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What Happened to Mathematics?

posted Feb 6, 2017, 7:32 PM by Emily Tai   [ updated Feb 13, 2017, 11:31 PM by Jay Weiser ]
By Roman Kossak

“Let nobody ignorant of geometry enter here” was a warning at the entrance to Plato's Academy.

"The Book of Nature is written in the language of mathematics," wrote Galileo.

Mathematics used to be the Queen of Sciences. It is highly paradoxical that now, when our lives have become so dependent on mathematics-driven technology, the popular view of mathematics is changing. A public debate is going on about mathematics and its importance in general education, and much of it is clouded in misunderstandings.

In her presentation at the UFS plenary session last October, Executive Vice-Chancellor Rabinowitz devoted 20 minutes to proposed changes in teaching of mathematics at CUNY and policies regarding remediation based on "evidence-based research" and expert recommendations. In my opinion and in the opinion of many of us who are directly involved in teaching mathematics at CUNY, the changes described in the recently posted Strategic Framework for CUNY will result in eroded standards and a diminishing of the already weakened role of mathematics in general education.

The roots of our problems 

In the CUNY Strategic Framework we read “One of the greatest academic obstacles to graduation at community colleges across the country is traditional remedial programs."  It is not that simple. 

Putting aside the question whether "traditional remedial programs" are really an obstacle, we cannot turn away from a whole host of other factors. Liping Ma was senior scholar at the Carnegie Foundation for Advancement of Teaching. Her book Knowing and Teaching Elementary Mathematics has been widely read and discussed. In a more recent article, A Critique of the Structure of U.S. Elementary School Mathematics, Ma provides a comprehensive and well researched picture of the changes that were implemented over the last 50 years that have resulted in a dramatic lowering of the quality of mathematics education in the U.S. She concludes that "... instability, discontinuity of teaching and learning, and incoherence among concepts have damaged U.S. elementary student learning."

Those are strong words, but we see evidence of what she writes about every day in our classes. How should we respond? Should we just throw in the towel, and declare that teaching mathematics in college should be eliminated, because a majority of students are so unprepared for it? That would be a real tragedy. There is much that we can still accomplish, but that would require much more than quick fixes offered in the CUNY Strategic Plan.
 
A Communication breakdown

It is unfortunate that in the discussion of the role of mathematics in the college curriculum, we, the mathematicians, get little or no understanding from colleagues in other disciplines. One could argue that it is our own fault, but there is also something else. We are plagued by the myth that mathematics is a discipline only for mathematicians. When asked, most students in my classes declare themselves "bad at math." It hurts them, and it makes teaching a much harder task than it could be. Miles Kimball and Noah Smith have tackled the "I'm bad at math" myth. The authors conclude "Too many Americans go through life terrified of equations and mathematical symbols. We think what many of them are afraid of is 'proving' themselves to be genetically inferior by failing to instantly comprehend the equations (when, of course, in reality, even a math professor would have to read closely). So they recoil from anything that looks like math, protesting: 'I’m not a math person.' And so they exclude themselves from quite a few lucrative career opportunities. We believe that this has to stop."

Math misrepresentations

Speaking of myths, much damage has been done by paying too much attention to arguments that distort and misrepresent the real problems. An example is The Math Myth. a book written by Andrew Hacker, professor emeritus in the Department of Political Science at Queens College. Below is a link to Keith Devlin's review of Hacker's book. The Math Myth that permeates 'The Math Myth.'

Devlin is a distinguished mathematician and a popular science writer, who has considered the role of algebra in other pieces. He argues that, while the problems that Hacker is addressing are real, his diagnosis and suggested solutions suffer from his lack of understanding of mathematics, and the importance of algebra in particular. And so I would like to close with his comments: 

For a variety of reasons, the subject now taught in schools under the name of algebra is a travesty of the powerful way of thinking and problem solving developed in the Muslim world in the 8th and 9th Centuries, called “algebra” today after the Arabic term al-Jabr. If Hacker had instead used his New York Times connection to argue for a major make-over of 'school algebra' (as I think we should call the object of his criticisms), he would have garnered massive support from the pros, including me. As it is, his support came exclusively from those who, like Hacker himself, have no idea what algebra is or how significant it is in today’s world.

Roman Kossak is a Professor of Mathematics and Computer Science at Bronx Community College and the Ph.D. Program at the City University Graduate Center. He also serves as a UFS Senator.

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photo credit: https://pixabay.com/en/geometry-mathematics-cube-1044090/