How do students cope with and make sense of polysemy in mathematics? Zazkis (1998) tackled these questions in the case of 'divisor' and 'quotient'. When requested to determine the quotient in the division of 12 by 5, some of her pre-service teachers operated in the domain of integers and argued for 2, while others adhered to rational numbers and…

This is the second of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. In Part I, I discussed the formation of arithmetical units and composite…

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

Presents a number of transcript examples of correct and incorrect transferences by children. Considers the objects of transference including spoken words, written symbols, models and diagrams, arithmetic procedures, and structures. Discusses the use of transference in arithmetic education. (YP)

Describes four mathematics teachers' classroom discussions with small groups in their first year secondary (11-12 years old) classrooms. Analyzes interview results from one student in each group. Topic of the classroom was division of fractions. (YP)