学习—比较法和分阶段指导法对初中生代数样例学习的影响
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摘要
样例学习的研究兴起于20世纪50年代中期,到80年代逐渐受到重视,并随着认知负荷理论的提出而迅速发展。近些年来,样例学习的研究日益趋向复杂和细致化,注重与学习过程的动态结合。最新的样例学习研究得出,在认知技能获得的不同阶段,学习过程中学习者的认知负荷会发生相应的变化。自我解释问题解决与对多种解法的比较相结合是增加了无效的外在负荷,还是提高了有效的相关负荷,这正是根据学习阶段的不同而变化的。因此,有必要在前人研究的基础上,探讨学习-比较法和分阶段指导法在样例学习中的效果,并尝试将Vanlehn提出的认知技能获得三阶段与Sweller的认知负荷理论相结合,考察在认知技能获得的不同阶段中,学习者认识负荷的变化,试图进一步发展样例学习的研究。
研究以初中代数中一元二次方程的两种解法(配方法和因式分解法)为研究材料,探究三种学习方法(学习-比较法、比较法和系列呈现法)和两种指导方法(分阶段指导法和诱发自我解释法)的样例学习效果。被试为一所县级初级中学初二的120名学生。研究由两个实验组成,实验1考察三种样例学习方法(学习-比较法/比较法/系列呈现法)的学习效果差异。主要探讨在相同的指导条件下,与其他两种方法相比,学习-比较法对新手是否有促进效果以及原有知识水平是否会对学习方法的效果产生影响。实验2根据实验一所验得出的学习-比较法的优势效果以及为了改进诱发自我解释法的不足,进一步考察了在学习-比较的样例学习方法下,两种指导方法(分阶段指导法/诱发自我解释法)的学习效果差异,主要探讨相比于诱发自我解释法,分阶段指导方法是否会对样例学习有更大的促进作用以及原有知识水平与指导方法的互相作用。
研究得出如下结论：
(1)对于初中代数的样例学习来说,学习-比较法显著地优于比较法和系列呈现法。
(2)诱发自我解释条件下,样例学习表现出高知识水平的优势效应。原有知识水平较高学习者的样例学习显著优于中等和较低知识水平的学习者,中等知识水平学习者的样例学习效果又显著优于低等知识水平的学习者。
(3)当学习者原有知识水平较低时,分阶段指导法表现出显著的优势。分阶段指导的学习效果显著地优于诱发自我解释方法的方法；其他两种知识水平的学习者在指导方法上样例学习效果差异不显著。
Rising in the 1950s, the study of worked example learning is more and more popular in cognitive psychology and developed rapidly with cognitive load of the theory put forward in the 1980s. Recently, the relevant research related to the trend is increasingly complex and particularized, with emphasis on the dynamic combination. From the latest researches in worked example, at different stages of cognitive skills acquired, cognitive load of learners in the course of study will happen to the corresponding changes. The combination of Self-explanation problem solving with comparative multiple solutions can add more invalid external loads or increase effective load, it precisely deeps on the study phase. Therefore, It's necessary to test the effects of learned-comparative method and grading instructional explanations on the basis of these studies and combine the cognitive load put by Sweller with the theory of cognitive skills acquired in the three stages by Vanlehn. The cognitive load of learners at different stages is used to obtain the courses of worked example learning and finally tries to further extend the development of worked example learning studies.
Using two types of solutions of Quadratic Equation in algebra learning for junior middle school students as the study materials, it tested the effectiveness of three learning methods (learned-comparative method comparative method and uniform solution method)and two instructional methods (grading instructional explanations and prompting self-explanations). There were total 120 junior middle school students in two experiments. In Experiment 1, the effectiveness of three learning methods was tested, mainly in order to test if there were advantages of learned-comparative method for new learners, compared with the other two methods. According to the advantages of learned-comparative method form the former experiment and trying to improve the condition of prompting self-explanations, experiment 2 tested the effects of two instructional methods under the learned-comparative method. It mainly tried to validate the advantages of grading instructional explanations for the new learners and the interaction of the existing knowledge levels and instructional methods.
The results showed that:
(1) To algebra learning for junior middle students, learned-comparative method preformed significantly better than comparative and uniform solution methods;
(2) The advantage of high knowledge level was found on the condition of prompting self-explanations, the participants preformed significantly better than participants of the media and lower knowledge levels, and the same with the media and lower knowledge levels;
(3) The effectiveness of instructional methods was influenced by existing knowledge levels of learners. If the participant had a lower knowledge level, the learned-comparative method preformed significantly better than prompting self-explanations. No effect of instructional methods on the other two knowledge levels was found.
研究以初中代数中一元二次方程的两种解法(配方法和因式分解法)为研究材料,探究三种学习方法(学习-比较法、比较法和系列呈现法)和两种指导方法(分阶段指导法和诱发自我解释法)的样例学习效果。被试为一所县级初级中学初二的120名学生。研究由两个实验组成,实验1考察三种样例学习方法(学习-比较法/比较法/系列呈现法)的学习效果差异。主要探讨在相同的指导条件下,与其他两种方法相比,学习-比较法对新手是否有促进效果以及原有知识水平是否会对学习方法的效果产生影响。实验2根据实验一所验得出的学习-比较法的优势效果以及为了改进诱发自我解释法的不足,进一步考察了在学习-比较的样例学习方法下,两种指导方法(分阶段指导法/诱发自我解释法)的学习效果差异,主要探讨相比于诱发自我解释法,分阶段指导方法是否会对样例学习有更大的促进作用以及原有知识水平与指导方法的互相作用。
研究得出如下结论：
(1)对于初中代数的样例学习来说,学习-比较法显著地优于比较法和系列呈现法。
(2)诱发自我解释条件下,样例学习表现出高知识水平的优势效应。原有知识水平较高学习者的样例学习显著优于中等和较低知识水平的学习者,中等知识水平学习者的样例学习效果又显著优于低等知识水平的学习者。
(3)当学习者原有知识水平较低时,分阶段指导法表现出显著的优势。分阶段指导的学习效果显著地优于诱发自我解释方法的方法；其他两种知识水平的学习者在指导方法上样例学习效果差异不显著。
Rising in the 1950s, the study of worked example learning is more and more popular in cognitive psychology and developed rapidly with cognitive load of the theory put forward in the 1980s. Recently, the relevant research related to the trend is increasingly complex and particularized, with emphasis on the dynamic combination. From the latest researches in worked example, at different stages of cognitive skills acquired, cognitive load of learners in the course of study will happen to the corresponding changes. The combination of Self-explanation problem solving with comparative multiple solutions can add more invalid external loads or increase effective load, it precisely deeps on the study phase. Therefore, It's necessary to test the effects of learned-comparative method and grading instructional explanations on the basis of these studies and combine the cognitive load put by Sweller with the theory of cognitive skills acquired in the three stages by Vanlehn. The cognitive load of learners at different stages is used to obtain the courses of worked example learning and finally tries to further extend the development of worked example learning studies.
Using two types of solutions of Quadratic Equation in algebra learning for junior middle school students as the study materials, it tested the effectiveness of three learning methods (learned-comparative method comparative method and uniform solution method)and two instructional methods (grading instructional explanations and prompting self-explanations). There were total 120 junior middle school students in two experiments. In Experiment 1, the effectiveness of three learning methods was tested, mainly in order to test if there were advantages of learned-comparative method for new learners, compared with the other two methods. According to the advantages of learned-comparative method form the former experiment and trying to improve the condition of prompting self-explanations, experiment 2 tested the effects of two instructional methods under the learned-comparative method. It mainly tried to validate the advantages of grading instructional explanations for the new learners and the interaction of the existing knowledge levels and instructional methods.
The results showed that:
(1) To algebra learning for junior middle students, learned-comparative method preformed significantly better than comparative and uniform solution methods;
(2) The advantage of high knowledge level was found on the condition of prompting self-explanations, the participants preformed significantly better than participants of the media and lower knowledge levels, and the same with the media and lower knowledge levels;
(3) The effectiveness of instructional methods was influenced by existing knowledge levels of learners. If the participant had a lower knowledge level, the learned-comparative method preformed significantly better than prompting self-explanations. No effect of instructional methods on the other two knowledge levels was found.
引文
丛聪.样例学习中的减减提示、自我解释和教学性解释对问题解决迁移的影响[D].长春：东北师范大学,2007.
郭菲菲.小学生样例学习去括号规则的实验研究[D].大连：辽宁师范大学,2006.
林洪新.小学生运算规则的样例学习[D].大连：辽宁师范大学,2006.
林洪新,张奇.小学生代数运算规则的样例学习[J].心理学报,2007,39(2)：257-266.
姜玉荣.小学数学问题解决中的自我解释[D].金华：浙江师范大学,2005.
裴利芳等.领域知识与自我解释间关系的实验研究[J].心理学报,1997,29(4)：386-392.
乔爽,林洪新.样例学习的认知负荷理论[J].辽宁教育行政学报,2009,26(1)：57-58.
任俊杰.样例学习方式和自我解释对大学生数学学习迁移的影响[D].长春：东北师范大学,2008.
唐学峰,莫雷.表面内容不同方面相似性对样例迁移的影响[J].心理科学,2004,26(4)：631-633
王小明.国外有关样例学习的研究[J].办国中小学教育,2007,1：48-51.
邵光华.数学样例学习的理论与实证研究[D].上海：华东师范大学,2003.
邢强,莫雷.多重样例的变异性和编码对迁移影响的实验研究[J].心理科学,2005,28(6)：1382-1387.
邢强,样例的外部表征对问题解决迁移的影响[J].广州大学学报(社会科学版),2004,3(3)：88-91.
邢强,莫雷,朱新明.样例学习研究的发展及问题[J].心理科学进展,2003,11(2)：165-170.
赵弘.样例的变异性对问题解决迁移的影响[J].辽宁师范大学学报(社会科学版),2007,30(4)：46-48.
张奇,赵弘.算术应用题二重变异样例学习的迁移效果[J].心理学报,2008,40(4)：409-417.
张奇,林洪新.四则混合运算规则的样例学习[J].心理学报,2005,37(6)784-790.
A. Aubteen Darabi, David W. Nelson, Fred Paas. Learner Involvement in Instructionon a Complex Cognitive Task:Application of a Composite Measure of Performance and Mental Effort. Journal of Research on Technology in Education,2007,40(1):39--48.
A. Aubteen Darabi, David W. Nelson, Srinivas Palanki. Acquisition of troubleshooting skills in a computer simulation:Worked example vs. conventional problem solving instructional strategies. Computers in Human Behavior,2007,23:1809-1819.
Alexander Renkl, Robert K. Atkinson. Learning From Examples:Fostering Self-Explanations in Computer-Based Learning Environments. Interactive Learning Environments,2002, 10(2):105-119.
Alexander Renkl, Robert K. Atkinson. Structuring the Transition From Example Study to Problem Solving in Cognitive Skill Acquisition:A Cognitive Load Perspective. Educational Psychology,2007,38(1):15-22.
Alexander Renkl, Tatjana Hilbert, Silke Schworm. Example-Based Learning in Heuristic Domains:A Cognitive Load Theory Account.Educational Psychology Reviews, 2009,21:67-78.
Alexander Renkl, Tatjana S.Hilbert, Stephan Kessler, et al. Learning to prove in geometry: Learning from heuristic examples and how it can be supported. Learning and Instruction,2008,18:54-65.
Bethany Rittle-Johnson, Jon R. Star, Kelley Durkin. The Importance of Prior Knowledge When Comparing Examples:Influences on Conceptual and Procedural Knowledge of Equation Solving. Journal of Educational Psychology,2009,101 (4):836-852.
Chi, M. T. H, Bassok, M. Learning from examples via self-explanations. Knowing, learning and instruction,1989,251-282.
Cornelia S. GroBe, Alexander Renkl. Effects of multiple solution methods in mathematics learning. Learning and Instruction,2006,16:122-138.
Cornelia S. GroBe, Alexander Renkl. Finding and fixing errors in worked examples:Can this foster learning outcomes? Learning and Instruction,2007,17:612-634.
Fred Paas, Tamara van Gog. Optimising worked example instruction:Different ways to increase germane cognitive load. Learning and Instruction,2006,16:87-91.
Hans G. K. Hummel, Fred Paas, E. J. R. Koper. Cueing for transfer in multimedia programmes:process worksheets vs. worked-out examples. Journal of Computer Assisted Learning,2004,20:387-397.
Jana Reisslein, Robert K. Atkinson, Patrick Seeling, et al. Encountering the expertise reversal effect with a computer-based environment on electrical circuit analysis. Learning and Instruction,2006,16:92-103.
John Sweller. The worked example effect and human cognition. Learning and Instruction, 2006,16:165-169.
Kent J. Crippen, Boyd L. Earl. The impact of web-based worked examples and self-explanation on performance, problem solving,and self-efficacy. Computers & Education,2007,49:809-821.
Kevin K. H. Chungi, Y. H. Tam. Effects of cognitive-based instruction on mathematical problem solving by learners with mild intellectual disabilities. Journal of Intellectual & Developmental Disability,2005,30(4):207-216.
Paas F, Renkl A, Sweller J. Cognitive load theory and instructional design:Recent developments. Educational Psychologist,2003,38:1-4.
Peter Gerjets, Katharina Scheiter, Richard Catrambone. Can learning from molar and modular worked examples be enhanced by providing instructional explanations and prompting self-explanations? Learning and Instruction,2006,16:104-121.
P.W.M. Van Gerven, F.G.W.C. Paas, J.J.G. Van Merrie'nboer r, et al. Cognitive load theory and aging:effects of worked examples on training efficiency. Learning and Instruction, 2002,12:87-105.
Renkl, A. Learning from worked-out examples:A study on individual differences. Cognitive Science,1997,21:1-29.
Richard Catrambone, Mashiho Yuasa. Acquisition of procedures:The effects of example elaborations and active learning exercises. Learning and Instruction,2006,16: 139-153.
Robert K. Atkinson, Alexander Renkl. Interactive Example-Based Learning Environments: Using Interactive Elements to Encourage Effective Processing of Worked Examples. Educational Psychology Reviews,2007,19:375-386.
Robert K. Atkinson, Alexander Renkl, Mary Margaret Merrill. Transitioning From Studying Examples to Solving Problems:Effects of Self-Explanation Prompts and Fading Worked-Out Steps. Journal of Educational Psychology,2003,95(4):774-783.
Robin Stark, Heinz Mandl, Hans Gruber, et al. Conditions and effects of example elaboration. Learning and Instruction,2002,12:39-60.
Robin Stark, Veronika Kopp, Martin R. Fischer. Case-based learning with worked examples in complex domains:Two experimental studies in undergraduate medical education. Learning and Instruction,2009,1-12.
Rolf Schwonke, Alexander Renkl, Carmen Krieg, et al. The worked-example effect:Not an artefact of lousy control conditions. Computers in Human Behavior,2009,25:258-266.
Roxana Moreno. When worked examples don't work:Is cognitive load theory at an Impasse? Learning and Instruction,2006,16:170-181.
Silke Schworm, Alexander Renkl. Computer-supported example-based learning:When instructional explanations reduce self-explanations. Computers and Education, 2006,46:426-445.
Tamara van Gog, Fred Paas, Jeroen J.G.van Merrienboer. Effects of process-oriented worked examples on troubleshooting transfer performance. Learning and Instruction,2006, 16:154-164.
Tamara van Gog, Fred Paas, Jeroen J.G. van Merrienboer. Effects of studying sequences of process-oriented and product-oriented worked examples on troubleshooting transfer efficiency. Learning and Instruction,2008,18:211-222.
Tatjana S. Hilbert, Alexander Renkl. Learning how to use a computer-based concept-mapping tool:Self-explaining examples helps. Computers in Human Behavior, 2009,25:267-274.
Ulrike-Marie Krause, Robin Stark, Heinz Mandl. The effects of cooperative learning and feedback e-learning in statistics. Learning and Instruction,2009,19:158-170.
郭菲菲.小学生样例学习去括号规则的实验研究[D].大连：辽宁师范大学,2006.
林洪新.小学生运算规则的样例学习[D].大连：辽宁师范大学,2006.
林洪新,张奇.小学生代数运算规则的样例学习[J].心理学报,2007,39(2)：257-266.
姜玉荣.小学数学问题解决中的自我解释[D].金华：浙江师范大学,2005.
裴利芳等.领域知识与自我解释间关系的实验研究[J].心理学报,1997,29(4)：386-392.
乔爽,林洪新.样例学习的认知负荷理论[J].辽宁教育行政学报,2009,26(1)：57-58.
任俊杰.样例学习方式和自我解释对大学生数学学习迁移的影响[D].长春：东北师范大学,2008.
唐学峰,莫雷.表面内容不同方面相似性对样例迁移的影响[J].心理科学,2004,26(4)：631-633
王小明.国外有关样例学习的研究[J].办国中小学教育,2007,1：48-51.
邵光华.数学样例学习的理论与实证研究[D].上海：华东师范大学,2003.
邢强,莫雷.多重样例的变异性和编码对迁移影响的实验研究[J].心理科学,2005,28(6)：1382-1387.
邢强,样例的外部表征对问题解决迁移的影响[J].广州大学学报(社会科学版),2004,3(3)：88-91.
邢强,莫雷,朱新明.样例学习研究的发展及问题[J].心理科学进展,2003,11(2)：165-170.
赵弘.样例的变异性对问题解决迁移的影响[J].辽宁师范大学学报(社会科学版),2007,30(4)：46-48.
张奇,赵弘.算术应用题二重变异样例学习的迁移效果[J].心理学报,2008,40(4)：409-417.
张奇,林洪新.四则混合运算规则的样例学习[J].心理学报,2005,37(6)784-790.
A. Aubteen Darabi, David W. Nelson, Fred Paas. Learner Involvement in Instructionon a Complex Cognitive Task:Application of a Composite Measure of Performance and Mental Effort. Journal of Research on Technology in Education,2007,40(1):39--48.
A. Aubteen Darabi, David W. Nelson, Srinivas Palanki. Acquisition of troubleshooting skills in a computer simulation:Worked example vs. conventional problem solving instructional strategies. Computers in Human Behavior,2007,23:1809-1819.
Alexander Renkl, Robert K. Atkinson. Learning From Examples:Fostering Self-Explanations in Computer-Based Learning Environments. Interactive Learning Environments,2002, 10(2):105-119.
Alexander Renkl, Robert K. Atkinson. Structuring the Transition From Example Study to Problem Solving in Cognitive Skill Acquisition:A Cognitive Load Perspective. Educational Psychology,2007,38(1):15-22.
Alexander Renkl, Tatjana Hilbert, Silke Schworm. Example-Based Learning in Heuristic Domains:A Cognitive Load Theory Account.Educational Psychology Reviews, 2009,21:67-78.
Alexander Renkl, Tatjana S.Hilbert, Stephan Kessler, et al. Learning to prove in geometry: Learning from heuristic examples and how it can be supported. Learning and Instruction,2008,18:54-65.
Bethany Rittle-Johnson, Jon R. Star, Kelley Durkin. The Importance of Prior Knowledge When Comparing Examples:Influences on Conceptual and Procedural Knowledge of Equation Solving. Journal of Educational Psychology,2009,101 (4):836-852.
Chi, M. T. H, Bassok, M. Learning from examples via self-explanations. Knowing, learning and instruction,1989,251-282.
Cornelia S. GroBe, Alexander Renkl. Effects of multiple solution methods in mathematics learning. Learning and Instruction,2006,16:122-138.
Cornelia S. GroBe, Alexander Renkl. Finding and fixing errors in worked examples:Can this foster learning outcomes? Learning and Instruction,2007,17:612-634.
Fred Paas, Tamara van Gog. Optimising worked example instruction:Different ways to increase germane cognitive load. Learning and Instruction,2006,16:87-91.
Hans G. K. Hummel, Fred Paas, E. J. R. Koper. Cueing for transfer in multimedia programmes:process worksheets vs. worked-out examples. Journal of Computer Assisted Learning,2004,20:387-397.
Jana Reisslein, Robert K. Atkinson, Patrick Seeling, et al. Encountering the expertise reversal effect with a computer-based environment on electrical circuit analysis. Learning and Instruction,2006,16:92-103.
John Sweller. The worked example effect and human cognition. Learning and Instruction, 2006,16:165-169.
Kent J. Crippen, Boyd L. Earl. The impact of web-based worked examples and self-explanation on performance, problem solving,and self-efficacy. Computers & Education,2007,49:809-821.
Kevin K. H. Chungi, Y. H. Tam. Effects of cognitive-based instruction on mathematical problem solving by learners with mild intellectual disabilities. Journal of Intellectual & Developmental Disability,2005,30(4):207-216.
Paas F, Renkl A, Sweller J. Cognitive load theory and instructional design:Recent developments. Educational Psychologist,2003,38:1-4.
Peter Gerjets, Katharina Scheiter, Richard Catrambone. Can learning from molar and modular worked examples be enhanced by providing instructional explanations and prompting self-explanations? Learning and Instruction,2006,16:104-121.
P.W.M. Van Gerven, F.G.W.C. Paas, J.J.G. Van Merrie'nboer r, et al. Cognitive load theory and aging:effects of worked examples on training efficiency. Learning and Instruction, 2002,12:87-105.
Renkl, A. Learning from worked-out examples:A study on individual differences. Cognitive Science,1997,21:1-29.
Richard Catrambone, Mashiho Yuasa. Acquisition of procedures:The effects of example elaborations and active learning exercises. Learning and Instruction,2006,16: 139-153.
Robert K. Atkinson, Alexander Renkl. Interactive Example-Based Learning Environments: Using Interactive Elements to Encourage Effective Processing of Worked Examples. Educational Psychology Reviews,2007,19:375-386.
Robert K. Atkinson, Alexander Renkl, Mary Margaret Merrill. Transitioning From Studying Examples to Solving Problems:Effects of Self-Explanation Prompts and Fading Worked-Out Steps. Journal of Educational Psychology,2003,95(4):774-783.
Robin Stark, Heinz Mandl, Hans Gruber, et al. Conditions and effects of example elaboration. Learning and Instruction,2002,12:39-60.
Robin Stark, Veronika Kopp, Martin R. Fischer. Case-based learning with worked examples in complex domains:Two experimental studies in undergraduate medical education. Learning and Instruction,2009,1-12.
Rolf Schwonke, Alexander Renkl, Carmen Krieg, et al. The worked-example effect:Not an artefact of lousy control conditions. Computers in Human Behavior,2009,25:258-266.
Roxana Moreno. When worked examples don't work:Is cognitive load theory at an Impasse? Learning and Instruction,2006,16:170-181.
Silke Schworm, Alexander Renkl. Computer-supported example-based learning:When instructional explanations reduce self-explanations. Computers and Education, 2006,46:426-445.
Tamara van Gog, Fred Paas, Jeroen J.G.van Merrienboer. Effects of process-oriented worked examples on troubleshooting transfer performance. Learning and Instruction,2006, 16:154-164.
Tamara van Gog, Fred Paas, Jeroen J.G. van Merrienboer. Effects of studying sequences of process-oriented and product-oriented worked examples on troubleshooting transfer efficiency. Learning and Instruction,2008,18:211-222.
Tatjana S. Hilbert, Alexander Renkl. Learning how to use a computer-based concept-mapping tool:Self-explaining examples helps. Computers in Human Behavior, 2009,25:267-274.
Ulrike-Marie Krause, Robin Stark, Heinz Mandl. The effects of cooperative learning and feedback e-learning in statistics. Learning and Instruction,2009,19:158-170.