Examples?
The effects of learning from worked examples heavily depend on how well this learning method is implemented. Following are ten instructional principles that should be taken into account when implementing this learning method.
Self-Explanation Principle
The importance of explanations has already been stressed in this chapter; learners' self-explanations are crucial for fully exploiting the potential of learning from worked examples ("self-explanation effect"; Chi et al., 1989). Two main types of productive self-("self-explanations can be differentiated: (a) elaborating on individual examples in order to foster their understanding and (b) comparing examples, which typically helps to form or differentiate abstract problem categories (Gerjets, Scheiter, & Schuh, 2008; Nokes-Malach, VanLehn, Belenky, Lichtenstein, & Cox, 2013).
Elaborating on individual examples: The most important self-explanation type when elaborating on individual examples are principle-based explanations. They relate solutions to abstract principles, such as mathematics theorems, physics laws, and guidelines for proper argumentation (e.g., Chi et al., 1989;
Renkl, 1997; Schworm & Renkl, 2007). For example, Atkinson, Renkl, and Merrill (2003) encouraged students to justify worked solution steps in terms of the underlying probability principle. The learners could select a probability principle from a menu of potentially relevant principles. Such self-explaining helps students solve not only similar problems but also novel (transfer) problems later on. Schworm and Renkl (2007) had their learners identify argumentative elements of proper scientific argumentation when they watched video-based worked examples, which enabled them to argue about another topic in a differentiated way.
Comparing examples: Figure 2 illustrates self-explaining when comparing examples. The (future) teachers might refer in their self-explanations to themeaningful building block principle (i.e., the
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solution steps should be labeled as meaningful building blocks of a procedure) when they explain why the right example is superior to the left example for high-school students (Schworm & Renkl, 2006).
Rittle-Johnson, Star, and Durkin (2009) guided their learners to explain the difference between the two possible worked solution methods and the conditions that must be met so that the more parsimonious method can be applied. Flexible problem solving was taught by this comparison procedure.
The two main possibilities of fostering self-explanations are training and prompting. Many tried-and-tested prompting procedures request that the learners type their self-explanations into text boxes.
Sometimes such self-explanations are supported by menus providing a list of potential principles (e.g., Conati & VanLehn, 2000). Self-explanations can also be trained (e.g., Renkl, Solymosi, Erdmann, &
Aleven, 2013). Renkl, Stark, Gruber, and Mandl (1998) found the following elements of training useful:
(a) information on the importance of self-explanations, (b) modeling self-explanations, that is, a teacher demonstrates this activity by articulating productive self-explanations, and (c) coached practice.
A qualification of this principle is that self-explanation demands can overwhelm the learners when working memory load is already high due to complex learning tasks in relation to learners' prior knowledge and/or to suboptimal instructional design (e.g., Kalyuga, 2010; Sweller, 2006). In addition, poor prior knowledge can be a barrier to provide correct self-explanations (see Ambrose & Lovett, this volume).
Explanation-Help Principle
As just argued, learners are sometimes unable to self-explain correctly and productively. Help in the form of instructional explanations should then be provided. In addition, as instructional explanations are often just superficially processed (Wittwer & Renkl, 2008), prompts to further process the instructional explanations enhance their effects (Berthold & Renkl, 2010). Aqualification is that too easily available instructional explanations (e.g., the learners can demand them without having first tried to provide substantial self-explanations) can reduce learners' self-explanation efforts and learning outcomes (Schworm & Renkl, 2006; see also Clark & Bjork on desirable difficulties, this volume). For this reason, learners working on the screen displayed in Figure 2 could just demand an explanation when they have first typed in some self-explanations into the box.
Example-Set Principle
This principle goes beyond using multiple examples which is already inherent in the present learning method. Sets of examples are typically used to direct the learners' attention to crucial aspects (e.g., Bransford & Schwartz, 1999). The specific goals of example sets can be quite varied. We have already mentioned the case of providing different solution procedures in order to teach the conditions for applying the simpler solution method and, thus, to foster flexible problem solving (e.g., Rittle-Johnson et al., 2009). "Structure-emphasizing example sets” (Quilici & Mayer, 1996) combine examples in a way that (a) each problem category (e.g., probability problems with and without order relevant) is exemplified by a set of different cover stories (i.e., surface) and (b), the same set of cover stories is used across the problem categories. Learners observe that cover stories and solution-relevant mathematical structures do not necessarily co-vary, and that relying on surface features can mislead when trying to find the correct solution. Aqualification is that example-set effects are not reliable if the learners are not explicitly prompted to compare the examples (Scheiter, Gerjets, & Schuh, 2003). Only prompted or guided example comparison assures the desired learning outcomes (e.g., Gentner, Loewenstein, &
Thompson, 2003; Richland & McDonough, 2010).
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Easy-Mapping Principle
Worked examples lose their effectiveness when learners have difficulty relating different information sources to each other (e.g., text, picture, or equations; see also Figure 1; e.g., Tarmizi & Sweller, 1988).
Visual search processes may require so much cognitive capacity that self-explanations are blocked.
Facilitating the mapping between information sources frees cognitive resources for self-explaining, and worked examples are again effective. In Figure 1, color coding was used to facilitate mapping between tree diagram and equation (Berthold & Renkl, 2009). Another possibility is to rely on the modality effect, which means that spoken (instead of written) text is combined with a picture (e.g., Ginns, 2005, see also Mayer, this volume). In addition, a cue can signal to which pictorial element the current narrated text is referring (for more options on how to facilitate mapping see, Renkl, in press-b). Aqualification is that it is open when to best use which procedure to facilitate mapping (e.g., color coding or modality arrangement with signaling).
Meaningful-Building Blocks Principle
Frequently, students learn a solution procedure just as a "fixed chain" of steps (Catrambone, 1998).
When students work on transfer problems for which a modified solution procedure applies, they can fail because the chain cannot be broken into meaningful building blocks that can be flexibly reassembled. To enable students for such transfer, individual steps should be presented as meaningful building blocks of a solution procedure (for an example see Figure 2, right side). Hence, examples should be designed in way that the sub-goals that are achieved by the individual solution steps are easily identifiable. Such salience of single steps can be attained by visually isolating the steps (e.g., by circles) and by assigning labels (see also Spanjers, van Gog, & van Merriënboer, 2012). Salient subgoals lead to self-explanations about what these steps accomplished. Another way to make (sub-) goals salient is to use a step-by-step presentation of worked solutions (Atkinson & Derry, 2000; Schmidt-Weigand, Hänze, & Wodzinsksi, 2009; Renkl, in press-b, for a more thorough discussion). Aqualification of the meaningful-building blocks principle is that up to now the really convincing evidence has srcinated just from studies on mathematics.
Studying Errors Principle
Self-explaining correct and incorrect worked solutions is usually more beneficial than self-explaining correct solutions only (Siegler & Chen, 2008); explaining incorrect solutions helps to avoid these errors in later problem solving (Durkin & Rittle-Johnson, 2012). Note that in Figure 2, the (future) teachers compared well-designed and suboptimal versions of a worked example for high-school students. When worked examples are presented as video models, learners usually profit more from coping models that initially also commit errors and show how they can be overcome, as compared to mastery models showing just smooth performance (Kitsantas, Zimmerman, & Cleary, 2000; Zimmerman & Kitsantas, 2002). A qualification is that only learners with sufficient prior knowledge might profit from studying errors in examples (Große & Renkl, 2007). Providing errors too early in the learning process overwhelms learners. Weaker learners need additional support by explicitly marking errors (Große & Renkl) or by expert explanations as to why certain moves were correct or not (Stark, Kopp, & Fischer, 2011).
Model-Observer Similarity Principle
Recent research has increasingly employed worked examples in the form of videos displaying model persons that show the respective solutions (e.g., Rummel et al., 2009; Schworm & Renkl, 2007). The model-observer similarity is one of the classic factors influencing learning, as determined by
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observational learning research (e.g., Bandura, 1986; Schunk & Zimmerman, 2007). When models are too dissimilar, observers do not identify and, thus, do not imitate. Furthermore, when models are dissimilar in the sense that they are too advanced, observers do not believe that they can show the appropriate behavior on their own, that is, they lack self-efficacy. Braaksma, Rijlaarsdam, and van den Bergh (2002) displayed both competent and non-competent models in their worked examples to learn argumentative writing. In one condition, the participants were instructed to focus on the competent model and, in another condition, on the non-competent model. Weak students profited more from a focus on the non-competent model, stronger students learned best when focusing on the competent model. This pattern can be interpreted as similarity effect. A qualification of this principle is that it is not fully clear which similarity features are most crucial.
Focus-On-Learning Domain Principle
Worked examples for complex learning contents such as scientific argumentation (Schworm &Renkl, 2007) or mathematical proof (Hilbert et al., 2008) run the risk of overwhelming learners' cognitive capacities. For example, Schworm and Renkl (2007) used stem-cell research as content domain to exemplify proper scientific argumentation; Hilbert et al. (2008) used some geometry contents to teach heuristic strategies in proof finding. If the students have difficulty understanding these exemplifying domain contents (i.e., stem-cell research or geometry) or if their attention is sub-optimally directed by instructional design deficits (Schworm & Renkl, 2007), the learners' attention is largely bound to the exemplifying domain. Hence, achieving the central learning goals is hindered (Renkl, Hilbert, &
Schworm, 2009). Instructional design should use easy-to-process exemplifying domains and processing prompts that focus on the learning domain. Aqualification is that there might also be learning situations in which deeply processing and remembering superficial features from the exemplifying domain may facilitate transfer to related problems. For example, when argumentation skills are exemplified in the area of one medical treatment problem (e.g., surgery or conservative treatment) the transfer of these argumentation skills to other medical topics can be facilitated by overlapping exemplifying domain contents.
Imagery Principle
In the imagery principle, students first read a worked solution, then turn away from the screen or work sheet and imagine performing the solution procedure (e.g., Cooper, Tindall-Ford, Chandler, & Sweller, 2001; Ginns, Chandler, & Sweller, 2003). This effect is consistent with the broader research on learning by mental imagery (e.g., Hall, Munroe-Chandler, Cumming, Law, Ramsey, & Murphy, 2009) whereby mental imagery can have effects similar to actually performing the task. Aqualification is that imagining is not effective when working memory load is very high (e.g., due to two information sources that must be integrated and mentally manipulated; Tindall-Ford & Sweller, 2006). In addition, learners with low prior knowledge simply cannot imagine the solution when looking away from the example. Hence, it is a sensible procedure to first provide an example for study and second an example for imagery (Ginns et al., 2003).
Fading Principle
Worked examples are effective in initial stages of cognitive skill acquisition. In later stages, when automation is one of the main goals, problem solving is superior (Renkl, in press-b). A tried-and-tested method for structuring the transition from studying worked steps to problem solving is to gradually fade worked steps (e.g., Renkl & Atkinson, 2003; Atkinson et al., 2003; Kissane, Kalyuga, Chandler, & Sweller, 2008). In such a procedure, a complete example is presented first. Second, an isomorphic example is
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presented in which a single step has been omitted. After trying to supplement the faded step, the learner receives feedback about the correct solution. Then, in the following examples, the number of blanks increases until only the problem formulation is left, that is, a problem to be solved. Such a fading procedure has proven to be effective. Ideally, the fading procedure is adapted to the individual learner’s progress. Salden, Aleven, Renkl, and Schwonke (2009) faded a specific worked step when the learner provided correct self-explanations on a preceding isomorphic step, thereby indicating understanding of the respective knowledge component. Aqualification is that the fading principle has just been well established with worked examples providing mathematical solution procedures. It is open how to fade effectively in less well-structured skills domains.