Traditional Views of Mathematics

Most adults will acknowledge that mathematics is an important subject, but few understand what the discipline is about. For many, mathematics is a collection of rules to be mastered, arithmetic computations, mysterious algebraic equations, and geometric proofs. This perception is in stark contrast to a view of mathematics that involves making sense of mathematical objects such as data, form, change, or patterns. A substantial number of adults are almost proud to proclaim, "I was never any good at mathematics." How has this debilitating perspective of mathematics as a collection of arcane procedures and rules become so prevalent in our society? The best answer can be found in the traditional approaches to teaching mathematics. Traditional teaching, still the predominant instructional pattern, typically begins with an explanation of whatever idea is on the current page of the text followed by showing children how to do the assigned exercises. Even with a hands-on activity, the traditional teacher is guiding students, telling them exactly how to use the materials in a prescribed manner. The focus of the lesson is primarily on getting answers. Students rely on the teacher to determine if their answers are correct. Children emerge from these experiences with a view that mathematics is a series of arbitrary rules, handed down by the teacher, who in turn got them from some very smart source.