Teaching general problem solving does not lead to mathematical skills or knowledge

Sweller, J., Clark, R. E., & Kirschner, P. A. (2010). Teaching general problem solving does not lead to mathematical skills or knowledge. Notices of the American Mathematical Society, 57, 1303-1304.Problem solving is central to mathematics. Yet problem-solving skill is not what it seems. Indeed, the field of problem solving has recently undergone a surge in research interest and insight but many of the results of this research are both counterintuitive and contrary to many widely held views

Mathematical ability relies on knowledge, Too

Sweller, J., Clark, R. E., & Kirschner, P. A. (2010). Mathematical ability relies on knowledge too. American Educator, 34(4), 34-35.Problem solving is central to mathematics. Yet problem-solving skill is not what it seems. Indeed, the field of problem solving has recently undergone a surge in research interest and insight, but many of the results of this research are both counterintuitive and contrary to many widely held views

Putting Students on the Path to Learning:The Case for Fully Guided Instruction

Clark, R. E., Kirschner, P. A., & Sweller, J. (2012). Putting students on the path to learning: The case for fully guided instruction. American Educator, 36(1), 6-11.Disputes about the impact of instructional guidance during teaching have been ongoing for more than a half century. On one side of this argument are those who believe that all people—novices and experts alike—learn best when provided with instruction that contains unguided or partly guided segments. This is generally defined as instruction in which learners, rather than being presented with all essential information and asked to practice using it, must discover or construct some or all of the essential information for themselves. On the other side are those who believe that ideal learning environments for experts and novices differ: while experts often thrive without much guidance, nearly everyone else thrives when provided with full, explicit instructional guidance (and should not be asked to discover any essential content or skills

Biological evolution and human cognition are analogous information processing systems

The mechanisms that govern biological evolution and human cognition are analogous, as both follow the same principles of natural information processing systems. In this article, we describe the following five principles that provide an analogy between biological evolution and human cognition: (a) Randomness as Genesis Principle and (b) Borrowing and Reorganizing Principle, which indicate how natural information processing systems obtain information; (c) Narrow Limits of Change Principle and (d) Information Store Principle, which indicate how information is processed and stored; and (e) Environmental Organizing and Linking Principle, which indicate how stored information is used to generate actions appropriate to an environment. In human cognition, these analogs only apply to cognitive processes associated with biologically secondary knowledge, the knowledge typically taught in educational institutions. Based on these five principles, cognitive load theory researchers have provided diverse prescriptions to optimize instructional activities and materials. We conclude by discussing general instructional implications and future research directions based on this analogy

Cognitive load theory: New conceptualizations, specifications, and integrated research perspectives

Over the last few years, cognitive load theory has progressed and advanced rapidly. The articles in this special issue, which document those advances, are based on contributions to the 3rd International Cognitive Load Theory Conference (2009), Heerlen, The Netherlands. The articles of this special issue on cognitive load theory discuss new conceptualizations of the different categories of cognitive load, an integrated research perspective of process-oriented and cognitive load approaches to collaborative learning, an integrated research perspective of cognitive and social-cognitive approaches to example-based learning, and a specification of the theory focusing on the acquisition of generalized knowledge structures as a means to facilitate flexible problem-solving skills. This article provides a short introduction to the theory, discusses some of its recent advances, and provides an overview of the contributions to this issue

The worked example effect, the generation effect, and element interactivity

The worked example effect indicates that examples providing full guidance on how to solve a problem result in better test performance than a problem-solving condition with no guidance. The generation effect occurs when learners generating responses demonstrate better test performance than learners in a presentation condition that provides an answer. This contradiction may be resolved by the suggestion that the worked example effect occurs for complex, high-element interactivity materials that impose a heavy working memory load whereas the generation effect is applicable for low-element interactivity materials. Two experiments tested this hypothesis in the area of geometry instruction using students with different levels of prior knowledge in geometry. The results of Experiment 1 indicated a worked example effect obtained for materials high in element interactivity and a generation effect for materials low in element interactivity. As levels of expertise increased in Experiment 2, thus reducing effective complexity, this interaction was replaced by a generation effect for all materials. These results suggest that when students need to learn low-element interactivity material, learning will be enhanced if they generate rather than study responses but if students need to learn high-element interactivity material, study may be preferable to generating responses

Cognitive Architecture and Instructional Design: 20 Years Later

Cognitive load theory was introduced in the 1980s as an instructional design theory based on several uncontroversial aspects of human cognitive architecture. Our knowledge of many of the characteristics of working memory, long-term memory and the relations between them had been well-established for many decades prior to the introduction of the theory. Curiously, this knowledge had had a limited impact on the field of instructional design with most instructional design recommendations proceeding as though working memory and long-term memory did not exist. In contrast, cognitive load theory emphasised that all novel information first is processed by a capacity and duration limited working memory and then stored in an unlimited long-term memory for later use. Once information is stored in long-term memory, the capacity and duration limits of working memory disappear transforming our ability to function. By the late 1990s, sufficient data had been collected using the theory to warrant an extended analysis resulting in the publication of Sweller et al. (Educational Psychology Review, 10, 251-296, 1998). Extensive further theoretical and empirical work have been carried out since that time and this paper is an attempt to summarise the last 20 years of cognitive load theory and to sketch directions for future research