Illustrated first is the case in which a wrong procedure (with fractions) leads to a correct result. Trying to justify why it works in this case and looking for similar patterns involved interesting algebraic considerations as well as use of computers. (MNS)

A series of common misconceptions with regard to infinite sets is considered. Several notions of infinite numbers proposed by different mathematicians are compared. It is argued that so-called errors should rather be called alternative conceptions. (MNS)

The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)

The transformation of a solid to its net is based on something quite different from simple perceptual impression. It is a mental operation performed by manipulating mental images. The aim of this study was to observe pre-service and in-service teachers' ability to visualize the transformation of a curved solid to its net and vice versa, and to try…

We report a study of 10-14 year old children's use of additive strategies while solving ratio and proportion tasks. Rasch methodology was used to develop a diagnostic instrument that reveals children's misconceptions. Two versions of this instrument, one with "models" thought to facilitate proportional reasoning and one without were…

Examples of answers college students studying to be elementary teachers gave to sample student errors and questions in mathematics are presented. The bulk of the prospective answers are judged to have serious flaws. The analysis of such "poor" answers is suggested as a useful vehicle in teacher training programs. (MP)

Findings on ratio and on fractions from a research project on strategies and errors in secondary mathematics are discussed, with typical errors described. Pupils seemed to learn rules without understanding. (MNS)

Presents an activity applicable at the beginning of the year to review necessary algebra concepts that are often misunderstood by students. Presents a true/false worksheet made up of examples illustrating common algebra and trigonometry errors made by students. (MDH)

Discusses the use of feedback from students and the analysis of students' error patterns to understand why students develop misconceptions in mathematics. Looks at learning vis-a-vis the abstract nature of mathematics and the students' cognitive development. (MDH)

Reports a case study exploring how 2 16-year olds were enabled to capitalize on the potential of errors to stimulate and support mathematical inquiry. Discusses variations within the strategy of using errors to enhance mathematics instruction. Appendix includes list of instructional episodes and error activities. (Contains 56 references.) (MKR)

We present a methodology for designing better learning environments. In Phase 1, 6th-grade students' (n = 223) prior knowledge was assessed using a difficulty factors assessment (DFA). The assessment revealed that scaffolds designed to elicit contextual, conceptual, or procedural knowledge each improved students' ability to add and subtract…

Using Kazemi's and Stipek's (2001) framework of classroom practice, the discourse between students enrolled in a mathematics-for-teachers course and their instructor is examined. The teacher's practice is in transition from a focus on having students share multiple strategies toward a practice that additionally includes the mathematical…

The 12th iteration of the International Conference on Educational Data Mining (EDM 2019) is organized under the auspices of the International Educational Data Mining Society in Montreal, Canada. The theme of this year's conference is EDM in Open-Ended Domains. As EDM has matured it has increasingly been applied to open-ended and ill-defined tasks…

The Enright Arithmetic Program is a diagnostic-prescriptive program designed to facilitate an effective remedial effort. The program is based on establishing for each student the set of skills that student needs to learn and also identifies the error pattern causing the student's current failure. Practice materials for each needed skill are…

Recall of multiplication number facts is a major educational objective in elementary grades, yet some children never acquire total mastery. A microcomputer multiplication number facts training program was developed which incorporated programmed instructional features including feedback, positive reinforcement, vanishing, branching and pairing.…