To encourage students to do geometry, the art of Islamic geometric ornamentation was chosen as the central theme of a lesson strand which was developed using the newly presented didactical tool called "Learning by Acting". The Dutch students who took these lessons in 2010 to 2013 were challenged to act as if they themselves were Persian…

In this paper I argue my opposition to the consensus which has dominated the literature that young children view shapes as a whole and pay no attention to shape structure and that geometrical thinking can be described through a hierarchical model formed by levels. This consensus is linked to van Hiele's weok by van Hiele-based research. In the…

This paper introduces the notion of "crystalline concept" as a focal idea in long-term mathematical thinking, bringing together the geometric development of Van Hiele, process-object encapsulation, and formal axiomatic systems. Each of these is a strand in the framework of "three worlds of mathematics" with its own special characteristics, but all…

Describes episodes from work with a small group of 8th grade students who were working independently on a geometry course. Uses Geometer's Sketchpad for the tasks. Discusses students' reasoning skills and their interpretation of the painting in terms of the mathematical properties and relationships. (KHR)

Discusses some aspects of learning to read the process of the variation in congruence and relate it to the original geometry of the sphere since it touches on more general questions about how models are appropriated and used. Presents a learning episode that implemented projective models for both spherical and hyperbolic geometry in Object Logo.…

Presents a study aimed at exploring (a) developmental pedagogy perspectives in early childhood conceptions of shape in space, and (b) evaluating the teacher's work in terms of what is of benefit to children from being involved in this approach to learning. (MM)

Addresses the concept of mathematical definition as well as the definitions of different mathematics concepts. Focuses on the possibility of defining a mathematical concept in several ways based on logical relationships between different mathematical statements related to the concept. The choice of one of these statements as definitional plays a…

Explores how teachers can support English-language learners in learning mathematics. Uses discourse perspective to analyze participation in mathematical discussions. Examines a lesson from a third-grade mathematics discussion of the geometric shapes of a tangram puzzle. Contains 20 references. (ASK)

Presents an exploratory study with expert university students to determine how students could reseal the rupture and restore a sense of unity between the figural and conceptual components of conic sections. Suggests certain tools of semiotic mediation which could be introduced to enable students to achieve the conceptual oversight that is possibly…

Reflects on some aspects of learning mathematics that emerged along the way in creating a turtle-based exploratory tool for non-Euclidean geometry. Contains 14 references. (ASK)

Described are four hour-long sessions of children working with the definition and use of a procedure for triangles in Logo programming. The conclusion is that turtle geometry is not a trivial activity. (MNS)

How students are convinced that they have the correct solution to a problem, free of contradiction, is discussed. The role of counterexamples and the need for a situational analysis of problem-solving behaviors are each included. (MNS)

The mathematics curriculum should be imbedded into the cultural environment of the student. Discussed is the mathematical educational potential of decorative motif. (PK)

Historical issues concerning the role of mathematics in the school curriculum are considered, with numerous examples illustrating varying emphases. (MNS)

Four methods of filling a square using programing with Logo are presented, with comments on children's solutions. Analysis of the mathematical or programing concepts underlying a few simple algorithms is the focus. (MNS)