This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

Demonstrated are binary operations on whole numbers which are commutative but not associative, or associative but not cummutative. Also presented are sets of numbers within which the Unique Factorization Theorem does not hold true. (JP)

Describes why a traditional arithmetic curriculum is no longer appropriate. Also presents the rationale behind some of the newer methods of mathematics instruction in the elementary schools. (BD)

Explains methods by which a student can check the correctness of his work and so increase his self-confidence. (MM)

Through a research grant funded by the Vocational Division of the Indiana State Department of Public Instruction, a developmental research project was undertaken to develop machine trades-related mathematics materials using the terminology, concepts, and methods of modern mathematics. The two volume set is designed to be utilized by first and…