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New York City
December 2002

Math in The City: A View from the College Classroom
By Stanley Ocken & Robert Feinerman

Kim Brown’s recent article, “Math Adds up at CCNY Teacher Training Program,” [Education Update, Nov. 2002] paints a warm picture of Prof. C. T. Fosnot’s Mathematics in the City teacher training program. We are writing as professors of mathematics, engaged in both teaching and research at the City University of New York. We are profoundly disturbed by the philosophy of mathematics education proffered in that article, by the weak content of many curricula that have been implemented on the basis of that philosophy, and by the effect of both on students who will be entering college mathematics classrooms in the next decade.

The curricula we refer to, developed during the last decade and now being implemented nationally, are those based on the vision of the 1989 NCTM Standards. That vision (later revised in the Year 2000 update) called for a de-emphasis of the formal algorithmic and algebraic component of the curriculum, a call that was heeded in the most extreme way by curriculum developers and graduate schools of education. Concerning such curricula, the draft report of the Commission on Mathematics Education, convened by former New York City Schools Chancellor Harold Levy, asserts: “despite their many strengths, the NCTM standards do not contain the rigor, algorithmic approach, formal methods, and logical reasoning which are required” of students who will go on to become scientists, engineers, mathematicians, computer scientists, physicians, and educators of mathematics.”

We fully concur. Judging by their product, the developers of NCTM standards-based curricula were motivated by sentiments expressed in Ms. Brown’s article, each of which is italicized below and followed by our reactions.

[Teachers] are submerged in a mathematics environment where math is not a foreign language…

Mathematics used in college courses is formulated in a difficult symbolic language. To succeed in those courses, students need twelve years of carefully structured instruction in order to learn the language fluently and to use it to solve hard problems. Those who lack fluency will be shut out of careers listed above, with the greatest negative consequences for children of immigrants, a group whose entry into the mainstream of American society has historically been facilitated by demonstration of mathematical rather than linguistic competence.

Children need to understand the meaning behind the math.

In much of mathematics education literature, the “meaning” referred to is provided by reference to a concrete or pictorial model. That’s not enough. If the K-12 curriculum does not offer a coherent path for moving from concrete/pictorial to symbols (and many NCTM-inspired curricula do not) then students will be totally unprepared for advanced mathematics courses. The world’s highest performing students use the Singapore curriculum, whose driving principle is that children must begin with “the concrete and pictorial stages, followed by the abstract stage to enable them to learn mathematics meaningfully.” [emphasis added]

Just understanding rules doesn’t enable you to do the math.

Understanding rules, knowing when and how to apply them, does enable you to do the math. Students are flunking advanced algebra and calculus courses not because they don’t understand the “meaning” of mathematics, but rather because they are afraid and unable to deal with symbolic expressions used to represent real-world problems. Their failure rate will only increase if they are raised on a K-12 diet that is deficient in algebra and mathematical formalism.

Mathematics is about ongoing observation of the world around you.

Mathematics is about many things, including modeling the outside world. Bridge design requires deep mathematics. One certainly has to calculate, to a very high degree of precision, exactly how long the bridge should be. Unfortunately, prominent mathematics educators disparage the idea that math problems have “single answers.” Bridge-builders, take note!

They also wanted to help them [the teachers] see themselves as mathematicians

We are unfamiliar with the above usage of the term “mathematicians,” which ordinarily refers to researchers at the frontiers of mathematics knowledge who publish their work in refereed journals. The objection here is not a quibble about redefining membership in our profession, but rather is conditioned by the attempts of mathematics educators to redefine the nature of mathematics itself. Fosnot’s unconditional rejection of all of the views:

“that meaning can be passed on to learners via symbols; that whole concepts can be broken into discrete subskills; that concepts can be taught out of context;” while formulated as a vision of pedagogy, forces a redefinition of mathematics content diametrically at odds with the needs of college mathematics and science students.

Our nation’s K-12 classrooms need not mathematicians, but rather mathematics teachers who are knowledgeable in content as well as pedagogy. Revitalizing the teaching workforce can be accomplished only when curriculum developers recognize their responsibility to prepare students for the rigors of college mathematics, and when university mathematics departments play a substantive role in teacher training and professional development programs.#

Stanley Ocken is Professor of Mathematics at the City College of the City University of New York, where he is working, together with preservice teachers, to develop a text and software resources for their introductory math content course.

Robert Feinerman is Professor of Mathematics and Computer Science at Lehman College of CUNY, Department Chair, Chair of the CUNY Math Chairs, was CUNY’s representative to Chancellor Levy’s Commission on Mathematics Education and is a member of Community School Board #10 in the Bronx.

City: State:

Education Update, Inc., P.O. Box 20005, New York, NY 10001.
Tel: (212) 481-5519. Fax: (212) 481-3919.Email: ednews1@aol.com.
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