The production and use of explicit models of mathematics are important elements of research in Didactics of Mathematics. In this paper, we present and compare two different European approaches to didactical modelling. The first, centred around the notion of basic idea (Grundvorstellung), arose in German-speaking countries as a development within…

The researchers in this study investigated the impact of mathematics-focused parental involvement on Kindergarten to Grade 8 children and parents as well as factors prompting that impact. Qualitative analysis consisting of parent, child, and teacher interviews and 3-year quantitative testing showed significant improvements in students' mathematics…

Discusses characteristics in feminist pedagogy literature and situates them with respect to four dialectical aspects (passivity/active participation, omission/inclusion, silence/speech, and powerlessness/empowerment). These characteristics are combined with nondiscriminatory classroom practices to develop a frame of reference for inclusive…

Draws from research studies on the introduction of symbolic systems on computers and calculators and considers 'new' techniques that accompany new technological instruments, their role in conceptualizing, and their links with 'usual' paper/pencil techniques as the key to analyzing the role of technology in education. This view implies non-obvious…

Some aspects of classroom incidents in which the pupil has indicated he does not understand something about the mathematics being covered, and which require immediate decision-making on the part of the teacher, are explored. (DT)

Investigated historical works for pedagogical techniques. Found the use of instructional discourse, logical sequencing of mathematical problems and exercises, and employment of visual aids. Concludes that much of present day mathematical pedagogy evolved from distant historical antecedents. (30 references) (Author/MKR)

Problem solving is presented as a resource for creating curriculum through reflections on intuition such as: exploring available intuitions, making explicit the intuitions used, and using intuition to generalize. (MP)

Methods of handling a student's incorrect mathematical generalization are discussed. (DT)

Explores two mathematics teachers' ways of employing theme-based resources in their lessons. Provides a detailed look at how teachers of diverse pedagogic orientations use thematic contexts in their teaching of mathematics. (Contains 39 references.) (Author/ASK)

The iconographic means of illustrating mathematical facts is discussed along with several examples of graphical solutions to descriptive mathematics problems proposed by pupils. (MN)

We find that students in the big mathematics service courses at the Johns Hopkins University who were encouraged to use calculators in K-12 have somewhat lower grades than those who weren't.

Approaches to developing a good mathematics textbook for the junior high student are discussed, with the pitfalls and difficulties reviewed. Examples from new Polish textbooks are presented to illustrate possible solutions. (MP)

A series of examples is provided of types of mathematical exposition which cause students difficulty for reasons other than lack of understanding of some mental process. (SD)

The author shows some causes of failure in the creation of mathematical concepts. One is the stiffening of concept cores, which prevents identification of atypical exemplars and solution of atypical problems and causes a bifurcation between the natural system of everyday concepts and the formal system of school concepts. (Author/MDH)

The effects of a teaching program in probability devised for students in grades five to seven were analyzed. Most of the notions were too difficult for fifth graders; 60-70 percent of the sixth graders and 80-90 percent of the seventh graders were able to understand and use correctly most of the concepts. (MNS)