In this paper we give a general definition of structural reasoning, followed by a typology that instantiates the definition in mathematical practices. Five major categories of structural reasoning, some with subcategories, are offered: (a) pattern generalization, (b) reduction of an unfamiliar structure into a familiar one, (c) recognizing and…

Examines operations of generalization, identification, discrimination, and synthesis in mathematical concept development from early childhood to late adolescence according to Vygotsky's theory of development. (MDH)

Discussed are the issues of inconsistencies and compartmentalization and the use of inconsistencies in the classroom. Included are discussions on paradoxes, the naive student, logical reasoning ability, and the development of the students' cognitive structures. (KR)

Discusses a system of classification for students' inconsistent ideas in mathematics, the sources of students' mathematical inconsistency, and instructional strategies for helping students to resolve apparent learning inconsistencies. Language, curriculum, and instruction are included in the discussion. (KR)

Discusses the use of writing to enhance learning in mathematics from a conceptual development perspective. Shuell's phases of learning are described as a general model for conceptual development and subsequently matched with Britton's categories for transactional-informative writing. Sample mathematics assignments for each writing category are…