Discussed are the concepts of intuition, the general properties of an intuitive knowledge, and the classification of intuitions as problem solving of affirmative. An example of intuition using multiplication and division is described in some detail. (MNS)

Mathematical games designed for children from kindergarten to grade five using buttons as counters are described. Each game description includes a brief discussion of the number and mathematical concepts it teaches. (JD)

This study presented contextual problems involving rational numbers and proportional reasoning to 7th-grade students with different curricular experiences. Evidence indicates that students in reform curricula, who are encouraged to construct their own conceptual and procedural knowledge of proportionality through collaborative problem-solving…

Investigates 10-year-old children's abilities to reason by analogy in solving addition and subtraction comparison problems involving unknown compare sets and unknown reference sets. Children responded in a consistent manner to the tasks involving the basic addition problems, indicating substantial relational knowledge of these but responded in an…

Presents an alternative pedagogy implicit in Imre Lakatos's "Proofs and Refutations: The Logic of Mathematical Discovery." Lakatos reveals that learning mathematics is a discourse-laden activity in which it is acceptable, if not preferable, to refute conjecture. Provides examples of using a Lakatosian approach in an elementary classroom.…

Discusses students' progress through distinct levels in the development of their thinking as described by van Hiele levels. Focuses on the quadrilaterals and suggests some level 3 tasks and construction problems. (ASK)

This article builds on two previous ones in which we presented the processes of construction and consolidation of one student's knowledge structures about comparisons of infinite sets, according to a recently proposed theory of abstraction. In the present article, we show that under slight variations of context, knowledge structures that have…

Meaningful educational activities and cognitive tools might improve students' active involvements in the teaching-learning process and encourage their reflections on the concepts and relations to be investigated. It is claimed that usage of manipulatives not only increase students' conceptual understanding and problem solving skills but also…

This paper presents the results from a paper-and-pencil instrument designed to elicit students' thinking about the rate of change in particular situations. A scoring rubric was designed to classify students' solution strategies to algebra problems. The purpose of the study was to validate the results in different ways. First, the results from this…

A game of noughts and crosses (tic-tac-toe) is used to motivate some mathematical activities. Several "starter" questions for activities are included. (MK)

Discusses Vygotsky's theories about concept formation, his distinctions between everyday and theoretical concepts, and how empirical generalizations can lead to misconceptions. Examines the implications of these theories for mathematics instruction and its relationship to the current mathematics reform. (34 references) (MDH)

Presents a model for teaching reasoning using technology in the contexts of algebra and geometry. (MKR)

Presents research findings and teaching implications of mathematics as reasoning and students' reasoning abilities in mathematics. (20 references) (MKR)

Describes four projects that support the transition from an abstract to a concrete notion of the effective use of technology in the secondary school classroom: The Interactive Mathematics Program, Systemic Initiative for Montana Mathematics and Science, University of Chicago School Mathematics Project, and Connected Geometry. (MKR)

Describes and analyzes a learning episode in which two children in year 4 interact with each other and their teacher while playing a probability game involving chocolate M&Ms. Children developed key ideas in probability from a game that was designed to produce cognitive conflict. (ASK)