Provides a categorization of the processes and products of science and discusses the need for science educators to provide quantitative and symbolic understandings of science using the mathematical ideas of symbols, proportions and scaling, and axiomatic methods of inductive and deductive proof. (MKR)

Argues that intuitive and computational knowledge can be combined by focusing more explicitly on referential and quantitative meanings in division of fractions problems. Recommends teaching mathematics as problem solving, communication, reasoning, and connections to help students overcome misunderstandings and connect their intuitive knowledge…

Describes a general education course addressing the linguistic and logical aspects of the language of mathematics which is intended to develop students' abilities to read mathematics, express mathematical thoughts clearly, reason logically, and grasp the nature of proof. Students improved their algebraic procedural skills and attitudes toward…