This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…

An historical case is presented in which extra-mathematical certainties lead to invalid mathematics reasonings, and this is compared to a similar case that arose in the area of virtual education. A theoretical-methodological instrument is proposed for analysis of certainties. The article suggests the need for teachers to be aware that certainties…

This article reports on a study carried out with a group of 83 Mathematical Literacy teachers who were enrolled for an Advanced Certificate in Education programme at a South African university. The purpose of this study was to explore the Teachers' conceptions of the inflation rate. Data for the study was generated from the Teachers' responses to…

In this study we investigated the effects of two treatments supplementing students' (16 to 18 years of age and in pre-university education) regular course in economics. One treatment, labelled concept treatment, aimed at the solidification of the students' knowledge about economic concepts and their interrelations. The other treatment, labeled…

Describes a study with the main objective of constructing models based on strategies students use to solve chemistry problems and to show that these models form sequences of progressive transitions termed "problemshifts" that increase the explanatory/heuristic power of the model. Results implies that the relationship between algorithmic…

Describes a study in which concept maps drawn by high school students (n=12) were evaluated using quantitative measures. Results indicate that the concept maps are useful in assessing the understanding of relationships between the concepts required for multiple step problem solving in physics. Contains 12 references. (DDR)

Investigates students' mental models of chemical equilibrium using dynamic science assessments. Reports that students at various levels have misconceptions about chemical equilibrium. Involves 10th grade students (n=30) in the study doing a series of hands-on chemical experiments. Focuses on the process of constructing mental models, dynamic…

Discusses potential pedagogical difficulties arising from using physics-related contexts in high-school mathematics problems. Suggests that such problems should not require any external knowledge of physics by the students; meanwhile, the problems should not contradict the physics knowledge that the students may already have. Presents several…

An investigation was conducted to determine the effectiveness of utilizing analogies to effect conceptual change in mathematics. Forty-one high school seniors participated in a knowledge reconstruction process regarding their beliefs about everyday probability situations such as sports events or lotteries. These mathematics students were given…

Gifted secondary students not only solved problems better, faster, and with less assistance than average pupils, but also processed information in a different fashion. (MNS)

An example is discussed in which a drill exercise, initially involving whole number addition, can be used to develop concepts in equations of many variables. (MP)

Describes an investigation that explores students' understanding of the translation, rotation, and deformation of an object. Findings illustrate that students have difficulty appreciating that these different phenomena can occur simultaneously. Discusses some implications for teaching. (DDR)

Presents results of preliminary trials that suggest that the program devised helped UK Year 12 (A-level) learners develop useful concepts of current and voltage, acquire a more integrated understanding of circuit behavior, and overcome their tendencies towards localized and sequential reasoning. Provides learners with a valuable aid for problem…

This problem solving strategy is illustrated by examples from the fields of algebra, trigonometry, geometry, and calculus. (MP)

Analyzes didactic problems related to the inseparability of electric charge from the mass, the impossibility of its direct observation, and the meaning associated with the basic concepts of electricity. Contains 44 references. (DDR)