Recently, Lima lamented on the 'time-consuming and tiresome' pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pencil-and-paper solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula.…

The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design their own schemes of learning, curating their resources from a range of (often free) online sources. Both approaches seem problematic from the…

In this article, the author argues first, that critical-thinking skills do exist independent of disciplinary thinking skills and are not compromised by interaction effects with the major; and second, that standardized tests (e.g., the Collegiate Learning Assessment, or CLA, which is his example throughout the article) are the best way to measure…

Flexible knowledge, knowing multiple approaches for solving problems, is a hallmark of expertise in mathematics. Frequently, the author writes, students memorize only one method of solving a certain kind of problem, without understanding what they are doing, why a given strategy works, and whether there are alternative solution methods. Comparison…

Times of threshold change, such as the transformation from the industrial era to the knowledge economy of today, produce pressures to redesign the institutions people live with to respond to, or better, shape this change. In America's knowledge economy, there is broad agreement that the only way to preserve the nation's economic edge will be…

Often after students solve a problem they believe they have accomplished their mission and stop further exploration. The purpose of this article is to discuss ways to encourage students to "look back" so as to maximise their learning opportunities. According to Polya, by "looking back" at a completed solution, by reconsidering and re-examining the…

Assumes that the educational enterprise is practical rather than theoretical, and challenges the potential usefulness of the science of psychology for educational practitioners. Examines the validity and generativity of Eriksonian, Skinnerian, and Piagetian theory in this context. (CM)

This fourth in a series of edited transcripts based on a conference at Utah State University compares Gagne's Conditions of Learning with Merrill's Component Display/Design Theory, and suggests a merging of the two. Topics discussed include content structures, learning hierarchies, learning theories, learner control, problem solving, cognitive…

Explores the similarities and differences among three thinking skills programs that help students analyze and evaluate their own problem-solving skills. (MLF)

Based on the author's experiences, this article presents approaches to aid in developing interactive presentations. Galaxy and funnel methods offer more room for creativity when compared to metaphors such as step, line, and road models. Highlights include diagrams, personal narratives of advantages, disadvantages, and steps taken in creating an…

Summarizes the similarities between classification systems for catalog selection and information retrieval systems, and discusses system characteristics that allow the use of measures such as recall and precision in system evaluation. (27 references) (Author/CLB)

The pedagogical strategies of human tutors in problem solving domains are described and the possibility of incorporating these techniques into computerized tutors is examined. GIL (Graphical Instruction in LISP), an intelligent tutoring system for LISP programming, is compared to human tutors teaching the same material in order to identify how the…

Explains a generative theory of textbook design and describes three experiments that compared college students' solutions on transfer problems after reading science texts with illustrations adjacent to corresponding text and including annotations, and illustrations separated from text without annotations. (LRW)

Discusses cognitive processes associated with mental rotation and procedures for presenting and learning orthographic projection. Descriptions include a series of three experiments generated by cognitive load theory that investigated the effects of worked example formats on high school students using two- and three-dimensional representations. (19…

Compares seven positions on media influences on learning that were presented in a previous journal issue; discusses the conflict between advocates of a given approach versus integrated approaches to the solving of complex problems; and presents a model that links cognitive processes to computer-based prescriptions for improvements in learning. (35…