Describes the nature of investigations and their uses in mathematics education. The three types of investigation described, whimsical, real, and mathematical, are defined and illustrated. For each type of investigation, mathematical content and problem-solving strategies are identified, and a solution method is presented. (SLD)

Discusses the teaching of "big ideas" in mathematics in an environment that accommodates special learning differences. With multiple approaches that capitalize on the learning differences of students, those with special needs can respond within their specific limitations and succeed at levels previously considered beyond their reach. (SLD)

Introduces the constructivist theory of mathematical learning, and illustrates its application in a curriculum focusing on fundamental concepts. How knowledge is constructed, how concepts mature, and what it means to learn and to know mathematics are presented. Pedagogical implications of adopting a constructivist perspective on knowledge and…