Variable Learning II
Learning is generally enhanced when learners are required to take information that is presented in one format and "re-represent" it in an alternative format. The nature of both internal and external knowledge representations has implications for how people teach and learn. Internally both learners and teachers have some kind of mental representation of prior knowledge. External knowledge representation, which include verbal and auditory information, interact with mental representations in constructing new knowledge for learners.
In a cross-cultural study, American and Chinese elementary school teachers were interviewed regarding their teaching practices and mathematical knowledge (Ma, 1999). Teachers who had more developed “knowledge packages” demonstrated deeper understanding of how mathematical topics were related and were less likely to teach mathematics as a set of isolated principles and concepts. For example, when teaching multi-digit subtraction, these teachers were more likely to explain the concept of “decomposing” numbers into smaller units (e.g., 32 is three tens-units and two ones-units), which is also relevant to other mathematical procedures such as multiplying. Thus knowledge of how numbers work allows an individual to re-represent numbers in order to effectively execute a range of mathematical algorithms.
Knowledge representation forms an important aspect of problem solving. Mayer (1987) discusses different aspects of problem solving that can be improved through instruction. For instance, instruction on problem representation can enhance translation, an initial step in problem solving. In translating problems, the student converts verbal information into mathematical or other conceptual entity that retains the underlying relations among different entities. To enhance the translation process, four different processes may be executed: restating what is given, restating the problem statement, representing sentences as pictures or diagrams, and representing sentences as equations. Notice that these four processes are ways of re-representing information in an alternative format.
Re-representing information graphically or through other means improves not only teaching or problem solving but learning as well. In the form of a concept map or a related sort of graphical map, such as a knowledge map, the relationship between different concepts and principles are explicitly highlighted and explained. In a knowledge map, for instance, each link represents one of nine standard types of relationship. By representing information in such a format versus textual, recall for information can be enhanced (e.g., Chmielewski & Dansereau, 1998; Hall, Dansereau, & Skaggs, 1993; Wallace, West, Ware, & Dansereau, 1998).
However, not all knowledge maps are equally effective. Different features of a knowledge map may produce better learning as a demonstrated by a study involving students who learned about how a bill becomes a law from one of three different formats: text, unenhanced map, and enhanced map (Wallace et al., 1998). The enhanced map differed from the unenhanced map in that it used the gestalt principles of proximity and similarity (such as color and shape) to group related concepts and principles. On both immediate and delayed recall, students who studied using enhanced maps demonstrated superior performance over those using unenhanced maps or text. (See Mayer, 1993, for further information regarding what makes illustrations effective teaching/learning aids.)
Training individuals to structure and represent information in particular ways has been shown to improve retention of information and to produce positive transfer effects. Individuals who were given instruction on knowledge maps exhibited enhanced recall of textual information even when mapping was not explicitly used for reading a particular text passage (Chmielewski & Dansereau, 1998). In a separate study, teaching younger and older adults to recognize and textual signals that highlighted structural relationships (i.e., sequences, cause, problem/solution, comparisons, and listings) and to diagram these relationships improved their recall of information presented in text (Meyer & Poon, 2001). More impressive was the fact that this instruction yielded positive transfer for learning everyday materials, as recall was enhanced for content of informative videos. Thus, representing and re-representing information has implications for how people organize incoming information, recognize informational structure, and ultimately retain this information as well as learn other material. As with varying learning conditions, having students re-represent information may make learning more effortful yet produces better retention and transfer. The demonstration for this principle is currently being developed. Educational Applications Combine visuospatial and verbal formats for presenting material. Also require students to construct multiple representations of material to promote active learning. For instance, have students draw concept maps or diagrams for material that are primarily verbal and write verbal descriptions or summaries for visuospatial information. Use and encourage students to use graphical displays that illustrate the material accurately and effectively.
Suggested Readings Chmielewski, T. L. , & Dansereau, D. F. (1998). Enhancing the recall of text: Knowledge map training promotes implicit transfer. Journal of Educational Psychology, 90, 407-413. Individuals who were given instruction on knowledge maps exhibited improved recall of textual details, relative to an untrained group, even when mapping was not explicitly used. This positive transfer of map training (i.e., superior reading comprehension) was most likely not due to differences in motivation.
Hall, R. H., Dansereau, D. F., & Skaggs, L. P. (1993). Knowledge maps and the presentation of related information domains. Journal of Experimental Education, 61, 5-18. Whereas studying from knowledge maps enhanced recall for textual information compared to studying from text when the subject matter was the autonomic nervous system (ANS), no such benefit of knowledge maps was demonstrated for information on research designs. The authors speculate that this may be due to the greater familiarity students may have with examples given to explain the ANS, as well as to the ANS map being more simple structurally.
Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ: Lawrence Erlbaum Associates. Teaching practices and mathematical knowledge of elementary school mathematics teachers in the States were compared to those in China. Teachers exhibiting more developed “knowledge packages” of mathematical topics demonstrated superior conceptual understanding and more effective teaching practices.
Mayer, R. E. (1987). Learnable aspects of problem solving: Some examples. In D. E. Berger, K. Pezdek, W. P. Banks (Eds.) Applications of cognitive psychology: Problem solving, education, and computing (pp. 109-122). Hillsdale, NJ: Lawrence Erlbaum Associates. The chapter explores how different aspects of mathematical problem solving may be taught in the domain of algebra word problems. Relevant to problem representation are two processes: translation (i.e., transforming verbal information an internal representation) and integration (i.e., incorporating ideas into a coherent representation). Examples of training materials used to improve translation and integration are given.
Mayer, R. E. (1993). Illustrations that instruct. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 4, pp. 254-284). Hillsdale, NJ: Lawrence Erlbaum Associates. This book chapter explores the uses of text and illustrations as teaching aids, primarily in textbooks. The author examines how different types of illustrations (i.e., decorative, representational, organizational, and explanative) affect cognitive processes—selecting, organizing, or integrating information—that are involved in learning. Explanative illustrations show how elements in a system are related and underlying principles governing the system. Although underused in textbooks, these types of illustrations best promote all three types of cognitive processing that enhances learning.
Meyer, B. J. F., & Poon, L. W. (2001). Effects of structure strategy training and signaling on recall of text. Journal of Educational Psychology, 93, 141-59. Training older and younger adults to use textual cues that highlight conceptual relationships improved their overall recall of the text as well as recall for main ideas. Training produced positive transfer to remembering everyday materials such that these individuals also better recalled details from informative videos, relative to individuals who were given motivational training or no training.
Wallace, D. S., West, S. W. C., Ware, A., & Dansereau, D. F. (1998). The effect of knowledge maps that incorporate gestalt principles on learning. Journal of Experimental Education, 67, 5-16. Learning aids were presented in one of three different formats: text, unenhanced map, and enhanced map. The enhanced map differed from the unenhanced map in that it used the gestalt principles of similarity and proximity to group related concepts. Those who studied using enhanced maps demonstrated superior recall over those using unenhanced maps or text.