Some of you may have heard of this, some of you may have not. The “Calculus Rush” is a reference to when students (particularly those in high-school) “rush” to the next math class – that is, instead of actively developing their problem-solving skills with what they already know, they spread themselves thin by learning new material. Several articles have been written about this which you can find by googling for or “the rush to calculus” or some similar alliteration. This does not apply to every student and/or school, but it’s foolhardy to deny that this is a problem in education in general.
Calculus, by far, receives the most negative end of the pro-acceleration accusations (hence why it’s called the Calculus Rush and not the Geometry Rush). Even though this applies to a lot of math subjects whether it be algebra, geometry, precalculus, calculus, linear algebra, etc. Calculus in particular receives all the attention for a variety of reasons:
- Calculus, in theory, is the subject that transitions most students from a purely computational-based environment (another issue entirely) to a more conceptual and abstract one. While one certainly doesn’t need to study Spivak and bash rigor out of everything, it’s pretty important to intuitively understand why the stuff in calculus works to be able to use it effectively.
- For most high-schools, calculus is typically offered as AP courses (AB and BC) and is the highest-level mathematics available. As a result, calculus is perceived as the hallmark of mathematical achievement.
- Many students (and universities too, sadly) believe taking calculus indicates significant talent; therefore, it is required to be competitive.
Now here’s where people make the mistake: I am not saying it is bad to learn calculus. Calculus is really, really, really powerful as both a tool and how it changes your mindset of mathematical reasoning. What I am saying is that it is bad when a student attempts to learn material without sufficient preparation.
Okay, maybe you’re still not convinced. If this is such a problem, then schools should have fixed it already, right? Again, no. There are so many flaws with the education system that it’d be faster to list what’s not flawed. But then why do these issues persist? Well, there are a few prevailing reasons:
- One of the worst causes is parents. It’s natural to want to see your child succeed, be smart, and make a boatload of cash. Unfortunately, parents also have a tendency to overestimate their child abilities and overly-encourage (if not force) them into subjects that they aren’t sufficiently prepared for.
- Education is also really outdated. Most curriculums (even calculus ones) are constructed in a way that would be appropriate for a time when computers didn’t exist. Routine computation-based math problems can be done far faster on a Chromebook than students could ever compute by hand. Humans excel at novel problem-solving compared to computers, computers excel at computing things we already know how to do.
- The standard curriculum in algebra, geometry, and precalculus lacks a lot of mathematical rigor. A large part of mathematics is being able to concisely and precisely communicate logical arguments and reasoning but that gets lost under rote-memorization-based computation.
- Many universities and students perceive taking calculus as an elite qualification.
Admittedly, not much can be done about these points. It’s pretty hard if not impossible to make all parents and students aware that accelerating can easily go horribly wrong and it’s pretty hard (impossible) to force all schools and universities to change their views on allowing students who shouldn’t be taking calculus into a calculus class. Unfortunately, it’s simply an issue that goes on and can’t really be fixed quickly. However, for those students willing to try to avoid the stigma, there’s a couple of options:
- Get a very solid grasp on algebra, geometry, and trigonometry and using them as problem-solving tools. All three are needed to fully appreciate calculus. A great place to practice on some non-routine and challenging problems is through the Art of Problem Solving’s Alcumus system (disclaimer: I work for AoPS).
- Learn discrete mathematics (combinatorics, number theory, graph theory, sets, logic, etc.). Discrete math is a very good way to delve yourself into some very challenging problems which rely heavily upon understanding compared to your typical plug-and-chug problems. It’s also a really good place to begin writing proofs.
Hopefully, I was able to persuade you enough to consider another view on the calculus fever. Again, I’m not saying that it’s bad to learn calculus, but it’s bad to venture on without sufficient preparation. Everyone learns at a different pace and a different way, when they are ready to learn something, then they should learn it.