Presents a cultural, discursive psychology for mathematics education that takes language and discursive practices as central in that meanings precede us and we are constituted within language and the associated practices, in the multiple settings within which we grow up and participate. (Author/MM)

Presents and investigates a theoretical perspective on the development of understandings of mathematical operations with a particular focus on addition. Presents a case study on the development of a young boy and concludes that his attainment of aspects of operation sense supported transitions into algebraic ways of thinking. Contains 46…

Clarifies how the relationship between macro and micro social contexts has been addressed in the Vygotskian and Neo-Piagetian approaches to learning. Discusses how these insights can be used to broaden the basis for studying interactions in mathematics classrooms and concludes with ideas for new developments in socio-cultural theory. (Contains 92…

Presents a two-phase investigation of how Israeli students understand the concept of periodicity. Discusses related research with teachers and students (N=895) employing both qualitative and quantitative research methodologies. Concludes that students understand periodicity as a process. Students' errors and preferences are discussed with…

Features and tools to outline and shape the long-term learning process for ratio are presented, with examples. Ratio-anticipating activity and creating visual models and schemes are stressed, with the basis for a theory of teaching and learning ratio presented. (MNS)

Proposes a model for the growth of mathematical understanding based on the consideration of understanding as a whole, dynamic, leveled but nonlinear process. Illustrates the model using the concept of fractions. How to map the growth of understanding is explained in detail. (Contains 26 references.) (MKR)

Considers radical constructivism in light of poststructuralism and hermeneutic phenomenology and shows how this forces a reassertion of the teacher's role in the student's constructing of mathematical knowledge. (48 references) (Author/MKR)

Presented is a theory of how competence with written mathematical symbols develops, tracing a succession of cognitive processes that cumulate to yield competence. Arguments supporting the theory are drawn from the history, philosophy, and psychology of mathematics. (MNS)

Some potential difficulties involved in using "real-life situations" in teaching problem solving are illustrated with a racing car problem. The importance of developing mental images and the ability to abstract in the solution process is indicated. (MP)

Described is the Educational Leaders in Mathematics (ELM) Project, a four-stage inservice teacher program designed to stimulate teachers' development of a constructivist view of learning. The impact of the intervention was studied, and results indicated that teachers' beliefs were affected, producing changes in teaching strategies. (MDH)

Proposes that although the past 30 years have seen increasing efforts to make mathematics more relevant and useful, schools continue to fail. Argues that forced rote learning is the direct cause of this failure and that improved teaching methods must be developed. Urges that shifts in methodology be phased in gradually. (TW)