數學後設認知量表之發展與信效度考驗

An Evaluation of the Reliability and Validity of the Mathematical Metacognition Scale

10.6251/BEP.20141204

凃金堂(Chin-Tang Tu)

探索性因素分析 ； 測量恆等性 ； 數學後設認知 ； 驗證性因素分析 ； confirmatory factor analysis ； exploratory factor analysis ； mathematical metacognition ； measurement invariance

教育心理學報

47卷1期（2015 / 09 / 01）

109 - 131

繁體中文

本研究旨在發展適用中小學生的數學後設認知量表（Mathematical Metacognition Scale, MMS），本研究分預試與正式施測兩階段，兩階段皆採立意取樣的叢集抽樣方式，各抽取中小學生457人與861人。預試資料進行探索性與驗證性因素分析，驗證性因素分析結果獲得三個因素：後設認知知識、計劃與監控、評估，其內部一致性Cronbach's α係數分別為.87、.87、.72，12題的總量表Cronbach's α係數為.90，顯示本量表具有良好的信度。正式施測資料，進行測量恆等性考驗，考驗結果發現不同性別具測量恆等性，顯示本研究發展的數學後設認知量表，具有良好的建構效度。

The main purpose of this study was to develop the Mathematical Metacognition Scale (MMS) on 5th-8th graders in elementary and junior high schools. The present study included two phases: pretest and test. By adopting purposeful sampling and cluster sampling in both phases, 457 and 861 students were selected for the pretest and the test, respectively. Exploratory factor analysis and confirmatory factor analysis were conducted with the pretest data. The confirmatory factor analysis resulted in three factors including metacognitive knowledge, planning and monitoring, and evaluation. The Cronbach's alphas of the MMS subscales were .87, .87, .72, and .90 for the total score, which indicated good reliability. Measurement invariance was conducted to the test and indicated gender invariance. Therefore, it showed that the MMS has good construct validity.

1. 于富雲、陳玉欣(2007)。不同知識表徵建構的學習策略對自然科學習成效之影響。科學教育學刊，15，99-118。
   連結：
2. Ministry of Education, Singapore. (2000). Curriculum planning & development division, Ministry of Education 2001-Mathematics syllabus (primary). Singapore, Singapore: Ministry of Education..
3. Bagozzi, R. P.,Yi, Y.(1988).On the evaluation of structural equation models.Journal of the Academy of Marketing Science,16,74-94.
4. Bathgate, M. E.,Sims-Knight, J. E.,Schunn, C. D.(2012).Thoughts on thinking: Engaging novice music students in metacognition.Applied Cognitive Psychology,26,403-409.
5. Benton, C. W.(2013).Promoting metacognition in music classes.Music Educators Journal,100,52-59.
6. Carr, M.,Alexander, J.,Folds-Bennett, T.(1994).Metacognition and mathematics strategy use.Applied Cognitive Psychology,8,583-595.
7. Cheung, G. W.,Rensvold, R. B.(2002).Evaluating goodness-of-fit indexes for testing measurement invariance.Structural Equation Modeling,9,233-255.
8. Clark, L. A.,Watson, D.(1995).Constructing validity: Basic issues in objective scale development.Psychological Assessment,7,309-319.
9. Cross, D. R.,Paris, S. G.(1988).Developmental and instructional analyses of children's metacognition and reading comprehension.Journal of Educational Psychology,94,131-142.
10. Desoete, A.(Ed.),Veenman, M.(Ed.)(2006).Metacognition in mathematics education.New York, NY:Nova Science.
11. Flavell, J. H.(1987).Speculation about the nature and development of meatcognition.Metacognition, motivation, and understanding,Hillsdale, NJ:
12. Garofalo, J.,Lester, F.(1985).Metacognition, cognitive monitoring, and mathematical performance.Journal for Research in Mathematics Education,16,163-76.
13. Gregorich, S. E.(2006).Do self-report instruments allow meaningful comparisons across diverse population groups? Testing measurement invariance using the confirmatory factor analysis framework.Medical Care,44,78-94.
14. Hair, J.,Black, W.,Babin, B.,Anderson, R.(2010).Multivariate data analysis: A global perspective.Saddle River, NJ:Pearson Prentice Hall.
15. Horn, J. L.(1965).A rationale and test for the number of factors in factor analysis.Psychometrika,30,179-185.
16. Jackson, D. L.,Gillaspy, J. A.,Purc-Stephenson, R.(2009).Reporting practices in confirmatory factor analysis: An overview and some recommendations.Psychological Methods,14,6-23.
17. Jacobse, A. E.,Harskamp, E. G.(2012).Towards efficient measurement of metacognitionin mathematical problem solving.Metacognition and Learning,7,133-149.
18. Kaberman, Z.,Dori, Y. J.(2009).Metacognition in chemical education: Question posing in the case-basedcomputerized learning environment.Instruction Science,37,403-436.
19. Kapa, E.(2001).A metacognitive support during the process of problem solving in a computerized environment.Educational Studies in Mathematics,47,317-336.
20. Kelemen, W. L.,Frost, P. J.,Weaver, C. A. I.(2000).Individual differences in metacognition: Evidence against a general metacognitive ability.Memory & Cognition,28,92-107.
21. Kline, R. B.(2005).Principles and practice of structural equation modeling.New York, NY:The Guilford Press.
22. Kramarski, B.(2004).Making sense of graphs: Does metacognitive instruction make a difference on students' mathematical conceptions and alternative conceptions?.Learning and Instruction,14,593-619.
23. Kramarski, B.,Mevarech, Z. R.(2003).Enhancing mathematical reasoning in the classroom: The effects of cooperative learning and metacognitive training.American Educational Research Journal,40,281-310.
24. Larkin, S.(2010).Metacognition in young children.New York, NY:Routledge.
25. Lester, F. K.(1982).Building bridges between psychological and mathematics education research on problem solving.Mathematical problem solving: Issues in research,Philadelphia, PA:
26. Lester, P.,Bishop, L. K.(2000).Handbook of tests and measurement in education and the social sciences.Lanham, MD:The Scarecrow Press.
27. Leutwyler, B.(2009).Metacognitive learning strategies: Differential development patterns in high school.Metacognition and Learning,4,111-123.
28. Mok, Y. F.,Fan, R. M.,Pang, N. S.(2007).Developmental patterns of school students' motivational and cognitive-metacognitive competencies.Educational Studies,33,81-89.
29. Mokhtari, K.,Reichard, C.(2002).Assessing students' metacognitive awareness of reading strategies.Journal of Educational Psychology,94,249-259.
30. Muis, K. R.,Winne, P. H.,Jamieson-Noel, D.(2007).Using a multitrait-multi method analysis to examine conceptual similarities of three self-regulated learning inventories.British Journal of Educational Psychology,77,177-195.
31. Nimon, K.,Reio, T., J.(2011).Measurement invariance: A foundational principle for quantitative theory building.Human Resource Development Review,10,198-214.
32. Noar, S. M.(2003).The role of structural equation modeling in scale development.Structural Equation Modeling,10,622-647.
33. Nunnally, J. C.,Bernstein, I. H.(1994).Psychometric theory.New York, NY:McGraw-Hill.
34. O'Connor, B. P.(2000).SPSS and SAS programs for determining the number of components using parallel analysis and Velicer's MAP test.Behavior Research Methods, Instruments, and Computers,32,396-402.
35. O'Neil, H. F.,Brown, R. S.(1998).Differential effects of question formats in math assessment on metacognition and affect.Applied Measurement in Education,11,331-351.
36. Panaoura, A.,Philippou, G.(2003).The construct validity of an inventory for the measurement of young pupils' metacognitive abilities in mathematics.Proceedings of the 27th conference of the international group for the psychology of mathematics education,Honolulu, HI.:
37. Pennequin, V.,Sorel, O.,Nanty, I.,Fontaine, R.(2010).Metacognition and low achievement in mathematics: The effect of training in the use of metacognitive skills to solve mathematical word problems.Thinking and Reasoning,16,198-220.
38. Pett, M. A.,Lackey. N. R.,Sullivan, J. J.(2003).Making sense of factor analysis.Thousand Oaks, CA:Sage.
39. Poitras, E.,Lajoie, S.,Hong, Y. J.(2012).The design of technology-rich learning environments as metacognitive tools in history education.Instructional Science,40,1033-1061.
40. Pressley, M.,Gaskins, I. W.(2006).Metacognitively competent reading comprehension is constructively responsive reading: How can such reading be developed in students?.Metacognition and Learning,1,99-113.
41. Resnick, L. B.(Ed.)(1976).The nature of intelligence.Hillsdale, NJ:Lawrence Erlbaum.
42. Rickey, D.,Stacy, A. M.(2000).The role of metacognition in learning chemistry.Journal of Chemical Education,77,915-919.
43. Rosenzweig, C.,Krawec, J.,Montague, M.(2011).Metacognitive strategy use of eighth-grade students with and without learning disabilities during mathematical problem solving: Think-aloud analysis.Journal of Learning Disabilities,44,508-20.
44. Sass, D. A.(2011).Testing measurement invariance and comparing latent factor means within a confirmatory factor analysis framework.Journal of Psychoeducational Assessment,29,347-363.
45. Schmitt, N.,Kuljanin, G.(2008).Measurement invariance: Review of practice and limitations.Human Resource Management Review,18,210-222.
46. Schoenfeld, A. H.(1985).Mathematical problem solving.Orlando, FL:Academic Press.
47. Schraw, G.,Crippen, K. J.,Hartley, K.(2006).Promoting self-regulation in science education: Metacognition as part of a broader perspective on learning.Research in Science Education,36,111-139.
48. Schraw, G.,Dennison, R. S.(1994).Assessing metacognitive awareness.Contemporary Educational Psychology,19,460-475.
49. Schraw, G.,Moshman, D.(1995).Metacognitive theories.Educational Psychology Review,7,351-371.
50. Schumacker, R. E.,Lomax, R. G.(1996).A beginner's guide to structural equation modeling.Mahwah, NJ:Erlbaum.
51. Schwartz, B. L.,Metcalfe, J.(1992).Cue familiarity but not target retrievability enhances feeling-of-knowing judgments.Journal of Experimental Psychology: Learning, Memory, & Cognition,18,1074-1083.
52. Silver, E. A.(1985).Research on teaching mathematical problem solving: Some underrepresented themes and needed directions.Teaching and learning mathematical problem solving: Multiple research perspectives,Hillsdale, NJ:
53. Spector, P.(1992).Summated rating scale construction.Thousand Oaks, CA:Sage.
54. Sperling, R. A.,Howard, B. C.,Miller, L. A.,Murphy, C.(2002).Measures of children's knowledge and regulation of cognition.Contemporary Educational Psychology,27,51-79.
55. Steinmetz, H.,Schmidt, P.,Tina-Booh, A.,Wieczorek, S.,Schwartz, S. H.(2009).Testing measurement invariance using multigroup CFA: Differences between educational groups in human values measurement.Quality and Quantity,43,599-616.
56. Stevens, J.(2002).Applied multivariate statistics for the social sciences.Hillsdale, NJ:Erlbaum.
57. Veenman, M. V. J.,Spaans, M. A.(2005).Relation between intellectual and metacognitive skills: Age and task differences.Learning and Individual Differences,15,159-176.
58. Veenman, M. V. J.,Van Hout-Wolters, B. H. A. M.,Afflerbach, P.(2006).Metacognition and learning: Conceptual and methodological considerations.Metacognition and Learning,1,3-14.
59. Wang, M. C.,Haertel, G. D.,Walberg, H. J.(1990).What influences learning? A content analysis of review literature.Journal of Educational Research,84,30-43.
60. Zimmerman, B. J.,Martinez-Pons, M.(1990).Student differences in self-regulated learning: Relating grade, sex, and giftedness to SE and strategy use.Journal of Educational Psychology,82,51-59.
61. 余民寧(2006)。潛在變項模式：SIMPLIS 的應用。台北=Taipei, Taiwan:高等教育=Higher Education。
62. 林清山、張景媛(1993)。國中生後設認知、動機信念與數學解題策略之關系研究。教育心理學報，26，53-74。
63. 陳李綢(1992)。國小男女生後設認知能力與數學作業表現的關係研究。教育心理學報，25，67-90。
64. 蘇宜芬、林清山(1992)。後設認知訓練課程對國小低閱讀能力學生的閱讀理解能力與後設認知能力之影響。教育心理學報，25，245-267。
65. 凃金堂(2012)。量表編製與SPSS。台北=Taipei, Taiwan:五南=Wu Nan。
66. 凃金堂(1996)。國小學生後設認知與數學解題表現之相關研究。國教學報，8，133-164。

1. 陳英豪(2016)。公立高中數理資優男女生數學學習歷程與成就之差異性探討。資優教育，141，11-19。
2. 柯華葳(2019)。以學與教為經為緯的教育心理學。中華心理學刊，61(4)，417-438。
3. (2019)。數學讀報遊戲結合「認知－後設認知」策略對學生數學學習成效之探討。教育研究學報，53(2)，81-102。