Calculus I Class Struggle: How Can Someone Have an A?

[moose]

Are you serious?!??

I tutor for a Calculus I class at my high school... Anyway, the students were doing stuff like sketching possible graphs of f(x), given a few values for the first and second derivative of f(x). So there is a kid in the class who has an A, and today he told me that he was confused. He asked me what the graph does when the first derivative is positive.
...
...
...
How can someone have an A in a calculus class without understanding what a derivative is?

I casually explained to him how graphically, derivatives represent the slope of a function at the given point. He was like, oooohhhhh ok. WTH?

I wish I actually had some time with a few of these students and not just 1 minute encounters during which I can't actually help that much. I hate it when I see the teacher "explaining" things in such a horrible fashion... bleh
Out of everyone in the class, there seems to be only one student who understands this. It's this one girl who gets 100%s on all of her tests. I've shared some conversations with her and she actually knows her stuff...

EDIT: The worst part is that only 3 students have an A in the class. This means that people below the A must be doing REALLY bad.

 

[Gokul43201]

I tutor for a Calculus I class at my high school... Anyway, the students were doing stuff like sketching possible graphs of f(x), given a few values for the first and second derivative of f(x). So there is a kid in the class who has an A, and today he told me that he was confused. He asked me what the graph does when the first derivative is positive.
...
...
...
How can someone have an A in a calculus class without understanding what a derivative is?

I casually explained to him how graphically, derivatives represent the slope of a function at the given point. He was like, oooohhhhh ok. WTH?

You poor chap! And you thought the grades might be strongly correlated to an understanding of the subject?

I wish I actually had some time with a few of these students and not just 1 minute encounters during which I can't actually help that much.

Welcome to the real world of tutoring!

 

[moose]

You poor chap! And you thought the grades might be strongly correlated to an understanding of the subject?

I guess that makes me the ignorant one.

 

[JasonRox]

I guess that makes me more ignorant one.

I feel your pain.

I mark assignments for this class, and the average on the assignments is probably like 75-80%. Unfortunately, very few show signs of actually knowing the material.

It's not fun marking assignments when questions require a one line argument, but yet they need a full page of work to explain while the explanation is false.

 

[Moonbear]

How can someone have an A in a calculus class without understanding what a derivative is?

I casually explained to him how graphically, derivatives represent the slope of a function at the given point. He was like, oooohhhhh ok. WTH?

Did you see the other somewhat recent thread about the kid on Dr. Phil who was complaining she was doing well in the class but didn't understand anything? It's fairly common in courses like that to be able to get good grades just by memorizing methods of solving problems without understanding why you would want to solve such a problem, or what it means. I don't think I fully understood that when I took Calc I either...it wasn't until I took a physics class that the usefulness of calculus sunk in, or that the idea of a derivative representing the rate (slope) made sense to me. I don't think Calc is taught with enough word problems...at least not the way I was taught it. Word problems are what used to help me understand why or how one would use the "tricks" just learned...because without that understanding, that's all it is -- tricks with numbers.

 

[scorpa]

That is crazy, I taught myself calc through distance learning as my school did not offer it and by the sounds of it I got the better end of the deal. All of my homework questions were problem solving questions were you had to understand the concepts in order to complete the assignments. I had no problem transitioning to univeristy calc at all. How can you have an A in calc and not know what a derivative is?

 

[moose]

I don't think Calc is taught with enough word problems...at least not the way I was taught it. Word problems are what used to help me understand why or how one would use the "tricks" just learned...because without that understanding, that's all it is -- tricks with numbers.

The class does have word problems. The word problems are all nearly identical and far too simple though. Recently I was working on a computer program in which I had to calculate various things dealing with an eyeball. I calculated the iris's position, size, eccentricity, etc, when following a the mouse at a given distance away from the face (depth wise, not actual distance). I wanted to do this without any trig, and I created all of my equations using vectors. Anyway, I realized that word problems should be more like that example. I'm not saying this should be in Calc I or something, but in some class. It wasn't "hard" to do or anything, but it tested some concepts.

Anyway, back to the class... The course's word problems have no real meaning most of the time, are about useless things, and are repetitive.

You know what else is sad? Out of all of the schools in my school district, my school had 3 times more people get 5's on the AP Calc BC exam than all other schools in the district combined. He teaches towards the test. I wonder if people in other schools are learning more, or if they're learning a lot less.

 

[JasonRox]

I don't think Calc is taught with enough word problems...at least not the way I was taught it. Word problems are what used to help me understand why or how one would use the "tricks" just learned...because without that understanding, that's all it is -- tricks with numbers.

Are you crazy!?

Word problems are what I hated. It was neat to see what it can do, but that was it.

Maybe they should Calculus teach in different styles. Most schools have several Calculus courses (different sections), so why not make each section a different teaching style. The students can choose which style they think would be best.

 

[Daverz]

I think this is the old "don't know what you know" syndrome, not being able to apply what you know outside of a narrow context and setting. I wouldn't necessarily blame the teacher or the students; it can take a lot of practice and experience for some things to sink in and become internalized.

 

[Moonbear]

Word problems are what I hated. It was neat to see what it can do, but that was it.

I think the reason people hate them is that they are harder to do. It takes a lot more understanding of the material to know how to solve a word problem than to be handed an equation and be told to take the derivative of it. But that's why I enjoyed them. They gave the material some purpose and helped me understand why I'd need to solve a particular type of equation, just not learning to manipulate variables until I was able to solve for X. In the real world, X represents something...velocity or reaction rate or something you can actually get your teeth on and comprehend as a use for math.

But, I think what moose describes about word problems is also a common failure in those problems. It takes some skill to set up a good word problem so that it does force the student to think and not just hunt for the variables to start plugging into equations.

As for teaching different classes in different styles, I disagree. The reason is that a student won't know going into a class what style will work best for them, and it might even depend on the unit they are studying. Instead, a good teacher incorporates all (or at least many) teaching and learning styles into their lesson plan. If you present things in a variety of ways, everyone has a chance to grasp the concepts. That's also why you have someone teach the class, use audiovisual aids (even if it's just the chalkboard), and also have a textbook that says the same thing, so that students who learn by listening and students who learn by watching and students who learn by reading all have a chance to grasp the material. For some topics, you'll need all three to really grasp it if it's challenging, for others, just reading the book would be enough. For homework, you'll want some simple "solve for x" type equations, some that are more challenging, some that require you to remember what you did in the previous chapter to solve them, and then some word problems that test that you comprehend the application of the equations beyond passing tests.

 

[Office_Shredder]

You know what else is sad? Out of all of the schools in my school district, my school had 3 times more people get 5's on the AP Calc BC exam than all other schools in the district combined. He teaches towards the test. I wonder if people in other schools are learning more, or if they're learning a lot less.

Actually, the whole point of the test is that if you teach towards it, then you're covering everything the students should know. If teaching towards the test doesn't work, it's really the test's fault (for AP tests)

 

[russ_watters]

It isn't word problems per se - calculus just needs to be taught in conjunction with physics. That helped me a lot.

 

[arildno]

It isn't word problems per se - calculus just needs to be taught in conjunction with physics. That helped me a lot.

That's of course a matter of personal preference. I learned calculus in a "pure" mathematical setting and found that very enjoyable.

 

[Moonbear]

It isn't word problems per se - calculus just needs to be taught in conjunction with physics. That helped me a lot.

I think that's just because the physics provides the real life examples of how to apply the calculus, but I don't think it's a necessity to teach them together if you provide well-written word problems. But, I agree, that's when I really understood calculus was in physics...and again when I took physical chemistry and had to use all those stinking partial derivatives I had already started to forget because I hadn't gotten a solid understanding of them when I took calculus.

 

[GCT]

You poor chap! And you thought the grades might be strongly correlated to an understanding of the subject?

in high school...no, in college, yes.

 

[Pythagorean]

I think that's just because the physics provides the real life examples of how to apply the calculus, but I don't think it's a necessity to teach them together if you provide well-written word problems. But, I agree, that's when I really understood calculus was in physics...and again when I took physical chemistry and had to use all those stinking partial derivatives I had already started to forget because I hadn't gotten a solid understanding of them when I took calculus.

As a physics student, I'd have to agree. I don't understand most of my math classes until about a semester later, in a physics class.

There was one math teacher I had that used physical examples of almost everything, and I got the most out of that class.

For me, I've pretty much accepted that memorizing is ok for me, since I have prolonged exposure and will eventually understand what it was I memorized when I apply it.

 

[Nothing000]

Did you see the other somewhat recent thread about the kid on Dr. Phil who was complaining she was doing well in the class but didn't understand anything? It's fairly common in courses like that to be able to get good grades just by memorizing methods of solving problems without understanding why you would want to solve such a problem,

This is exactly what I am trying to avoid in school right now. I almost don't even care about grades right now, I am just trying to actually understand the stuff and why I need to understand it.

My sister went through school with the good grade/memorization method. She graduated, and got landed a job on her first interview making like 70k/yr.
But she is a nurse, so I think that is more accecptable to just memorize stuff in a field like that.

 

[Stevedye56]

This is exactly what I am trying to avoid in school right now. I almost don't even care about grades right now, I am just trying to actually understand the stuff and why I need to understand it.

This is exactly why I like getting graded on lab performace. Its easier in my opinion to perform a lab well than to take a test where there's much more room for error.

I know a few people in my Chem class who can memorize and pass the tests fine but when it comes time to perform the lab they are completely clueless. I on the other hand have no problem with labs but have always struggled with tests. I think it does more good to be able to perform it, although I also think that tests need to be administered also.

 

[rhuthwaite]

As a physics student, I'd have to agree. I don't understand most of my math classes until about a semester later, in a physics class.

I think I understand Maths (especially calculus) a lot better than physics, generally I have no clue about what is actually happening in the theory of physics, I just memorise it. Its the calculations I understand and can do really well.