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…

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)

Explores the gap between the ideological orthodoxies of mathematics education and the expectations and beliefs of parents. Three strategies are proposed: repetition and attention, narratives and stories, and giving instruction that credits students with their own intelligence. (MKR)

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.…

Teaching sequences designed to develop strategies for comparing numerals in grade two (in France) were analyzed. Children's strategies were noted, and an experiment confirmed underlying misconceptions concerning number. (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)

Presents activities that integrate story telling, history, and problem solving as a stimulus for discussion and creativity in the elementary mathematics classroom, and a way to relieve children's anxiety in an escalating curriculum. (MDH)

Describes a mathematics course for prospective elementary teachers that has teaching and learning mathematics via problem solving at its core. Presents a problem-solving activity involving number theory and reactions by the students and teacher to the activity. (MDH)