In the spirit of the networking of didactical theories, it is advocated in this presentation in favor of a mixed networking of philosophical theories, namely Husserlian phenomenology and hermeneutics, and didactical theories to produce a fertile interplay between philosophy and mathematics education. The cross-analysis of students' work on a…

Mathematical argumentation skills (MAS) are considered an important outcome of mathematics learning, particularly in secondary and tertiary education. As MAS are complex, an effective way of supporting their acquisition may require combining different scaffolds. However, how to combine different scaffolds is a delicate issue, as providing learners…

Metacognition can be described as an internal conversation that seeks to answer the questions, "how much do I really know about what I am learning" and, "how am I monitoring what I am learning?" Metacognitive regulation skills are critical to meaningful learning because they facilitate the abilities to recognize the times when…

This report analyzes the discursive interactions of four students to understand what heuristic methods they develop as well as how and why they build isomorphisms to resolve a combinatorial problem set in a non-Euclidian context. The findings suggest that results of their heuristic actions lead them to build isomorphisms that in turn allow them to…

Input from constructivist scholars and science teachers helps develop future biologists and biology teachers who better understand scientific investigation through their development and use of investigative software, as well as through laboratory and field activities. (SM)

This study examined the use of heuristic problem-solving strategies in math by seventh-graders under three different conditions: working individually; working in groups; and working as cooperative teams. No significant differences were found for the three conditions over a 5-week experimental period on a problem solving post-text (the Maryland…

Discusses research involving instruction to help students develop their mental managerial processes or metacognition, the role of a framework for problem-solving activities, the teacher as model or moderator, problem solving involving groups or pairs, and weaving writing into problem solving. (Contains 18 references.) (MKR)

Examined cognitive processing and performance of 12 average seventh-grade students during cooperative problem solving. Factors that impeded performance included lack of an experiential framework, imposition of unrequired restrictions, lack of individual monitoring of cognitive activity, and unproductive beliefs. Factors that enhanced performance…

Provided is a teacher's guide for a problem-solving activity that establishes a link between number patterns and geometry by focusing on the development of recurrence relations established when generating central polygonal numbers. Reproducible worksheets and a 3.0 BASIC program for the activity are given. (MDH)

Discusses Vee mapping, a technique to assist students in categorizing the relationship between the conceptual and procedural aspects of science. Presents a study to investigate elementary education majors' (n=27) use of the Vee heuristic and concept mapping for the construction of knowledge; attitudes toward learning science in collaborative…

During a six-week methods course for preservice elementary school teachers, student pairs were asked to solve a problem and record their experiences in a dairy. Presented are the dairy entries of two students as they worked on determining the number of squares that can be formed on a five-peg geoboard. (MDH)