Gifted Issues Discussion homepage Forums Identification, Testing & Assessment Misunderstanding Achievement Tests

I can see this point. If I understand it, the Calculus Trap article argues that students should be "learning how to take tools they have and apply them to complex problems."

What I don't get here is that calculus does exactly that: you have to use existing tools (algebra, geometry, arithmetic) and apply them to complex problems ("How many miles did you travel from 2 pm to 6 pm if your velocity could be described according to this formula: <insert quadratic equation>?" "A farmer has 168 meters of fencing and wants to maximize the area of a rectangular corral. What should its dimensions be?"). Etc.


Since when? 1979 or so? High schools have been offering calculus for decades.


Huh? So if you're good at math you can't take a math class that you'll really like? Umm.

If you're really into mathematics, you can join the Math Olympiad club, which meets after school on Tuesdays and Fridays. And your calculus will probably help you a lot, given that getting a calc problem right usually requires combining all sorts of other knowledge.


What in Robert's name does this have to do with taking calculus? The author seems to be implying that taking calculus is anathema to learning to enjoy using your mind. So, all the automatons are calc class, while the really interesting kids are in study hall counting the minutes to math club?

Any really good athlete I've ever met enrolled in one or more PE classes. I expect that many of them learned that they had talent for something in PE class. Unless they had their own high jump sets at home. Some of them majored in it. PE is a great break from sitting at a desk.

No, those are not complex problems in the way that the article means. If you understand the tools taught in calculus, they are absolutely routine: no thought required, beyond a routine translation of words into symbols. The Calculus Trap is exactly people's unthinking assumption that calculus must be challenging because it comes last at school. It isn't, as taught at school; it's easy and unchallenging, and there are many more useful things for young mathematicians to spend their time on.

[ETA if I sound bitter, this may explain: have I mentioned that DS7 has fallen into the calculus trap somehow - that is, he thinks learning calculus will somehow make him grown up - and is determined that he's doing that next? He'll get challenged, though, I shall see to that, bwahaha...]

I agree with Colinsmum. That article is by Richard Rusczyk. He is founder of AoPS and a guy writing some of the best math textbooks for smart kids. He argues that most kids never encounter hard problems in typical school environments. In my experience as a child and a parent, that has been true, even with enrichment, multi-year subject acceleration, and GT math classes. Math Olympiad at elementary level hasn't offered my children the kind of challenge offered by AoPS. The level of problems with AoPS courses or higher level math tests require great problem solving skills. If there is never a problem that isn't obvious (which was definitely my experience in school math before college), then a student has no chance to learn those skills. Like most skills, problem solving increases with practice. Like much of GT research, AoPS takes the approach that a kid ought to encounter difficult things and learn from working through mistakes and struggling with unsuccessful attempts rather than do repetitive easy problems in typical textbooks.

The problem sets in their classes are really hard. They often require trial and error, thinking through many different steps, considering deeply whether one possible solution meets every criteria demanded by the problem, etc. They don't expect all or even most students to be able to get them all right, which means a talented kid has more room to grow. Since I see most of the beauty in math as coming from the hard stuff rather than the plug-and-chug, I think this approach is most likely to hold the interest of a talented math kid.

I have no connection to AoPS, but I admire their program and their approach to math. In all the GT-friendly things my children have done, I see AoPS as coming closest to offering exactly what they needed for the reasons Rusczyk expresses in the calculus trap.

I disagree about calculus in general, but agree that maths as taught in schools puts too much emphasis on superficial stuff.

But this situation isn't calculus's fault. Calculus is a beautiful mathematical achievement, and the fact that schools dumb it down is an argument for better teaching and better schools that actually present challenging material to capable students.

Yeah, pipe dream. I know.

Having fallen into it myself, I definitely do agree with it and am working to avoid it with my kids. That said, my intent there was not to criticize you, but just to call attention to a different point of view.


I wouldn't take the name of the Calculus Trap as meaning any disrespect for calculus as a subject.