It is commonly argued that teachers need ongoing engagement with ideas about using student reasoning, pedagogy, and subject matter if they are to make sense of the complex demands of current reforms in mathematics education. Drawing on similar arguments about the potential benefits of using student work to organize professional development, this…

Reports case studies using personal construct psychology and the logic of fuzzy sets to elucidate the content and organization of two elementary school teachers' knowledge of fractions and mathematical pedagogy. Results identified four personal constructions that affected classroom events; knowledge of fractions, general pedagogical knowledge,…

Describes a research and development project, Cognitively Guided Instruction, to illustrate how theory and research inform the teaching and learning of mathematics. The project engaged first grade teachers with research-based knowledge about the development of children's mathematical thinking, studying teachers' use of this knowledge in the…

Describes a study that explores the perceptions that children (N=36) have about what it means to engage in mathematics. The study, which took place in reform-minded classrooms, concludes that children have a variety of perceptions and most do not feel that success is determined by speed and accuracy. Contains 20 references. (DDR)

This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…

Investigated changes over four years for three elementary teachers participating in Cognitively Guided Instruction (CGI), which emphasized students' mathematical thinking and supported teachers through workshops, mentoring, and collaboration. Interviews and observations indicated that CGI allowed teachers to engage in ongoing practical inquiry…

This paper describes a research-based teacher professional development program for elementary school mathematics and includes an overview of cognitively guided instruction (CGI). Also described are the CGI professional development program and the research base for CGI with regard to children's thinking; teachers' knowledge and beliefs about…

This book, with accompanying CD-ROMs, was written to help readers understand children's intuitive mathematical thinking and use that knowledge to help children learn mathematics with understanding. Based on more than twenty years of research, this book portrays the development of children's understanding of basic number concepts. Detailed…