The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…

Within the commognitive perspective, ritual and explorative routines are used in a very particular way to distinguish students' routines according to whether they are driven by social reward or by generating a substantiated narrative. Explorative routines in this theorisation may refer not to inquiry-based activity but to the result of a student's…

The metaphors that students form and encounter have been shown to exert a powerful influence on how they think about mathematics. In this paper, we explore the linguistic metaphors about learning and doing mathematics that were prevalent in 11 advanced mathematics lectures. We present four metaphor clusters that were common in the corpus that we…

The processes and products involved in discovery learning are analyzed, some of the relationships among the terms involved are established, and a framework for the identification of these terms is set up. (DT)

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)

This paper provides a log and discussion of experiments conducted by a five-and-one-half-year-old child under the direction of the author. (SD)

Outlines a guided discovery activity for ascertaining the conditions which allow for the correct tracing of networks. (JP)

A formula comparable to Pick's formula for area of a polygonal region on a geoboard is presented for the situation in which the standard unit is an equilateral triangle instead of a square. (JP)

In this article, the author examines the character of the conversations generated in an elementary teacher group as they worked on mathematical problems together and analyzed their students' work. Two distinct forms of talk--"exploratory" and "expository"--were found. The first type of talk occurred most prominently when discussions centered on…

This report describes several student investigations in an undergraduate mathematics degree course. (MP)

This empirical investigation, implemented with a computer program, examined the influence of graphical and numerical representations on the discovery process involving iteration sequence properties and concomitant problem-solving abilities for 79 eleventh grade students and 22 secondary mathematics teachers. Results indicate that heuristics and…

Described is the attempt to identify relationships between pedagogy and student behavior in a mathematical microworld. The patterns of teaching associated with LOGO-based computer activities involving ratio and proportion and the teachers role in helping students bridge the gap between LOGO- and school-mathematics practices are explored. (MDH)

Used 2 12-year-old children to investigate deductive and inductive reasoning in plane geometry. A LOGO microworld was programmed to measure distances and turns relative to points on the plane. Learning environments like this may enhance formation of inductive geometrical understandings. (Contains 44 references.) (LDR)

Teacher's abilities to remain sufficiently faithful to predefined learning scenarios are examined via case studies. The behavior of 2 teachers during problem-solving sessions in geometry with 13-14 year olds exhibited 2 types of factors that tend to hamper scenario reproducibility: constraints on the teacher resulting from the teaching situation;…