Investigation is a systematic approach to the world of observable facts. It requires the problem solvers to be able to organize and direct a plan of attack. It is a goal of all problem solving to train the powers of observation. Solving problems by borrowing the solution from the problem is adaptation. Feedback is a systematic repetition of the adaptation process in situations where the problem and solution are in a continually changing relationship.
Models reduce risk, cost and complexity to manageable scales.
It is the purpose of science to describe the world in an orderly scheme or language that will enable us to look ahead. Prediction is a search for laws on which to base a forecast. The universal human need to tell stories, to explain what has happened and what structures the universe and the individual's experience, is the foundation of theory making. For students who view math as a school survival skill, who have trouble seeing their way into mathematics and understanding its relevance in their lives, the goal of Challenge is to show math in a new light and to help students understand how to solve complex problems. Each of the titles shows men and women using mathematics as a tool to make their tasks easier.