유아의 이동기하 능력에 관한 연구 = Motion geometry concepts in young children

다국어 초록 (Multilingual Abstract)

Transformational geometry focuses on how shapes appear as they are moved about in space like slides, turns, or flips. Some studies have reported that young children are limited in their ability to transform shapes. However, young children have many opportunities to make transformational moves as they play with pattern blocks, tangrams, and geoboards. The movements are a natural part of completing pictures or creating designs with these manipulative materials. Thus, even young children may have intuitive notions of slides, turns, and flips.
This study was conducted to examine whether or not 3-, 4-, and 5-year olds could identify the transformation images that resulted from slides, turns, andflips. 90 children were individually interviewed twice to select the results of changing a shape's orientation through slide, turn, and flip. In the first interview, each child was asked to manipulate a plastic triangle for selecting transformation images. One week after, the child was asked again to mentally perform such transformations without a manipulative.
The results revealed that young children could apply transformations such as slides, turns, and flip shapes. They performed these tasks easily if they could manipulate the shapes. Even 3-year olds could identify the transformation images if they were permitted to move a shape. However, the younger children had a difficulty to mentally perform such transformations without a manipulative. Five-year olds could do mental transformations of slides and flips but not turns without manipulating a shape. Three- and four-year olds tended to perform mental transformations poorly. Results also depended on the type of transformations; Slides appeared to be the easiest motions for the children, then flips and turns.

국문 초록 (Abstract)

본 연구는 만 3, 4, 5세 유아 각 30명씩 총 90명을 대상으로 제시된 도형을 옮기고, 뒤집고, 돌린 결과를 예측하는 유아의 이동기하능력이 구체물의 제시 유무에 따라 어떻게 다른지를 조사하였다. 연구결과, 유아들은 연령이 높아질수록, 그리고 조작할 수 있는 구체물이 있을 때 이동기하능력이 높은 것으로 나타났다. 구체물이 있는 경우에는 만 3세 유아들도 옮기기, 뒤집기, 돌리기 과제를 부분적으로 할 수 있는 것으로 나타났다. 구체물이 주어지지 않는 경우에는 유아들이 과제 수행에서 어려움을 나타냈다. 그러나 만 5세 유아들은 조작할 수 있는 구체물이 없어도 옮기기와 뒤집기 과제의 수행 점수가 높은 것으로 나타났다. 유아들의 이동기하능력은 옮기기, 뒤집기, 돌리기 순으로 높게 나타났다.

참고문헌 (Reference)

1 한종화, "탐구중심 유아수학교육프로그램의 구성 및 적용효과" 2003

2 한기완, "초등학교수학에서 공간감각지도에 관한 연구" 2001

3 최정남, "도형에 관한 탐구학습이 공간추론능력에 미치는 효과" 2002

4 김수미, "공간능력 연구를 위한 몇 가지 제안" 15 : 101-118, 2003

5 Clements, D. H, "Your child's geometric world" 7 (7): 48-54, 1999

6 Copley, J, "The Young Child and Mathematics" NAEYC 2000

7 Casey, B.,, "Storytelling sages and effective medium for teaching early childhood mathematics" 19 (19): 167-172, 2004

8 Tartre,L.A, "Spatial orientation skill and mathematical problem solving" 21 (21): 216-229, 1990

9 Del Grande,J, "Spatial Sense" 73 (73): 14-20, 1990

10 Shah, "Selected Geometric Concepts Taught to Children Ages Seven to Eleven" 119-128, 1969

11 NCTM, "Principles and Standards for School Mathematics" NCTM 2000

12 Rosser, "Order of acquisition of related geometric competencies in young children" 75-90, 1988

13 김지영, "NCTM의 수학교육 내용기준에 근거한 유아수학능력평가도구 개발" 2004

14 Piaget, "Mental imagery in the child" Basic Books 1971

15 Kennedy, L. M.,, "Guiding children's learning of mathematics" Wadsworth/Thomson Learning 2004

16 Lindquis, M. M, "Geometry must be vital" 7 (7): 409-415, 2001

17 Ortiz,E, "Geometry game" 1 (1): 231-233, 1994

18 "Geometric and spatial thinking in early childhood education" Lawrence Erlbaum Associates Pub 267-297, 2004

19 "Geometric and spatial thinking in early childhood education" Lawrence Erlbaum Associates 2003

20 NAEYC & NCTM, "Early childhood mathematics: Promoting good beginning. Position statement" 2002

21 Smith, S, S, "Early childhood mathematics" Allyn & Bacon 2001

22 Perham, "An investigation into the effect of instruction on the acquisition of transformation geometry concepts in first grade children and subsequent transfer to general spatial ability Concerning the development of spatial and geometric concepts ERIC Clearinghouse for Science" 229-241, 1978

23 Rosser, "An information- processing analysis of children's accuracy in predicting the appearance of rotated stimuli" 2204-2211, 1984

24 Williford, "A study of transformational geometry instruction in the primary grades Journal for Research in Mathematics Education" 260-271, 1972