This book provides practical guidance for parents, teachers, and other early years workers who want to give children a good start in mathematical development. Showing how competent children are as mathematicians from an early age, the book offers an overview of young children's mathematical behaviour at home and in early years settings. This book…

This paper presents some preliminary results of the longitudinal aspect of a research project on self-confidence and understanding in mathematics. We have collected a survey data of 3057 fifth-graders and seventh-graders and a follow-up data of ten classes (191 pupils) one and a half years later. The longitudinal data indicates that the learning…

Spontaneity has been linked to high quality learning experiences in mathematics (Csikszentmihalyi & Csikszentmihalyi, 1992; Williams, 2002).This paper shows how spontaneity can be identified by attending to the nature of social elements in the process of abstracting (Dreyfus, Hershkowitz, & Schwarz, 2001). This process is elaborated…

"The Expert Mathematician" is designed to help middle school students develop the thinking processes for mathematical applications and communication. A three-year program of instruction, "The Expert Mathematician" uses a software and consumable print materials package with 196 lessons that teach the "Logo" programming…

This study explores difficulties that prospective elementary mathematics teachers have with the concepts of ratio and proportion, mainly when they are engaged in solving problems using algorithm procedures. These difficulties can be traced back to earlier experiences when they were students of junior and high school. The reflection on these…

Nathan entered third grade having already constructed a Generalized Number Sequence (GNS) for whole numbers that enabled him to coordinate sequences of multiples to find a common multiple of two whole numbers. Nathan was able to apply the operations of his GNS to his understanding of part-whole relations and his emerging use of fractional…

In this paper we report an analysis of a teaching sequence in which Grade 11 students were asked to produce some graphs corresponding to the relationship between time and distance of a cylinder moving up and down an inclined plane. The students were also asked to carry out the experience using a TI 83+ graphic calculator equipped with a sensor,…

Within an elaborated social-constructivist perspective, I conducted a teaching experiment with two fourth graders to study how a teacher and students can jointly produce the content-specific reversible fraction conception. Ongoing and retrospective analysis of the data revealed the non-trivial process by which students can abstract multiplicative…

Research into children's measurement conceptions is discussed, presenting a review of the literature in the field that includes studies conducted by J. Piaget and his colleagues and training programs that have been designed to support the development of measurement skills. This literature is used as a background to argue that new investigations…

The tension between providing opportunities for mathematical understandings and the need to teach widely-used notations and algorithms is explained in terms of a folk pedagogical conflict. Divergent pedagogical practices are shown to follow from different mental and epistemological assumptions and manifest themselves in equally divergent student…

This phenomenological study took place over a 16-week semester during which 12 elementary school teachers explored mathematical ideas for elementary school students while using computer microworlds. Four themes were manifested in the case study of one teacher: learning on her own, authority and control, mathematics as manipulating, and frustration…

Examples of children's discussions about Escher Kaleidocycles are utilized to show the importance of connecting mathematics to its sources in sense experience, rather than just teaching the conventions which are meaningless to many students. (IS)

Describes the experiences of a secondary mathematics education student as a MATHCOUNTS coach for sixth graders. Explains the program, coaching duties, and how the approach evolved in trying to shift student focus from finding the right answer to finding a logical approach to solving problems. Discusses the experience in terms of the National…

A mathematics teacher shares a family discussion about Pythagorean triples as her child discovers new ideas about generating a triple. This idea can be useful for introducing students to the Pythagorean theorem. Observes that middle school students tend not to share creative insights in spite of supportive families and teachers. Presents…

Discusses a framework for assessing middle school students' thinking in conditional probability and independence. Establishes four levels of thinking from subjective to numerical reasoning for both constructs. Students (n=15) from grades 4-8 were interviewed. Profiles reveal that levels of probabilistic thinking were stable across the two…