The objectives of elementary school mathematics fall under one of two headings—knowing or knowing how. “Knowing” refers to that core of facts, concepts, and processes believed essential for all students to master (e.g., the addition facts, the concept of addition, the addition algorithm). “Knowing how” refers to those problemsolving skills by which the facts, concepts, and processes are put to use (e.g., solving verbal problems in addition, solving addition problems in daily living, proving theorems associated with addition). The teaching of these skills is the ultimate aim of elementary school mathematics, since what we know cannot be applied in daily life unless we know how to use it.