Category Archives: Mathematics

Debate Over Math Curriculum Resurfaces

The debate over primary & secondary school math curricula that was sparked in part by a New York Times editorial a couple years ago has come up again in the Chronicle of Higher Education.

The main argument now, as before, is that subjects beyond basic arithmetic are too hard for many students and should not be required for graduation nor seen as necessary for gaining entrance into colleges. This includes subjects like geometry and algebra.

The original article was met with widespread scorn, and this one, which includes an interview with the author of the old article, should too. Basically, there are a huge number of problems with eliminating a requirement that high school students take algebra or even discouraging students from taking classes like algebra, trigonometry, and calculus. For subjects involving math, these courses represent something more like grammar and composition than an advanced course in literary analysis. They are fundamental subjects that must be mastered before a student is capable of succeeding and not arbitrary barriers to success. Entering college without any knowledge of calculus puts students in many fields at a serious disadvantage compared to most of their peers. Without algebra, even introductory classes in many fields are inaccessible, and the corresponding majors become impossible to complete in less than five or even six years.

What Hacker, the author of the original article, suggests doing will effectively lock many students out fields like engineering, physics, chemistry, mathematics, computer science, statistics, and even many (most?) social sciences. All that will be left will be humanities and the arts (and even then some classes may be impossible to complete). He makes the claim that “coding is not based on mathematics,” yet the opposite is true. In many ways, computer science is a subfield of mathematics. There is more to computer science than just programming, but a programmer that knows no serious math will quickly find that their options are limited.

Furthermore, at many colleges, lower-level math classes (basically, anything below calculus) aren’t even considered college material. This is true of the schools that I attended. If students matriculate without being able to take at least calculus, they’ll be forced to waste a lot of time and money taking non-credit remedial courses to catch up.

Hacker’s arguments seem to be based on the assumption that mathematics beyond arithmetic is uniquely expendable out of all the basic primary and secondary school subjects. Somehow other fields like statistics (which is really just a form of applied math) can be taught independently of mathematics. Anyone who has actually studied a field that requires a decent amount of math knows how important a strong background in as many math topics as possible can be. Physics uses topics like group theory, complex analysis, ordinary and partial differential equations, differential geometry, linear algebra, and many others quite regularly. Students don’t typically see any of these until after several semesters of calculus.

I can’t help but think that Hacker sees math as nothing more than rote memorization of basic formulae (which maybe isn’t surprising for someone who has so much disdain for any math harder than arithmetic). Even if literary analysis is just as rigorous as mathematics, that doesn’t mean that we should get rid of mathematics. We should demand that all subjects be as rigorous as possible. Being able to solve complex mathematical problems can be just as important as being able to read complicated works of literature and write coherently about them.


John Nash Dies in Car Crash

It’s being reported that mathematician and economics Nobel winner John Nash has been killed in a car crash in New Jersey. Nash was famously the subject of the movie A Beautiful Mind, where he was played by Russell Crowe. Nash was famous for his work in game theory.

Google Doodle on Emmy Noether

Today’s Google Doodle (the stylized version of the google logo on the google homepage) honors Emmy Noether, the mathematician behind Noether’s Theorem. Noether’s theorem is incredibly important to modern physics because it explicitly works out the relationship between continuous symmetries of nature and conserved quantities. Thus, invariance with respect to time translation requires conservation of energy, spatial translation invariance leads to conservation of momentum, rotational invariance leads to conservation of angular momentum, U(1) symmetry leads to charge conservation, and so on. Noether’s theorem pops up everywhere in modern physics.

Noether is also noteworthy as a rare female mathematician in an incredibly male-dominated time. In fact, she had a great deal of trouble securing a position as a professor in Germany due to other professors believing that women did not belong on the faculty. Even after finally getting a position, she eventually ended up at Bryn Mawr College after being forced out of her position by the anti-Semitic policies of the Nazis.

Today would have been Noether’s 133rd birthday.