the child's grasp of reading, writing, and arithmetic at an earlier age. It is of highest importance that teachers use methods which avoid mechan- ization and help the child assimilate mean- ingful learning into a complete schematic framework.2

To find the level of the child's arithme- tic knowledge the writer chose thirty children, nineteen boys and eleven girls, ages four and five, who were enrolled in a modified Montessori program. The chil- dren were given the Stanf ord-Binet Test of Intelligence, Form L-M, and an original arithmetic knowledge test. All testing was individual.

The mean intelligence quotient was 137 with a sigma spread of 11.5. The range in chronological age was 4.0 to 5.11 years.

In number sequence children frequently have learned to count by rote. The follow- ing questions were given orally and indi-

1 Chester W. Harris (ed.)* Encyclopedia of Educational Re- $earch (New York: The Macmillan Company, I960), p. 391.

» Evelyn G. Pitcher, "Learning Academic Subjects in the Kindergarten," Foctu, XIII (February, 1963). 35.

54 The Arithmetic Teacher

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Page 3: Quantitative thinking of preschool children

vidually. The percent of correct responses is given with the question.

Number sequence A. "I am going to count. When I stop,

tell me what is the next number I would say."

% correct 1. 1-2-3-4-5-? 97 2. 1-3-5-7-? 50 3. 5-10-15-? 40 4. 2-4-6-? 33

Ordinals B. "I am going to ask you to point to

one of these blocks. Show me the ."

% correct 1. first 100 2. fourth 66 3. middle 86 4. last 90 5. second from right 66

Number selection C. "Now show me children."

% correct 1. five children 100 2. eight children 83 3. two children 100 4. seven children 90 5. three children 83

Number quantity D. In front of child are pictures with

items in various quantities. Child is asked, "Show me the picture with ."

% correct 1. 2 pencils 93 2. 4 balloons 83 3. 3 cars 90 4. 7 children 66

% correct 5. 5 blocks 83 6. 8 bunnies 63 7. 6 houses 60

Child's age E. "Show me the cake with the number

of candles that tells how old you are." Cakes with 3-4-5-6-7 candles. Child pointed to cake with candles representing his age (percent correct: 100).

Identification of money F. Placed in front of the child are vari-

ous pieces of money. "Show me ."

% correct 1. a dime 56 2. half-dollar 50 3. nickel 50 4. dollar bill 73 5. quarter 53 6. penny 90 7. 5 pennies 50 8. 4 quarters 26 9. 2 dimes 30

10. ? makes a quarter 25 11. 2 half-dollars 20 12. 2 nickels 50

In summary, the preschool child pos- sesses quantitative ability to a degree which needs the attention of curriculum makers and teachers. Realizing that this sample (AT = 30) is limited and that the intelligence quotient is above the average, it is obvious that much arithmetical knowledge is learned incidentally, since these children had not been taught num- bers in a formal way. Consequently, teachers can build upon this foundation in adding to the child's basic knowledge of number and quantity.

The Montessori method was developed in Italy about 65 years ago and introduced to the U.S. before World War I without lasting success. About 85 private schools using the method have been started here since 1958. - From "What's So Special About Montessori Schools'* in Good Housekeeping, CLVIII (May, 1964), 164-66.

January 1965 55

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