Findings from international assessments present an opportunity to reconsider mathematics education across the grades. If concepts taught in elementary grades lay the foundation for continued study, then children's introduction to school mathematics deserves particular attention. We consider Davydov's theory (1966), which sequences…

To learn means coming to know something new at the end of, or subsequent to, a (learning) process. Because students do not yet know at the beginning of the process what they will know subsequent to the process, they cannot actively orient towards the object of learning. In this article, I propose a phenomenological perspective that theorizes…

This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…

This paper first reports on the methodology of a study of teacher knowledge for statistics, conducted in a classroom at the primary school level. The methodology included videotaping of a sequence of lessons that involved students in investigating multivariate data sets, followed up by audiotaped interviews with each teacher. These stimulated…

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.…

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)

Some pedagogical problems in Chinese numeration are described. They involve the teaching and learning of how to speak numerals with fluency in Chinese, using Hindu-Arabic written numbers. An alternative approach which stresses regularity is proposed. (MNS)

How children perceive doubling and halving numbers is discussed, with many examples. The use of calculators is integrated. The tendency to avoid division if other ways of solving a problem can be found was noted. (MNS)

A model for learning mathematics is proposed which involves the components of using, discriminating, generalizing, and synthesizing. The ways pupils use Logo programs as tools within their projects and how the nature of their programming tools become more explicitly understood and generalized are discussed. (RH)

Presented is a general overview of mathematics anxiety, its definition, and techniques to measure it. Included are a brief discussion of gender-related issues and an analysis of research on effects of mathematics anxiety on elementary teachers. Contained are some intervention strategies and treatments, conclusions and implications for further…

The constructivist perspective, which holds that children's learning of subject matter is an interaction between what they are taught and what they bring to a learning situation, could be used to improve mathematics teacher education. (PK)

Four important schools of thought which have addressed the problem of meaning in arithmetic are examined: connectionist, structural, operational, and constructivist. The author argues that the constructivist perspective is a potentially fruitful framework within which to recase the issues involved in the analysis of meaning in arithmetic. (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)

Trends in computer programing language design are described and children's difficulties in learning to write programs for mathematics problems are considered. Languages are compared under the headings of imperative programing, functional programing, logic programing, and pictures. (DC)

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)