Drawing on the work of Gattegno, it is suggested that a powerful way of teaching mathematics is to introduce symbols as relationships between visible or tangible resources. The symbols are abstract (formal) from the beginning and yet there are concrete resources to support their use. Drawing on data from a research project in primary schools in…

This communication supports an argument that preservice elementary teachers ought to study number language as part of their mathematics content courses, just as they study relationships between numeration and quantity. In particular, the paper spells out some ways in which number language can be seen as problematic by carefully detailing various…

Describes theoretical points concerning the idea of semiotic means of objectification. Analyzes classroom activity by observing the interface between the spoken and the seen. Discusses the role of a category of linguistic terms related to actions of showing or pointing out something that constitute a key element in the mathematical discursive…

Discusses the life of David Hawkins, one of the most influential educators involved in school reform in the 1960s. Focuses on the aesthetic as the center of Hawkins' vision of schooling. Compares Hawkins' perspective to Dewey's in terms of the aesthetic. (KHR)

Focuses on the legacy of paradigmatics instruction in the Greek mathematics classroom, suggesting that it is based on false understanding of pragmatic logic as simply the translation of ideas into action. Offers discursive analysis of two short interactional sequences between the teacher and children in a 6th grade classroom in a primary school in…

Focuses on elementary school teachers' perceptions of creativity and logic and their places within mathematics education. Explores themes arising from the ways in which creativity and logic were talked about, addressing the extent to which the teachers believed that mathematics was creative or logical and whether these two characteristics were…

Discusses a class on subtraction or difference-finding, problems such as "There are eight white flowers and five red flowers, how many more white flowers are there than red flowers?" used in the teaching of Japanese first grade children. Describes three instances of introductory teaching of "difference-finding" problems in the first grade.…

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)

Discusses the role of play in the learning of mathematics. Describes a play for the third grade mathematics classroom that focuses on negative numbers and number concepts, and revisits Vygotsky from this point of view. Concludes that mathematically imaginative play can contribute greatly to mathematics learning in elementary school. (Contains 20…

Reflects on four years of teaching a course called Principle of Major Teachers for pre-service elementary school teachers. Identifies and describes the discord between their formal mathematical knowledge and their informal language used in the context of elementary number theory. Presents encouraging results from a code-switching experiment.…

Outlines the approach of a study that aimed to observe young children as they constructed meanings for randomness in computer-based setting. Provides a snapshot of two children working with the tools made available in that setting. Uses this picture to begin the formulation of a theoretical framework for the construction of meaning in one…

Presents and criticizes current theories of multiplication in order to pave the way for an alternative foundation for the concept of multiplication. Formulates a uniform concept of multiplication that recognizes anew the importance of the roles of multiplier and multiplicand. (Contains 22 references.) (ASK)

Argues that any mathematical construct can acquire multiple referential meanings beyond its specific mathematical meaning as it is assigned several different mappings when applied to different real-world situations. Claims that the teaching of mathematics in schools is a vehicle for an ideology concerning mathematical activity and its outcomes.…

Argues that inventions are of the utmost importance in knowledge development, and that conventions play an important role in inventions by providing support for their development. This position borrows from Piaget's perspective regarding figurative and operative aspects of thought. Contains 22 references. (DDR)

Proposes three thought experiments on various contexts of teaching mathematics. The experiments are intended to raise questions about the mathematics curriculum and to engage discussion about what topics should have high priority in arithmetic teaching. (DDR)