Examines the development of students' understandings about fractions during six weeks of instruction. Reports that all students possessed informal knowledge disconnected from their knowledge of fraction symbols and procedures and that knowledge of rote procedures often interfered with students' attempts to build on their informal knowledge.…

Examined is the situation in which pupils invent mathematics on their own and teachers' reactions to this situation. The assimilation of students' original ideas into correct mathematical concepts is discussed. (CW)

Discusses ways teachers can encourage students to construct useful meanings for the fractional unit. Provides three examples of representations of common fractions and illustrates misconceptions in fraction problems. Includes a brief summary of constructivist mathematics education and an example in which a teacher misunderstands a fractional unit.…

This guide focuses on the Square One TV game shows, which explore areas ranging from probability and statistics to geometry. Eight game shows are described including the game rules, materials, directions, strategies for playing the games, actual game questions, and reproducible student pages. Follow-up activities provide ideas for using the games…