Combining Generation and Expository Instruction to Prepare Students to Transfer Big Ideas Across School Topics

Approaches combining generation and expository instruction have been shown to be beneficial for transfer. This symposium focuses on the approaches of inventing and productive failure. Both approaches delay expository instruction. Students are asked to work on a generation activity with a problem or with contrasting cases. This activity is aimed to foster transfer of the knowledge gained during subsequent expository instruction. The goal of the symposium is to contribute to a better understanding of how the generation activity is best designed to foster transfer. The contributions of this symposium varied the amount and type of generating by varying the materials (e.g., content of cases), the task (e.g., inventing vs. selfexplaining), or the setting (collaborative vs. individual) of the generation activity. Mediating processes are also addressed. The symposium will clarify moderating conditions and mediating processes of how generation activities combined with expository instruction deploy their full potential. Overall Focus and Major Issues of the Symposium Generative learning activities as well as expository instruction have their unique advantages for learning (Lee & Anderson 2013). Attempts to combine the two have been shown to be beneficial for transfer (Kapur, 2012; Schwartz & Martin, 2004). Transfer of big ideas across school topics is a much wanted outcome of instruction, but hard to achieve (Barnett & Ceci, 2002). The big ideas studied in the different contributions to this symposium comprise linear functions (Schalk et al.), ratios in science and mathematics (Glogger et al., Hallinen et al.), and fraction expansion (Maziotti et al.) all of which have great significance for various school subjects. In this symposium we focus on two forms of combining generation and expository instruction to foster transfer: First, inventing asks learners to generate a principle or method that allows evaluating several cases from the learning domain. ‘Cases’ in the present studies refer to examples of a domain such as the diagram of a linear function with a positive gradient, or buses with densely packed passengers as cases of a type of density. The cases usually vary critical features of the domain so that contrasting the cases helps to identify and understand the critical features. The inventing with contrasting cases activity is used as preparation for future learning from expository instruction. Second, in the approach of productive failure, the generative phase includes a complex problem. Learners usually fail to solve this problem in a canonical way. However, the combination with subsequent expository instruction is theorized to make the failure productive (Kapur, 2012). The expository instruction encompasses contrasting of suboptimal (students’) and canonical solution methods. The benefit in transfer of these activities could be based on the deep processing of good examples (or solution methods) in an early stage of skill acquisition (Lee & Anderson, 2013). The deep processing could result in a richly elaborated mental representation of the examples. At the same time, the understanding of a deep structure, an abstract principle that "interconnects" the examples (and can be abstracted by contrasting and comparing), can be the basis for transfer (Barnett & Ceci, 2002). Contrasting cases were shown to help recognizing deep similarities between cases and abstracting generalizable principles (e.g., Alfieri, Nokes, & Schunn, 2013). The deep processing and abstracting of principles prepares to learn from the subsequent expository instruction and to transfer “big ideas” across topics. The contributions to this symposium focus on ways how to best foster deep processing and abstracting deep structures. They analyze primarily experimental variation of the generation phase. Major issues of this set of studies refer to the questions of what conditions moderate and what processes mediate the effectiveness of different combinations of generation and expository instruction. ICLS 2014 Proceedings 1179 © ISLS Moderating conditions can be the type and amount of generation. The type and amount of generation can vary depending on the task, the materials, and the setting. Regarding the task, the level of generation is highest in an inventing or productive failure task (all contributions encompass such a condition). For example, an index to evaluate the density in buses has to be invented. A somewhat lower amount of generation is required when students self-explain already evaluated cases (Schalk et al.). They still have to think towards the abstract principle that forms the basis for the evaluation of the presented cases. The next lower level of generation is to self-explain a completely worked example of the inventing problem (index and resulting evaluation of cases are provided, Glogger et al.). The type and amount of generation can also vary with the specifics of the material, here the characteristics of the cases. Characteristics of the cases that were varied in the studies of this symposium include the concreteness of the cases (idealized, abstract vs. concrete cases in Schalk et al.) and contents of the cases (isolate the main effects of key variables or include main effect and interaction of variables in Hallinen et al.). Finally, the kind of generation can vary depending on the setting such as collaborative or individual work, addressed in the study of Mazziotti et al. Mediating processes can explain how the generation phase affects processing of the subsequent expository instruction and, in the end, how transfer is fostered. Processes discussed in this symposium are motivational such as self-efficacy and cognitive such as cognitive load (Glogger et al.). The potential significance of each contribution is summarized in the following: Schalk, Barth, and Schumacher could show that the kind of material and the kind of task interact when students learn about linear functions: Specifically, their results suggest that self-explanation prompts should be combined with concrete cases, while invention prompts should be combined with idealized cases. They did not find differences between the generative preparatory conditions and a tell-and-practice condition. Glogger, Gaus, and Renkl found that a higher level of generation (inventing) led to deeper encoding of the deep structure of physics ratios such as density than a lower level of generation (worked examples). Deep encoding mediated transfer. A comparison with a previous study suggests that students react differently to the task of inventing or explaining worked examples, respectively, depending on their experience with generative group activities. Mazziotti, Loibl, and Rummel could show that productive failure in mathematics (fraction expansion) is also beneficial for a new age group, namely, elementary school children. Additionally, they varied if students worked on the preparation problem in groups or individually. A simple comparison did not reveal differences in learning outcomes depending on the social setting. However, further analyses of video data will provide more differentiated information about effective processes during collaborative generative activities. Hallinen, Chin, Blair, and Schwartz summarize several studies on the use of contrasting cases in combining generation and expository instruction, about task orientation, and about the content of materials. They could show that more complex material (including main effects and interaction of key variables instead of just the main effects of variables) enhances future problem solving. Consistent with the symposium as a whole, they conclude that the well-chosen combination of well-designed materials and an explicit focus on generation (such as an invention task) are two key aspects to transfer big ideas across school topics. The symposium will give the audience a chance to generate and invent hypotheses about key ideas in the symposium by providing some materials from the studies. The interactivity of the symposium will further be facilitated by discussion questions posed by the presenters. Understanding the Gradient of Linear Functions: Comparing Students’ Transfer Performance Resulting from Different Preparatory Constructive Learning Activities and Tell-and-Practice Instruction Lennart Schalk, Armin Barth, Ralph Schumacher Introduction A major challenge to science and math education is to enable students to use the knowledge learned in the classroom flexibly. An important aim is therefore to foster the construction of knowledge structures which enable transfer to new situations. In the present study, we compared different approaches of how to introduce a novel concept in math education which is of high importance for science in general, namely learning how to determine gradients of linear functions. One way to introduce a new topic is to tell (i.e., directly instruct) learners about the concept and have them practice its application in several tasks; another way is to withhold the expository instruction and start with a preparatory constructive learning activity. These activities have been shown to better support transfer in comparison to the tell-and-practice approach (e.g., Schwartz, Chase, Oppezzo, & Chin, 2011). We implemented contrasting cases in learning materials to prepare an expository instruction on how to determine the gradient of linear functions. Contrasting cases help to recognize deep similarities between cases ICLS 2014 Proceedings 1180 © ISLS and to abstract generalizable schemata (e.g., Alfieri, Nokes, & Schunn, 2013) which in turn can enhance the effectiveness of an expository instruction (e.g., Schwartz et al., 2011). However, contrasting cases could be implemented in several different ways. First, cases can vary in concreteness. Cases could make a reference to concrete, realistic situations (e.g., using realistic concepts to label the axes of coordinate systems in which linear functions are depicted