A mathematician once lamented that — despite popular belief — his job did not entail simply multiplying bigger and bigger numbers together.

One may be quite forgiven for believing this, however. The truth stays hidden until a student reaches the transition course, a staple at many universities. These classes go by many names, but all share one feature in common: They mark the point in a potential math major’s career when he stops doing math the way he has been taught since first grade and starts doing math the way a mathematician does. Less formula, more proof.

I too had to take such a course once. Thanks to the efforts of a dedicated high school teacher, I was already well-exposed to the way proofs worked, and yet the university insisted I take the course anyway. It irked me then that I had to prove I could do something I’d been doing for three years. And it still irks me now that such classes exist. Transition courses are needed because something else has gone critically wrong in the teaching of mathematics: We should not be waiting until college to drop key fundamentals of mathematics — or of any other subject — onto students.

Any change that must be made, however, must come far before the time a student enters college.

And change is happening.

Many states, Illinois included, are adopting the common core standards for teaching English and mathematics. In addition to formalizing the mish-mash of curricula across the country, the standards attempt to build upon knowledge continuously rather than lob random topics at students in no particular order.

Compare this to the way we currently teach proofs. In geometry, proofs are shoved into the curriculum, tedious and unconnected to anything that came before; and as soon as the course is over, the proofs disappear back into the ether along with all memory of them. The usefulness of proofs, their ubiquity and, for that matter, their importance in the profession of mathematics all get lost.

But wouldn’t you know it, the only time proofs are mentioned in the common core standards are in the context of geometry.

Head, meet desk.

Any good science curriculum does not just teach the scientific method and switch back to textbook studies as soon as that is over; a good science curriculum mixes both knowledge and the understanding of how we came to that knowledge. The scientific method gets incorporated again and again, in physics, in chemistry and in biology.

Why should mathematics be any different?

As the educational standards now lie, the transition courses cheat students in two big ways.

First, they lie to students about what mathematics is. Many skilled calculus students play to their strengths and continue forward in math only to run into a brick wall at the transition course; they never were told what was expected of them.

Second, they rob students of a particular aspect of mathematics that they may find interesting and enjoyable. Last semester, to help my students understand a bit better what I did for a living, I asked them to watch a lecture by famous mathematician Terence Tao; afterward, many students told me how interesting they found his presentation of Euclid’s proof that there are infinitely many primes. They had never seen that proof before.

Their interest made me incredibly happy.

But also sad since they had no opportunity to see more aspects of mathematics before now.

_Joseph is a graduate student._