國小高年級學生在立方積木三視圖的推理表現

Fifth and Sixth Graders' Reasoning Performance with Orthogonal Views of Cubic Blocks

10.6278/tjme.201804_5(1).001

陳韻如(Yun-Zu Chen)；楊凱琳(Kai-Lin Yang)；林福來(Fou-Lai Lin)

三視圖 ； 方塊計數 ； 空間推理 ； 測驗 ； spatial reasoning ； orthogonal views ； instrument ； cube enumeration

臺灣數學教育期刊

5卷1期（2018 / 04 / 01）

1 - 34

繁體中文

本研究的目的在了解國小高年級學生在立方積木三視圖的推理表現，並探討年級、操作工具和任務類型對學生解題的影響。本研究中，界定立方積木為限制內嵌於2 × 2 × 2的正方體且不得懸空的立體圖形。研究者自編立方積木三視圖測驗，該測驗包括「視圖與立體圖的對應」、「由底層和視圖計數」和「視圖與視圖的對應」三種分測驗，測驗的目的在以三視圖評估學生空間推理的表現。研究樣本為台北市國小高年級學生：五年級學生127名、六年級學生133名。施測時按操作工具的有無將學生以班級為單位隨機分派為積木操作組和心智想像組。研究結果發現：（1）六年級學生的表現顯著優於五年級學生。而操作工具的有無，學生的作答表現並無顯著差異。（2）「視圖與視圖的對應」顯著較「視圖與立體圖的對應」和「由底層和視圖計數」困難。進一步檢驗不同視圖所造成的影響，發現在積木由堆疊產生的情境下，提供俯視圖有助於學生的推理表現。（3）依據學生三視圖的作答表現，共區分出四種類型：試誤法、序列思考、協調，和整合。

The aim of this study was to investigate fifth- and sixth-grade students’ spatial reasoning performance with orthogonal views of cubic blocks. The cubic blocks were restricted to a 2 × 2 × 2 structure, with no flying ones. Three variables were considered in the study: grades, manipulatives, and tasks. The developed instrument comprised three categories of tasks: choosing isometric versus orthogonal views, cube enumeration given a base, and a compatibility task. The participants in the study were 127 fifth graders and 133 sixth graders from schools in Taipei, divided into two groups. The first group was assessed using tangible cubes (manipulatives), and the second group was tested without them. The results of the study were as follows: First, sixth graders significantly out-performed fifth graders, but the groups with and without manipulatives exhibited no significant difference. Second, the compatibility task was significantly more difficult than the other tasks. Further examination of the effects of the different given views proved the benefits of the top view. Finally, students were classified into the following four categories based on their performance: trial-and- error, sequential thinking, coordination, and integration.

1. 張碧芝、吳昭容(2009)。影響六年級學生立方體計數表現的因素—空間定位與視覺化的角色。教育心理學報，41(1)，125-145。
   連結：
2. 教育部 （ 2008 ）。國民中小學九年一貫課程綱要數學學習領域。臺北： 作者。取自http://teach.eje.edu.tw/9CC2/9cc_97.php 【Ministry of Education. (2008). Grade 1-9 curriculum guidelines: Mathematics. Taipei: Author. Retrieved from http://teach.eje.edu.tw/9CC2/9cc_97.php(in Chinese)】
3. 教育部（2015）。十二年國民基本教育數學領域課程綱要（草案）。臺北：作者。【Ministry of Education.(2016). 12-year basic education mathematics curriculum (Draft). Taipei: Author. (in Chinese)】。
4. Acock, A. C.(2008).A gentle introduction to Stata.College Station, TX:Stata Press.
5. Battista, M. T.,Clements, D. H.(1996).Students' understanding of three-dimensional rectangular arrays of cubes.Journal for Research in Mathematics Education,27(3),258-292.
6. Batturo, A. R.(Ed.)(1996).New directions in geometry education.Brisbane, Australia:Centre for Math. and Sc. Education.
7. Ben-Chaim, D.,Lappan, G.,Huang, R. T.(1988).The effect of instruction on spatial visualization skills of middle school boys and girls.American Educational Research Journal,25(1),51-71.
8. Biggs, J. B.,Collis, K. F.(1982).Evaluating the quality of learning: The SOLO taxonomy (Structure of the Observed Learning Outcome).New York, NY:Academic Press.
9. Chick, H. L.,Watson, J. M.,Collis, K. F.(1987).Using the SOLO taxonomy for error analysis in mathematics.Paper presented at the Mathematics Education Research Group of Australia,Townsville, Australia:
10. Cohen, J.(1988).Cohen, J. (1988). Statistical power analysis for the behavioral sciences.Hillsdale, NJ:Eribaum.
11. Cooper, L. A.(1990).Mental representation of three-dimensional objects in visual problem solving and recognition.Journal of Experimental Psychology: Learning, Memory, and Cognition,16(6),1097-1106.
12. Cooper, M.,Sweller, J.(1989).Secondary school students' representations of solids.Journal for Research in Mathematics Education,20(2),202-212.
13. George, D.,Mallery, P.(2003).SPSS for Windows step by step: A simple guide and reference,11.0 update.Boston, MA:Allyn & Bacon.
14. Girden, E. R.(1992).ANOVA: Repeated measures.Newbury Park, CA:Sage.
15. Grouws, D. A.(Ed.)(1992).Handbook of research on mathematics teaching and learning.Reston, VA:NCTM.
16. McGee, M. G.(1979).Human spatial abilities: Psychometric studies and environmental, genetic, hormonal, and neurological influences.Psychological Bulletin,86(5),889-918.
17. National Research Council(2006).Learning to think spatially.Washington, DC:The National Academies Press.
18. Parzysz, B.(1988)."Knowing" vs "seeing". Problems of the plane representation of space geometry figures.Educational Studies in Mathematics,19(1),79-92.
19. Pittalis, M.,Christou, C.(2010).Types of reasoning in 3D geometry thinking and their relation with spatial ability.Educational Studies in Mathematics,75(2),191-212.
20. Pittalis, M.,Christou, C.(2013).Coding and decoding plane representations of 3D shapes.The Journal of Mathematics Behavior,32(3),673-689.
21. Ragni, M.,Knauff, M.(2013).A theory and a computational model of spatial reasoning with preferred mental models.Psychological Review,120(3),561-588.
22. Sack, J. J.(2013).Development of a top-view numeric coding teaching-learning trajectory within an elementary grades 3-D visualization design research project.The Journal of Mathematical Behavior,32(2),183-196.
23. Shyi, G. C. W.,Huang, S. T. T.(1995).Constructing three-dimensional mental models from viewing two-dimensional displays.Chinese Journal of Psychology,37(2),101-122.
24. Siegler, R. S.(1998).Emerging minds: The process of change in children's thinking.New York, NY:Oxford University Press.
25. Uttal, D. H.,Meadow, N. G.,Tipton, E.,Hand, L. L.,Alden, A. R.,Warren, C.,Newcombe, N. S.(2013).The malleability of spatial skills: a meta-analysis of training studies.Psychological Bulletin,139(2),352-402.
26. van Nes, F.,van Eerde, D.(2010).Spatial structuring and the development of number sense: A case study of young children working with blocks.The Journal of Mathematical Behavior,29(3),145-159.
27. Wai, J.,Lubinski, D.,Benbow, C. P.(2009).Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance.Journal of Educational Psychology,101(4),817-835.
28. 左台益、梁勇能(2001)。國二學生空間能力與van Hiele 幾何思考層次的相關性研究。師大學報：科學教育類，46(1-2)，1-20。
29. 江淑卿(2007)。從心智模式論點探討兒童邏輯推理能力之發展。臺北市立教育大學學報：教育類，38(1)，1-32。
30. 林玉珠(2009)。臺北市=Taipei，國立臺北教育大學=National Taipei University of Education。
31. 林慧美(2011)。臺北市=Taipei，國立臺北教育大學=National Taipei University of Education。
32. 邱皓政(2015)。量化研究與統計分析：SPSS（PASW）資料分析範例。臺北=Taipei:五南=Wunan。
33. 康鳳梅、鍾瑞國、劉俊祥、李金泉(2002)。高職機械製圖科學生空間能力差異之研究。師大學報：科學教育類，47(1)，55-69。
34. 劉湘川、許天維、林原宏、郭伯臣(1994)。試題層次分析法在國小數學科上的應用。測驗統計年刊，2，1-15。
35. 謝進昌、黃秋華(2006)。運用定錨點技術診斷學生學習表現。國教學報，18，75-101。