Math Wars - Critics of Reform

Critics of Reform

Those who disagree with the inquiry-based philosophy maintain that students must first develop computational skills before they can understand concepts of mathematics. These skills should be memorized and practiced, using time-tested traditional methods until they become automatic. Time is better spent practicing skills rather than in investigations inventing alternatives, or justifying more than one correct answer or method. In this view, estimating answers is insufficient and, in fact, is considered to be dependent on strong foundational skills. Learning abstract concepts of mathematics is perceived to depend on a solid base of knowledge of the tools of the subject.

Supporters of traditional mathematics teaching oppose excessive dependence on innovations such as calculators or new technology, such as the Logo language. Student innovation is acceptable, even welcome, as long as it is mathematically valid. Calculator use can be appropriate after number sense has developed and basic skills have been mastered. Constructivist methods which are unfamiliar to many adults, and books which lack explanations of methods or solved examples make it difficult to help with homework. Compared to worksheets which can be completed in minutes, constructivist activities can be more time consuming. (Reform educators respond that more time is lost in reteaching poorly understood algorithms.) Emphasis on reading and writing also increases the language load for immigrant students and parents who may be unfamiliar with English.

Critics of reform point out that traditional methods are still universally and exclusively used in industry and academia. Reform educators respond that such methods are still the ultimate goal of reform mathematics, and that students need to learn flexible thinking in order to face problems they may not know a method for. Critics maintain that it is unreasonable to expect students to "discover" the standard methods through investigation, and that flexible thinking can only be developed after mastering foundational skills.

Some curricula incorporate research by Constance Kamii and others that concluded that direct teaching of traditional algorithms is counterproductive to conceptual understanding of math. Critics have protested some of the consequences of this research. Traditional memorization methods are replaced with constructivist activities. Students who demonstrate proficiency in a standard method are asked to invent another method of arriving at the answer. Some teachers supplement such textbooks in order to teach standard methods more quickly. Some curricula do not teach long division. Critics believe the NCTM revised its standards to explicitly call for continuing instruction of standard methods, largely because of the negative response to some of these curricula (see below).