题名

Connecting Principled Information and Worked Examples: Effects of Content Abstractness and Solution Complexity

并列篇名

連結原理與實例:抽象內容與複雜解答的效果

DOI

10.6251/BEP.201906_50(4).0007

作者

廖心玫(Hsinmei Liao)

关键词

Analogical mapping ; Example complexity ; Principle abstractness ; 例題複雜性 ; 原理抽象性 ; 類比映對

期刊名称

教育心理學報

卷期/出版年月

50卷4期(2019 / 06 / 01)

页次

707 - 727

内容语文

英文

中文摘要

Two experiments were conducted to investigate the effect of content abstractness (Experiment 1) and solution complexity (Experiment 2) for connecting principled information and worked examples. College students who had not learned the selected statistical distribution studied the principled information and two examples. In Experiment 1, the participants completed tasks for principle-example mapping and example-example mapping. Overall, their performance in principle-example mapping was lower than that in example-example mapping. They also committed more one-to-many errors and mapped fewer parallel contents and more nonparallel contents in principle-example mapping in comparison with those in example-example mapping. However, these effects were weaker when one example in the example-example pair was relatively complex. In Experiment 2, the participants completed tasks for principle-simple example mapping and principle-complex example mapping. Their performance in principle-complex example mapping was lower than that in principle-simple example mapping. In addition, the participants made more one-to-many errors and mapped fewer parallel elements and slightly more nonparallel elements. This study adds direct evidence to the research literature concerning the process of connecting a principle to its example. Abstractness causes principle-example mapping difficulty but not example-example mapping difficulty. Because a general element in the principle may be mapped onto several possible candidates in the example, mapping of corresponding elements between the principle and example is less accurate. However, principle-example mapping provides learners an opportunity to examine elements not demonstrated in the examples, and such learning tends to be more accurate in comparison to example-example mapping. Furthermore, pairing a simple example with the principle appears to facilitate learning of the parallel content, whereas pairing a complex example with the principle tends to promote learning of the nonparallel content. The implications of these findings are discussed.

英文摘要

本研究透過兩個實驗調查抽象內容(實驗1)與複雜解答(實驗2)對連結原理與實例的影響。未曾學習過特定機率分配的大學生研讀某原理與兩個實例。在實驗1中,參與者完成原理-實例映對以及實例-實例映對作業。整體而言,他們在原理-實例映對的表現低於實例-實例映對的表現。與實例-實例映對相較,他們也犯了較多一對多錯誤,而且在原理-實例映對作業上對比出較少對等的內容但較多非對等的內容。然而,當實例-實例作業中一個例題較為複雜時,這些效果變得較為微弱。在實驗2中,參與者完成原理-簡單實例以及原理-複雜實例映對作業。結果發現,他們在後者的表現低於前者。此外,參與者在後者犯了較多一對多錯誤,並且對比較少的對等內容但稍多的非對等內容。這項研究為文獻增加了關於連結原理與實例之歷程的直接證據。與實例-實例映對相比,抽象性確實導致原理-實例映對的困難。部分原因是該原理中的一般元素可以對應到實例中幾個可能的候選者。這種效果的結果是原理和實例之間的相應元素的映對不太準確。然而,原理-實例映對為學習者提供了檢驗未出現於實例中的元素的機會,並且與實例-實例映對相比這種學習往往較為準確。(儘管總體而言,原理-實例映對不如實例-實例映對準確。)另一方面,原理-實例映對也受到實例的解決方案複雜性的影響。將簡單實例與原理配對似乎有助於學習對等內容,而將複雜實例與原理配對則傾向於促進對非對等內容的學習。文末針對這些發現的意涵進行討論。

主题分类 社會科學 > 心理學
社會科學 > 教育學
参考文献
  1. Huang, Y. H.,Yu, X.(2014)。不同範例與解題組合對初學者在學習上的影響。Bulletin of Educational Psychology,45(4),497-515。
    連結:
  2. Liao, H.(2014).Learners’ attempt in connecting a probability principle and its worked example.Journal of the Humanities and Social Science,15,1-36.
    連結:
  3. Tu, C. T.(2011)。運用「範例(worked-out example)」在國小數學問題解決的教學實驗研究。Bulletin of Educational Psychology,43(1),25-50。
    連結:
  4. Alfieri, L.,Nokes-Malach, T. J.,Schunn, C. D.(2013).Learning through case comparisons: A meta-analytic review.Educational Psychologist,48(2),87-113.
  5. Atkinson, R. K.,Derry, S. J.,Renkl, A.,Wortham, D.(2000).Learning from examples: Instructional principles from the worked examples research.Review of Educational Research,70(2),181.
  6. Atkinson, R. K.,Renkl, A.(2007).Interactive example-based learning environments: Using interactive elements to encourage effective processing of worked examples.Educational Psychology Review,19(3),375-386.
  7. Bassok, M.,Holyoak, K. J.(1989).Interdomain transfer between isomorphic topics in algebra and physics.Journal of Experimental Psychology: Learning, Memory, and Cognition,15(1),153-166.
  8. Catrambone, R.(1995).Following instructions: Effects of principles and examples.Journal of Experimental Psychology: Applied,1(3),227-244.
  9. Catrambone, R.,Holyoak, K. J.(1990).Learning subgoals and methods for solving probability problems.Memory & Cognition,18(6),593-603.
  10. Chi, M. T. H.,Bassok, M.,Lewis, M. W.,Reimann, P.,Glaser, R.(1989).Self-explanations: How students study and use examples in learning to solve problems.Cognitive Science,13(2),145-182.
  11. De Bock, D.,Deprez, J.,Dooren, W. V.,Roelens, M.,Verschaffel, L.(2011).Abstract or concrete examples in learning mathematics? A replication and elaboration of Kaminski, Sloutsky, and Heckler's study.Journal for Research in Mathematics Education,42(2),109-126.
  12. Eiriksdottir, E.,Catrambone, R.(2015).The effects of timing of exposure to principles and procedural instruction specificity on learning an electrical troubleshooting skill.Journal of Experimental Psychology: Applied,21(4),383-394.
  13. Fisher, K. J.,Borchert, K.,Bassok, M.(2011).Following the standard form: Effects of equation format on algebraic modeling.Memory & Cognition,39(3),502-515.
  14. Gentner, D.,Loewenstein, J.,Thompson, L.(2003).Learning and transfer: A general role for analogical encoding.Journal of Educational Psychology,95(2),393-408.
  15. Gick, M. L.,Holyoak, K. J.(1980).Analogical problem solving.Cognitive psychology,12(3),306-355.
  16. Goldstone, R. L.,Son, J. Y.(2005).The transfer of scientific principles using concrete and idealized simulations.Journal of the Learning Sciences,14(1),69-110.
  17. Große, C. S.,Renkl, A.(2006).Effects of multiple solution methods in mathematics learning.Learning and Instruction,16(2),122-138.
  18. Kaminski, J. A.,Sloutsky, V. M.,Heckler, A. F.(2008).The Advantage of Abstract Examples in Learning Math.Science,320(5875),454-455.
  19. Kirby, K. N.,Gerlanc, D.(2013).BootES: an R package for bootstrap confidence intervals on effect sizes.Behavior Research Methods,45(4),905-927.
  20. Klausmeier, H. J.,Feldman, K. V.(1975).Effects of a definition and a varying number of examples and nonexamples on concept attainment.Journal of Educational Psychology,67(2),174-178.
  21. Koedinger, K. R.,Alibali, M. W.,Nathan, M. J.(2008).Trade-offs between grounded and abstract representations: evidence from algebra problem solving.Cognitive Science,32(2),366-397.
  22. Littell, R.,Milliken, G.,Stroup, W.,Wolfinger, R.,Schabenberger, O.(2006).SAS for mixed models.Cary, NC:SAS Institute Inc.
  23. McNeil, N. M.,Fyfe, E. R.(2012)."Concreteness fading" promotes transfer of mathematical knowledge.Learning and Instruction,22(6),440-448.
  24. Novick, L. R.(1988).Analogical transfer, problem similarity, and expertise.Journal of Experimental Psychology: Learning, Memory, and Cognition,14(3),510-520.
  25. Paas, F. G. W. C.,Van Merriënboer, J. J. G.(1994).Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach.Journal of Educational Psychology,86(1),122-133.
  26. Perry, M.(1991).Learning and transfer: Instructional conditions and conceptual change.Cognitive Development,6(4),449-468.
  27. Reed, S. K.,Bolstad, C. A.(1991).Use of examples and procedures in problem solving.Journal of Experimental Psychology: Learning, Memory, and Cognition,17(4),753-766.
  28. Reed, S. K.,Stebick, S.,Comey, B.,Carroll, D.(2012).Finding similarities and differences in the solutions of word problems.Journal of Educational Psychology,104(3),636-646.
  29. Renkl, A.(2002).Worked-out examples: instructional explanations support learning by self-explanations.Learning and Instruction,12(5),529-556.
  30. Renkl, A.(2014).Toward an instructionally oriented theory of example-based learning.Cognitive Science,38(1),1-37.
  31. Renkl, A.(1997).Learning from worked-out examples: A study on individual differences.Cognitive Science,21(1),1-29.
  32. Renkl, A.,Stark, R.,Gruber, H.,Mandl, H.(1998).Learning from worked-out examples: The effects of example variability and elicited self-explanations.Contemporary Educational Psychology,23(1),90-108.
  33. Rittle-Johnson, B.,Alibali, M. W.(1999).Conceptual and procedural knowledge of mathematics: Does one lead to the other?.Journal of Educational Psychology,91(1),175-189.
  34. Rittle-Johnson, B.,Star, J. R.(2007).Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations.Journal of Educational Psychology,99(3),561-574.
  35. Rittle-Johnson, B.,Star, J. R.,Durkin, K.(2009).The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving.Journal of Educational Psychology,101(4),836-852.
  36. Ross, B. H.(1987).This is like that: The use of earlier problems and the separation of similarity effects.Journal of Experimental Psychology: Learning, Memory, and Cognition,13(4),629-639.
  37. Ross, B. H.,Kilbane, M. C.(1997).Effects of principle explanation and superficial similarity on analogical mapping in problem solving.Journal of Experimental Psychology: Learning, Memory, and Cognition,23(2),427-440.
  38. Siler, S. A.,Willows, K. J.(2014).Individual differences in the effect of relevant concreteness on learning and transfer of a mathematical concept.Learning and Instruction,33,170-181.
  39. Sweller, J.,Cooper, G. A.(1985).The use of worked examples as a substitute for problem solving in learning algebra.Cognition & Instruction,2(1),59-89.
  40. Tso, T. Y.,Lu, F. L.,Tzeng, S. C.,Wu, H. M.,Chen, M. J.,Tan, N. C.(2011)。以分段方式降低任務複雜度對專家與生手閱讀幾何證明的影響。Bulletin of Educational Psychology,43,291-314。
  41. Vosniadou, S.(Ed.),Ortony, A.(Ed.)(1989).Similarity and analogical reasoning.New York, US:Cambridge University Press.