Connections to history of mathematics and notational systems
Connections to history of mathematics and notational systems
A definition for notations
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
3. Paula: "capital numbers"
Making sense of conventions
Capital numbers: Paula's invented tool
4. Thomas: commas and periods in numbers
Thomas's developing understanding of periods and commas in numbers
5. Sara: notations for fractions that help her "think of something"
With Analúcia Schliemann and David Carraher
Solving algebraic problems during class
Solving algebraic problems during an interview
6. Jennifer and her peers: data tables and additive relations / Susanna Lara-Roth
Second grade: looking at children's self-designed tables
7. Jennifer, Nathan, and Jeffrey: relationships among different mathematical notations
The problem presented to the children
The children's reactions to the problem
The children's interpretations of Jennifer's graph
