This classroom note shows how Fibonacci numbers with negative subscripts emerge from a problem-solving context enhanced by the use of an electronic spreadsheet. It reflects the author's work with prospective K-12 teachers in a number of mathematics content courses. (Contains 4 figures.)

Students often make mistakes in physics courses and are expected to identify, correct, and learn from their mistakes, usually with some assistance from an instructor, textbook, or fellow students. This aid may come in many forms, such as problem solutions that are given to a class, tutoring to an individual student, or a peer discussion among…

Students' attitudes and approaches to problem solving in physics can profoundly influence their motivation to learn and development of expertise. We developed and validated an Attitudes and Approaches to Problem Solving survey by expanding the Attitudes toward Problem Solving survey of Marx and Cummings and administered it to physics graduate…

The long awaited blessings of having a child bring simultaneous bouts of confusion and uncertainty regarding the vast parenting responsibilities that come with raising that child. When the child has a disability, sometimes the tasks can seem especially daunting. In this article, the authors aim to guide parents of children who display challenging…

Self-assessments can play a powerful role in developing a child's motivation and achievement. Self-assessments require students to think carefully about what they have learned and how they learn and to develop critical-thinking and problem-solving skills. Students who engage in the productive practice of self-assessment, inevitably strengthen…

We investigated the neural basis of repetition priming (RP) during mathematical cognition. Previous studies of RP have focused on repetition suppression as the basis of behavioral facilitation, primarily using word and object identification and classification tasks. More recently, researchers have suggested associative stimulus-response learning…

The purpose of this study was to investigate the anger and anger expression styles with respect to coping with stress and interpersonal problem-solving. The participants were 468 (258 female and 210 male, between 17-30 years old) university students. Pearson product-moment correlation coefficients and multiple hierarchical regression analysis were…

Project-Based Learning (PBL) is an innovative approach to learning that teaches a multitude of strategies critical for success in the twenty-first century. Students drive their own learning through inquiry, as well as work collaboratively to research and create projects that reflect their knowledge. From gleaning new, viable technology skills, to…

Background: There is a need for validated, standardised tools for the assessment of executive functions in adults with intellectual disabilities (ID). This study examines the validity of a test of planning and problem solving (Tower of London) with adults with ID. Method: Participants completed an adapted version of the Tower of London (ToL) while…

As a teacher of technical writing, the author applauds the emphasis on the strategies of research and on documented, problem-solving writing across the curriculum and on bringing writing-for-the-workplace into the first-year writing classroom. However, as a teacher of literature, he rejects the notion that responding to literature has no practical…

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

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…

Solving ill-structured problems is regarded as an important learning outcome in education as it allows learners to apply theories learnt into real practice. An asynchronous online discussion, with extended time for reflection, is an appropriate learning environment to engage learners in solving ill-structured problems. However, scaffolds may be…

We present a quantitative model for predicting the level of difficulty subjects will experience with specific problems. The model explicitly accounts for the number of subproblems a problem can be broken into and the difficultly of each subproblem. Although the model builds on previously published models, it is uniquely suited for blending with…

The issue of the area of irregular shapes is absent from the modern mathematical textbooks in elementary education in Greece. However, there exists a collection of books written for educational purposes by famous Greek scholars dating from the eighteenth century, which propose certain techniques concerning the estimation of the area of such…