Worked example principle - Revision history

Koedinger: /* Laboratory experiment support */

2017-07-12T15:52:29Z

Laboratory experiment support

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	=== Laboratory experiment support ===		=== Laboratory experiment support ===

	See Cooper & Sweller and many others [Atkinson, Ayres, Catrambone, Paas, Renkl, van Gog, van Merrienboer ...].		See papers Cooper & Sweller and many others, such as Atkinson, Ayres, Catrambone, Paas, Renkl, van Gog, van Merrienboer ... See the recommendation "Repeatedly alternating problems with their solutions provided and problems that students must solve" [http://www.nctq.org/dmsStage/Learning_About_Learning_Report on this web page] which is a web-based update of this IES practice guide: Organizing Instruction and Study to Improve Student Learning. Some relevant references can be found within [http://www.nctq.org/dmsView/App_G this page.]

	=== In vivo experiment support ===		=== In vivo experiment support ===

Koedinger: /* Experimental support */

2009-05-07T21:07:28Z

Experimental support

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	== Experimental support ==		== Experimental support ==

			As summarized in Clark & Mayer, 2003 (pp 179): "There is a lot of evidence for the effectiveness of learning from worked examples.  As an example, in one study twelve [statistics] problems were used.  In the conventional group the learners solved all twelve problems as practice.  In the worked examples group, the learners received eight problems already worked out to study and then four problems to solve as practice.  Students in the worked examples group spent significantly less time studying and scored higher on a test than did those in the conventional group.  Furthermore, the worked examples group scored higher not only on test problems similar to those used during practice but also on different types of problems requiring application of the principles taught (Paas, 1992).  The investigators conclude that 'training with partly or completely worked-out problems leads to less effort-demanding and better transfer performance and is more time efficient' (p. 433).  In fact, in one study, the use of worked examples allowed learners to complete a three-year mathematics course in two years (Zhu and Simon, 1987).  Positive effects of worked examples have been reported in a variety of courses teaching well-defined problems, including algebra, geometry, statistics, and programming".

	"There is a lot of evidence for the effectiveness of learning from worked examples.  As an example, in one study twelve geometry problems were used.  In the conventional group the learners solved all twelve problems as practice.  In the worked examples group, the learners received eight problems already worked out to study and then four problems to solve as practice.  Students in the worked examples group spent significantly less time studying and scored higher on a test than did those in the conventional group.  Furthermore, the worked examples group scored higher not only on test problems similar to those used during practice but also on different types of problems requiring application of the principles taught (Paas, 1992).  The investigators conclude that "training with partly or completely worked-out problems leads to less effort-demanding and better transfer performance and is more time efficient" (p. 433).  In fact, in one study, the use of worked examples allowed learners to complete a three-year mathematics course in two years (Zhu and Simon, 1987).  Positive effects of worked examples have been reported in a variety of courses teaching well-defined problems, including algebra, geometry, statistics, and programming". Clark & Mayer, 2003(pp 179)		=== Laboratory experiment support ===

	~~=== Laboratory experiment support ===~~		See Cooper & Sweller and many others [Atkinson, Ayres, Catrambone, Paas, Renkl, van Gog, van Merrienboer ...].

	=== In vivo experiment support ===		=== In vivo experiment support ===
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	[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. Following Renkl and Atkinson's (2003) example fading methods, the example-enhanced version of the tutor, after first presenting fully-worked-out examples, gradually reduced the number of solution steps given, thus increasing the number of open steps that students had to solve. Salden et al. found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.		[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. Following Renkl and Atkinson's (2003) example fading methods, the example-enhanced version of the tutor, after first presenting fully-worked-out examples, gradually reduced the number of solution steps given, thus increasing the number of open steps that students had to solve. Salden et al. found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.

	Paas (1992): Across 12 tasks, interleaving 2 worked examples and 1 problem to solve		Paas (1992): Across 12 tasks, interleaving 2 worked examples and 1 problem to solve leads to:
	* ~~leads to~~ shorter learning time-on-task than solving all active problem solving (computing mean, median, mode).		* shorter learning time-on-task than solving all active problem solving (computing mean, median, mode)
	* ~~Similar~~ time on task and accuracy for solving the 4 active problem solving items		* similar time on task and accuracy for solving the 4 active problem solving items
	* ~~Better~~ near and far transfer for worked examples vs. active problem solving.		* better near and far transfer for worked examples vs. active problem solving
	* greater perceived mental effort for active problem solving than worked examples		* greater perceived mental effort for active problem solving than worked examples

	== Theoretical rationale ==		== Theoretical rationale ==

Corbett: /* In vivo experiment support */

2009-05-07T20:36:13Z

In vivo experiment support

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	[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. Following Renkl and Atkinson's (2003) example fading methods, the example-enhanced version of the tutor, after first presenting fully-worked-out examples, gradually reduced the number of solution steps given, thus increasing the number of open steps that students had to solve. Salden et al. found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.		[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. Following Renkl and Atkinson's (2003) example fading methods, the example-enhanced version of the tutor, after first presenting fully-worked-out examples, gradually reduced the number of solution steps given, thus increasing the number of open steps that students had to solve. Salden et al. found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.

			Paas (1992): Across 12 tasks, interleaving 2 worked examples and 1 problem to solve
			* leads to shorter learning time-on-task than solving all active problem solving (computing mean, median, mode).
			* Similar time on task and accuracy for solving the 4 active problem solving items
			* Better near and far transfer for worked examples vs. active problem solving.
			* greater perceived mental effort for active problem solving than worked examples

	== Theoretical rationale ==		== Theoretical rationale ==

Aleven: /* In vivo experiment support */

2008-07-09T19:31:44Z

In vivo experiment support

← Older revision		Revision as of 19:31, 9 July 2008
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	[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.		[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.

	[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. Following Renkl and Atkinson's (2003) example fading methods, the example-enhanced version of the tutor, after first presenting fully-worked-out examples, gradually reduced the number of solution steps given, thus increasing the number of open steps that students had to solve. ~~They~~ found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.		[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. Following Renkl and Atkinson's (2003) example fading methods, the example-enhanced version of the tutor, after first presenting fully-worked-out examples, gradually reduced the number of solution steps given, thus increasing the number of open steps that students had to solve. Salden et al. found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.

	== Theoretical rationale ==		== Theoretical rationale ==

Aleven: /* References */

2008-07-09T19:31:00Z

References

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	* Paas, F. (1992). Training strategies for attaining transfer of problem solving skill in statistics: A cognitive load approach. Journal of Educational Psychology, 84, 429–434.		* Paas, F. (1992). Training strategies for attaining transfer of problem solving skill in statistics: A cognitive load approach. Journal of Educational Psychology, 84, 429–434.

			* Renkl, A. & Atkinson, R. K. (2003). Structuring the transition from example study to problem solving in cognitive skills acquisition: A cognitive load perspective. Educational Psychologist, 38, 15-22.

	* Salden, R., Aleven, V., Renkl, A., & Schwonke, R. (2008). Worked examples and tutored problem solving: redundant or synergistic forms of support? In C. Schunn (Ed.) Proceedings of the Annual Meeting of the Cognitive Science Society, CogSci 2008. New York, NY: Lawrence Erlbaum. Cognition and Student Learning Prize.		* Salden, R., Aleven, V., Renkl, A., & Schwonke, R. (2008). Worked examples and tutored problem solving: redundant or synergistic forms of support? In C. Schunn (Ed.) Proceedings of the Annual Meeting of the Cognitive Science Society, CogSci 2008. New York, NY: Lawrence Erlbaum. Cognition and Student Learning Prize.

Aleven: /* In vivo experiment support */

2008-07-09T19:30:45Z

In vivo experiment support

← Older revision		Revision as of 19:30, 9 July 2008
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	[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.		[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.

	[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. Following Renkl and Atkinson (2003) example fading methods, the example-enhanced version of the tutor, after first presenting fully-worked-out examples, gradually reduced the number of solution steps given, thus increasing the number of open steps that students had to solve. They found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.		[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. Following Renkl and Atkinson's (2003) example fading methods, the example-enhanced version of the tutor, after first presenting fully-worked-out examples, gradually reduced the number of solution steps given, thus increasing the number of open steps that students had to solve. They found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.

	== Theoretical rationale ==		== Theoretical rationale ==

Aleven: /* In vivo experiment support */

2008-07-09T19:30:27Z

In vivo experiment support

← Older revision		Revision as of 19:30, 9 July 2008
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	[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.		[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.

	[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. They found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.		[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. Following Renkl and Atkinson (2003) example fading methods, the example-enhanced version of the tutor, after first presenting fully-worked-out examples, gradually reduced the number of solution steps given, thus increasing the number of open steps that students had to solve. They found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.

	== Theoretical rationale ==		== Theoretical rationale ==

Aleven: /* In vivo experiment support */

2008-07-09T19:23:47Z

In vivo experiment support

← Older revision		Revision as of 19:23, 9 July 2008
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	[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.		[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.

	Salden, Renkl, Schwonke and Aleven (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. They found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.		[[Does_learning_from_worked-out_examples_improve_tutored_problem_solving? \| Salden, Renkl, Schwonke and Aleven ]] (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. They found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.

	== Theoretical rationale ==		== Theoretical rationale ==

Aleven: /* In vivo experiment support */

2008-07-09T18:31:08Z

In vivo experiment support

← Older revision		Revision as of 18:31, 9 July 2008
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	[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.		[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.

	Salden, Renkl, Schwonke and Aleven (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the ~~geometry tutor~~. They found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.		Salden, Renkl, Schwonke and Aleven (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the Geometry Cognitive Tutor. They found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.

	== Theoretical rationale ==		== Theoretical rationale ==

Aleven: /* In vivo experiment support */

2008-07-09T18:28:02Z

In vivo experiment support

← Older revision		Revision as of 18:28, 9 July 2008
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	[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.		[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems \| McLaren's three stoichiometry studies]] provide mixed support of the worked example principle. Although ''students did not learn more'' through the study of worked examples followed by problem solving, as in (Paas, 1992; Zhu and Simon, 1987; Trafton & Reiser, 1993), ''they did learn more efficiently'' as in the earlier studies. On the other hand, only normal pre-post gains were evaluated in the stoichiometry studies; [[robust learning]] was not measured. In addition, the control condition of these three studies was different -- and potentially much more rigorous -- than the earlier studies: students solved problems with the support of an ''intelligent tutor''. This may explain why students did not learn more: perhaps the additional support of the tutor -- in which students theoretically could create their own "worked examples" by clicking through to bottom out hints -- equalizes the advantage of learning from the examples.

	Salden, Renkl, Schwonke and Aleven studied the use of 'faded' examples as an adjunct to tutored problem solving with the geometry tutor. They found that the faded examples help students learn more efficiently and effectively, especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.		Salden, Renkl, Schwonke and Aleven (2008) studied the use of 'faded' examples as an adjunct to tutored problem solving with the geometry tutor. They found that the faded examples help students learn more efficiently and effectively (e.g., Schwonke, Renkl, Krieg, Wittwer, Aleven, & Salden, in press) especially when the examples are faded in an adaptive manner, responsive to the students' explanations of worked-out steps.

	== Theoretical rationale ==		== Theoretical rationale ==