The use of manipulatives is an essential key to teaching mathematics to young children. Throughout history, different types of manipulatives have been used to aid in comprehension of mathematical concepts including quipu, abaci and pattern blocks. Today, concrete and virtual manipulatives are the tools that early childhood teachers are using in…

Mathematics in textbooks and indeed in conventional classrooms is often presented as exercises or worksheets in which the mathematics itself has been processed into a form that is easily digested. This McDonald's version of mathematics ensures that the mathematical skill or technique is laid bare and typically the sole focus of attention. In this…

This proceedings includes the following papers: (1) "Structure of Attention in Teaching Mathematics" (John Mason); (2) "Communicating Mathematics or Mathematics Storytelling" (Kathy Heinrich); (3) "Assessing Mathematical Thinking" (Florence Glanfield and Pat Rogers); (4) "From Theory to Observational Data (and…

This book presents nine studies conducted by teacher researchers who explore the oral and written discourse of learning communities--communities of students, communities of teachers, and communities in which students and teachers learn together. The studies focus on journal writing, conversation, story telling, geometry, computer technology, and…