유아 수감각 검사도구 개발: 신뢰도 및 타당도 검증을 중심으로 = Development of a Number Sense Test for Young Children: Focusing on Analysis of Reliability and Validity

다국어 초록 (Multilingual Abstract)

The aim of this study was to develop a ‘Number Sense Test’ for young children focusing on analysis of validity and reliability in order to contribute fundamental basis to early childhood mathematics education. The ‘Number Sense Test’ was carried out with 438 children aged 3 to 5 years old (388 children without developmental delay and 50 children with developmental delay). First, item analysis was conducted in relation to the mean and standard variation and afterwards 38 items(6 items of intuitive quantity discrimination, 5 items of intuitive simple arithmetic, 9 items of intuitive size discrimination, 7 items of intuitive volume discrimination, 5 items of intuitive force discrimination, 3 items of intuitive pattern sequence and 3 items of intuitive analogy) were confirmed based on the pass rate. Second, concerned with reliability, Cronbach α was in the range of .71 to .84 and test-retest reliability ranged from .72 to .97. Related with validity, Pearson’s correlation coefficient between the total score and sub-factors was reported to range from .40 to .84. The implication and the possibility of field appliance of the ‘Number Sense Test’ were discussed based on the results of this study.

국문 초록 (Abstract)

본 연구는 발달지체 및 일반유아의 수감각 측정과 관련된 도구를 개발하고 해당 도구의 신뢰도와 타당도에 대한 검증을 목적으로 실시되었다. 만 3-5세 438명(일반유아 388명, 발달지체유아 50명)의 유아가 참여하였으며 수집된 자료를 기초로 7개 하위요인에 대한 64개 문항의 평균과 표준편차를 구하였다. 이후 개별 문항에 대한 통과율을 기초로 64개의 문항에서 최종 38개(‘직관적 수량비교’에서 6문항, ‘직관적 연산’에서 5문항, ‘직관적 크기비교’에서 9문항이, ‘직관적 부피비교’에서 7문항, ‘직관적 질량비교’에서 5문항, ‘직관적 패턴’에서 3문항, ‘직관적 유추’에서 3문항)의 문항을 선정하였다. 신뢰도 검증 결과, Cronbach α는 .71-.84, 검사-재검사 신뢰도는 .72-.97였으며 타당도 검증을 위해 산출된 총점 및 요인 간 상관계수는 .40-.84로 보고되었다. 연구 결과를 기초로 유아 수감각 검사의 학문적 의의와 교육 현장에서의 활용도에 대해 논의하였다.

참고문헌 (Reference)

1 문수백, "한국판 시지각 발달검사 사용자 매뉴얼" 학지사 2003

2 이미란, "한국 Bayley 영유아 발달검사의 신뢰도와 타당도 분석" 울산대학교 대학원 2006

3 한기정, "특수유아의 인지 발달을 위한 부교재" 교육과학사 1996

4 성태제, "타당도와 신뢰도" 학지사 2005

5 김연미, "인식론의 신경 생물학적 고찰 및 수학 활동과 관련된 두뇌의 활성화" 대한수학교육학회 20 (20): 21-43, 2010

6 최혜진, "유아수학능력검사 개발 연구" 부산대학교 대학원 2003

7 김경철, "유아수학교육에서의 수세기(counting)에 관한 이론적 고찰" 10 (10): 67-83, 1990

8 구효진, "유아 수감각 검사도구 개발을 위한 예비연구" 한국유아특수교육학회 12 (12): 25-57, 2012

9 신희선, "영유아발달선별검사 Development Review)의 한국에 서의 표준화 연구" 아동간호학회 12 (12): 333-340, 2006

10 이윤미, "수감각 발달을 위한 조기 수학 교수가 수학 학습장애 위험학생의 수개념과 연산능력에 미치는 효과 연구" 한국초등교육학회 21 (21): 287-312, 2008

11 Beran, M. J., "“Constructive” enumeration by chimpanzees (Pan troglodytes) on a computerized task" 4 : 81-89, 2001

12 Dehaene, S., "The number sense : how the mind creates mathematics" Oxford University Press 1997

13 Siegler, R. S., "The development of numerical understandings, In Advances in Child Development and Behavior, Vol. 16" Academic Press 1982

14 Griffin, S., "The development of math competence in the preschool and early school years, In Mathematical cognition" Information age publishing 1-32, 2003

15 Gelman, R., "The child’s understanding of number" Havard University Press 1978

16 Butterworth, B., "The Mathematical Brain" Macmillan 2000

17 Devlin, K., "The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip" Basic Books 2000

18 Rumbaugh, D. M., "Summation in the chimpanzee(Pan troglodytes)" 13 (13): 107-115, 1987

19 Czerny, P., "Sameness-difference judgments in Saimiri sciureus based on volumetric cues" 3 (3): 375-379, 1975

20 Marcus, G., "Rule learning by seven-month-old infants" 283 : 77-80, 1999

21 Flombaum, J. I., "Rhesus monkeys(Macaca mulatta)spontaneously compute addition operations over large numbers" 97 : 315-325, 2005

22 Nieder, A., "Representation of number in the brain" 32 : 185-208, 2009

23 Woodruff, G., "Primitive(sic)mathematical concepts in the chimpanzee : Proportionality and numerosity" 293 : 568-570, 1981

24 Piaget, J., "Play, dreams, and imitation in children" Norton 1962

25 Starkey, P., "Perception of numbers by human infants" 210 (210): 1033-1034, 1980

26 Gordon, P., "Numerical cognition without words: evidence from Amazonia" 306 : 496-499, 2004

27 Xu, F., "Number sense in human infants" 8 (8): 88-101, 2005

28 Xu, F., "Number discrimination in 10-month-old infants" 25 : 103-108, 2007

29 Frank, M. C., "Number as a cognitive technology : evidence from Pirah˜a language and cognition" 108 (108): 819-824, 2008

30 Griffin, S., "Number Worlds : Kindergarten Level" Number Worlds Alliance, Inc 2000

31 Gilmore, C. K., "Non-symbolic arithmetic abilities and achievement in the first year of formal schooling in mathematics" 115 (115): 394-406, 2010

32 Goswami, U., "Melting chocolate and melting snowmen : Analogical reasoning and causal relations" 35 (35): 69-95, 1989

33 Thomas, R. K., "Length judgments by squirrel monkeys: Evidence for conservation?" 12 (12): 349-352, 1976

34 Geary, D. C., "From infancy to adulthood: The development of numerical abilities" 9 : 11-16, 2000

35 Chen, Z., "From beyond to within their grasp : The rudiments of analogical problem solving in 10-and 13-month-olds" 33 (33): 790-801, 1997

36 Gelman, R., "First principles organize attention to and learning about relevant data: Number and the animate-inanimate distinction as examples" 14 : 79-106, 1990

37 Pica, P., "Exact and approximate arithmetic in an Amazonian indigene group" 306 : 499-503, 2004

38 Geary, D. C., "Evolution of paternal investment, In Handbook of evolutionary psychology" John Wiley & Sons 483-505, 2005

39 Wynn, K., "Enumeration of collective entities by 5-month-old infants" 83 (83): 55-62, 2002

40 Fuchs, L. S., "Enhancing first-grade children’s mathematical development with peer-assisted learning strategies" 31 : 569-583, 2002

41 Spelke, E. S., "Core knowledge" 10 (10): 89-96, 2007

42 Spelke, E., S, "Core knowledge" 55 (55): 1233-1243, 2000

43 Bjorklund, D. F., "Context effects in children’s selection and use of simple arithmetic strategies" 3 (3): 225-242, 2002

44 Gentner, D. R., "Children’s performance on a spatial analogies task" 48 (48): 1034-1039, 1977

45 최지희, "Bruner의 인지경로 단계별 지도가 발달지체유아의 수 감각 학습에 미치는 효과" 단국대학교 특수교육대학원 2010

46 McLean, M. E., "Assessing infants and preschoolers with special needs (2nd edition)" Merrill 1996

47 Geary, D. C., "An evolutionary perspective on learning disability in mathematics" 32 (32): 471-519, 2007

48 Wynn, K., "Addition and subtraction by human infants" 358 : 749-750, 1992

49 Barth, H., "Abstract number and arithmetic in preschool children" 102 : 14116-14121, 2005

50 Gelman, R., "A review of some Piagetian concepts, In Cognitive development, Vol. 3, In Handbook of child psychology" Wiley 1983

51 Muncer, S. J., ""Conservations"with a chimpanzee" 16 : 1-11, 1983