Includes bibliographical references (p. 107-115) and index.
Contents
1. Overview -- Research focus -- Connections to history of mathematics and notational systems -- Connections to history of mathematics and notational systems -- A definition for notations -- Organization of the book -- 2. George: written numbers and the written number system -- George's fine-motor skills and understanding of the number system -- George's use of dummy numbers -- The role of relative position in George's ideas about written numbers -- Reflections -- 3. Paula : "capital numbers" -- Making sense of conventions -- Capital numbers : Paula's invented tool -- Inventions -- Conventions -- Reflections -- 4. Thomas : commas and periods in numbers -- Thomas's developing understanding of periods and commas in numbers -- Reflections -- 5. Sara : notations for fractions that help her "think of something" -- With Analucia Schliemann and David Carraher -- Solving algebraic problems during class -- Solving algebraic problems during an interview -- Reflections -- 6. Jennifer and her peers : data tables and additive relations / Susanna Lara-Roth -- Second grade : looking at children's self-designed tables -- Jennifer in third grade -- Reflections -- 7. Jennifer, Nathan, and Jeffrey : relationships among different mathematical notations -- Details of the study -- The problem presented to the children -- The children's reactions to the problem -- The children's notations -- The children's interpretations of Jennifer's graph -- Reflections -- Final reflections.
