September 10, 2010
When More Math Is Less
I expect at least three quarters of the remedial mathematics students that I will teach this fall to flunk. This remedial class at a New York City community college exists because of the abysmal mathematics education in the United States and the liberal philosophy that each person deserves multiple chances to succeed regardless of the financial cost. Now in college, these students in remedial classes have another chance to learn what they should have learned in grades K-12.
Many of the students have taken this college class once or twice already. At least half of the class consists of recent graduates of New York City high schools. The remainder is composed of people who either are more than five years out of high school or who were born and schooled in other countries. About 3,000 of the 8,000 entering freshman at my community college in the City University of New York (CUNY) are in remediation.
These freshmen must have forgotten whatever division, fractions, decimals, and percents they learned in elementary school. Another opportunity to learn basic arithmetic was squandered in the New York high schools because there, algebra and geometry are taught in a manner for which the students do not need to be fluent in arithmetic. Algebra should not be taught until arithmetic is mastered because algebra includes arithmetic. In high school, instead of learning to do arithmetic, pupils are encouraged to use calculators (which are provided at no cost, so that poverty will not prevent a good student from passing). Unfortunately, dependence on calculators eliminates the need to understand arithmetic.
Only three of my 25 students are paying for their classes themselves. In fact, some students are paid to attend classes. About two years ago, the city lost more than eight million dollars paid to students who never came to classes. If students were to invest some of their own resources in their education, they may be forced to become more serious and disciplined.
At least CUNY has tried to raise academic standards. Five years ago, CUNY Chancellor Matthew Goldstein required the students of the New York City community colleges to pass the privately administered computerized mathematics examinations known as the Compass tests. Unfortunately, although the required minimum score of 30 on the Compass reflects somewhat increased mathematical standards, it falls woefully short of ideal. It had been hoped that the passing score on the Compass eventually would be raised to 35, but given the difficulty of helping students achieve a 30, this plan has been postponed. Brooklyn College, a four-year CUNY college, requires a Compass score of 55 for its graduates. Higher Compass scores increase the likelihood of securing of jobs because employers know that such scores imply a higher level of competence.
Since the New York State community colleges -- as opposed to New York City community colleges -- do not require the Compass or other independent examinations, teachers can curve grades to their liking. If the applicants to the city community colleges learned that it was easier to graduate from the state community colleges, would they apply in the state schools instead?
Clearly, mathematics education today is in a sorry state. Mathematics education professionals have failed. These professionals may be partially excused because learning and teaching are complex matters. The best teachers have always intuited the optimal approaches.
However, another major impediment to improving mathematical education is teachers' "compassionate" micromanagement. Mathematics is a brutal, unforgiving, impersonal, and unusually individualistic activity, yet mathematics educators are compelled by their philosophy to promote a warm, nurturing classroom environment full of group discussions. Educators are trapped in a paradox of their own making.
Every mathematics student reaches a stage in which he or she finds the mathematics difficult because he or she does not immediately fully understand all of the rules or structures involved. As in life, failure produces anxiety, which impedes concentration and lowers self-esteem. Our mathematics students must be taught how to experiment and accept failure as part of the process of learning mathematics. The disappointment resulting from the student's inability to solve immediately a problem is contrary to the politically correct educator's social contract to do no harm. However, students must be allowed to feel some stress in their mathematics classes in order to prevent a more deleterious outcome later.
The acquisition of mathematical knowledge, as opposed to other types of knowledge, requires an unusually individualized learning style. This type of learning is de-emphasized by a group-think attitude. The true learning of mathematics requires an avalanche of internal questions to be answered and choices to be made -- far too many for a teacher to supervise completely. One complete statement can be made, though: when it comes to mathematics education in New York City, things don't quite add up.
Peter Landesman (firstname.lastname@example.org) is a teacher, a mathematician, and an author of the 3D-maze book Spacemazes, with which children can have fun while learning mathematics.