Discusses formalizing in mathematics and provides anecdotal illustrations of formalizing in a constructivist environment, using students aged 12 and 8 involved in fraction work. (Contains 19 references.) (MKR)

The methodological issue of qualitative versus quantitative research is addressed, and the argumentation of research using interview methods for research is explored. Warrants of the type that are used in arguments generating conclusions from interview data are included. (KR)

The issue of how a child constructs higher order, logical mathematical intelligence within the context of a multiple-intelligences classroom is explored in this story. Teacher journal observations of one 5th-grade child are woven with selected literature on multiple intelligences and research trends in elementary mathematics education. The story…

Discusses the first session and events from other sessions of a mathematics circle consisting of the author and four preschool children. Presents discussions that ensued with the children when asked to solve problems related to Piaget's stages of cognitive development. (MDH)

Reexamines the traditional role of observation in science and science education. Proposes that since observation is based on some view of the world, it is not innocent and unbiased, but theory-dependent. Discusses possible implications for the science curriculum when reconsidering the role and status of observation in science. (TW)