Since 1980, increasing numbers of students are repeating their high school mathematics courses as undergraduates and enrollment in the developmental courses has continued to grow. In Fall 2000, more than three million students were enrolled in undergraduate mathematics courses taught in departments of mathematics. Thirty-one percent of these students (981,000) were enrolled in remedial mathematics courses (arithmetic, algebra I, algebra II). Of these students, 763,000 were at two-year colleges (57% of the total two-year math enrollment) [1].

The large number of students who enroll in remedial courses suggests that the traditional emphasis on showing students how to use a rule to get the answer has failed many students. They learned the rules and passed the course(s) but, despite having learned the rules, they don't know when to apply them. They have not made sense of symbolic notation, nor have they learned to think for themselves. For these students, algebra is nothing but rules applied, often incorrectly, to manipulate symbols, which are meaningless marks on paper [2, 3, 4].

Based on their prior mathematical experience, most students expect to be told which formulas to use, and how to get the correct answers. This narrow approach is where many students stop in their understanding of mathematics—this strict utilitarian perspective too often limits their mathematical vision. Students' descriptions of their prior mathematical experiences and their views of mathematics are remarkably similar:

I was used to having a formula and all I cared about was getting the right answer.