Traditional mathematics is often perceived as teaching a single path that leads to a single correct answer. This approach is de-emphasized in the new, higher standards.
The NCTM recommends "decreased attention" for "finding exact forms of answers".
"Although written tests structured around a single correct answer can be reliable measures of performance, they offer little evidence of the kinds of thinking and understanding advocated in the Curriculum Standards."
"Students might like mathematics but not display the kinds of attitudes and thoughts identified by this standard. For example, students might like mathematics yet believe that problem solving is always finding one correct answer using the right way. These beliefs, in turn, influence their actions when they are faced with solving a problem. Although such students have a positive attitude toward mathematics, they are not exhibiting essential aspects of what we have termed mathematical disposition."
The "decreased attention" statement above is one of many reasons for a bitter conflict between the self-described "traditionalists" and the reformers. The reformers point out that they do not oppose correct answers but would prefer to focus students' attention on the process leading to the answer rather than the answer itself. In a formal evaluation, it is difficult to credit the work of a student who approaches a problem informally and exhibits substantially correct analysis while failing to use, for example, proper terminology or exact computations. The PSSM-supported approach would be to encourage the student to develop his or her arguments and to formalize them in appropriate mathematical language. In more traditional instruction, such student's answer would often be simply marked incorrect or insufficient. It is important to note that PSSM offers only guidelines, along with some exemplary practices in supporting materials. However, the practical implementations of the guidelines sometimes fail in achieving the balance. The programs created in response to the reform have been criticized for overreaching in decreasing attention to some topics to the point of failing to teach them. In contrast, although the more traditional textbook series always claim adherence to and compliance with the Standards, in practice, this amounts to lip service. The situation is complicated further by the fact that any textbook that hopes to be sold nationally must comply not only with the national standards, but also with a host of state standards--often contradictory in both content coverage and pedagogical intent.
The emphasis on analysis rather than the answer is common in professional education, e.g. law school, but many question whether such thinking is appropriate for children in kindergarten who must first memorize their basic facts. Legal problems are often presented without a possibility of a single correct answer but rather encouraging multiple, deep analyses of the factors that might contribute to an answer. As a result, finding a single answer generally results in a lower grade on law school exams. Although this parallel is not perfect, many professionals in mathematics and in education continue to argue that this is a valid approach.