Ugh Challenge of learning math when it comes too easy.

[The_Z_Factor]

I'm having a problem. This problem happens to me everytime I do something that gets harder as I progress or something that takes a while to accomplish. So basically I'm reading a self-teaching (sort of) calculus book and trying to learn it. I also have a HUGE problem with math that is too easy for me. Now, at the moment I've been doing simple derivative problems that are extremely easy. Just this morning I finished a unit on the Product Rule, Quotient Rule, and the Power Rule. The next unit (that I'm going to do after I finish the problems to get a grip on the 3 previous rules), is dealing with the Power Rule and negative exponents. So anyways, at the moment I'm finding this stuff so easy its hard to make myself pay attention and continue reading. Most of the time I want to skip and go on to a really complex unit that I would have a lot of fun doing. Problem is that I need to know the simple stuff to get further. Thats my only motive behind doing this easy stuff. Now, I am only a sophomore in high school, and I haven't even taken algebra 2, actually not even geometry (next semester for that), so I don't have to learn this..but the complex calculus I've read before and some of the things you can do with calculus really interests me, so that's why I study it on my own.


So my problem is motivation. I want to learn it, I want to do it, but I can't make myself do it. I'm sure if I was in a classroom it'd be easier because my motivation to do the work would be a good grade, rather than a seemingly pointless motive such as "let's learn this just to learn it".. I don't know how to get myself motivated. I tell myself at times, "Well you can't do physics without calculus," or "think of how proud you'd be of yourself if you taught yourself high school calculus without the help of anybody but yourself". I'd had to say the latter is my biggest motive.

Ive looked for ways to motivate myself and google'd it and everything. I just can't seem to find anything to do it for me. One site I found, had I think 16 motivation tips, and one of them was something like, "Don't do your goal right when you feel like doing it, because you'll not want to do it anymore after a little while". It said put your goal a week or so ahead of you and build up on your motive to do this goal. I was thinking of doing this, maybe taking 2 or 3 days off and getting back to it, but the reason I don't do it is because I feel like if I put it off for even 2 days I might not have any motivation at all to go back to it and then just drop it, once again failing a big goal I've tried to achieve, which is what I don't want to do at all, or I might forget some of the material and have to review all that boring material. I don't even take notes on this stuff usually I read it 2 or 3 times and try to memorize it. Guess it works pretty well because I remember how to solve everything (but a lot of times I forget the steps used in solving certain problems, etc.).

Anyways, does anybody have any kind of tips or help they could give me to help get me motivated to do this? I've tried making myself do it, even when I'm not motivated, but usually give up because I just can't make myself interested in it at the time. In fact, motivation was the reason I dropped studying physics on my own (along with not knowing the math, which is the main reason I study calculus now).

 

[EnumaElish]

1. Try to find the "ideal" study environment.
2. Do not leave the study environment before you achieve a minimum level.
3. Take notes as if in class.
4. Promise a little incentive for yourself every time you achieve a goal.
5. Find a study partner?

 

[moe darklight]

well, I'm pretty bad at math, so I can't relate with finding stuff easy... but I can relate with other subjects... and also with trying to learn on your own. and also I have really bad ADD so I can relate to the not being able to pay attention part.

I wouldn't recommend this for most people, but it works for me:

I simply CANNOT learn in a quiet environment; my mind just starts zooming into every possible topic but the one at hand. The only way I can study is if the TV or radio is on... my mind doesn't get bored or tired that way because there's that constant "something" happening in the background that I can go to to snap myself out of it, and then come back.

try to study sitting on your bed with all the books you need around you and the TV on (watch seinfeld, or the OC [yes. I watch the OC. sue me ], or southpark, or whatever show you like)... also have a writing pad for doing the work. and get some tea or coffee and cookies and make an activity out of it.

if you get too bored with the calculus, switch to your biology or whatever...

I don't really have a time goal in mind... so I switch a lot from topic to topic... which means I take forever to finish any single topic, so you might not want to do that. unless you enjoy knowing a little of everything.

like I said. I wouldn't recommend this to everyone... some people can't work with noise. but it's the only way I can concentrate on things so it might work for you too... my dad is this way too and he came out one of the top of his class in university.

 

[The_Z_Factor]

moe darklight, I used to be just like you. I always did my schoolwork or any type of paperwork with music or tv on. I can't do that anymore though, because now my mind gets too distracted and I end up trying to do two things at once (trying to read something but also trying to listen to the tv,), so I have to study in silence. I was thinking perhaps to make me want to do it instead of using tips to make me do it, I should read a book by a mathematician or a story of a mathematician who did something great using math. Who knows, maybe it'll work

 

[Ben Niehoff]

So, my advice is this: If you understand the Product Rule, Quotient Rule, and Power Rule, then by all means, skip ahead to something more interesting. Have you done the Chain Rule yet? That one is very important. Once you have the Chain Rule, then you should try Implicit Differentiation.

Many books organize the homework problems by difficulty; there are often "bonus" problems toward the end of a chapter that are meant to be especially difficult. Try doing those. If you can't do them, then go back and read some more.

You can also make up problems for yourself. Just write down some complicated expressions using only products, quotients, and powers. To verify your answers, you can use a graphing calculator and plot some tangent lines.

 

[moe darklight]

Many books organize the homework problems by difficulty; there are often "bonus" problems toward the end of a chapter that are meant to be especially difficult.

off topic, but: why do textbooks always have detailed answers for the easy problems I get
anyway, and just the final answer for the harder problems that are where I need the help! *smilies aren't working for some reason... so picture some sort of angry smily, followed by a laughing smily so as to show the playful nature of my post*

 

[The_Z_Factor]

moe darklight, I think that it's meant to be hard and not explained so you can try to apply what you learned in the easy questions to a harder question, that may require an extra step or two, so that you fully understand it. If they explained every problem then once you get to a hard problem whenever that may be, that isn't explained, you'd have no clue how to do it. I guess you could say it helps you understand it better. Or it just helps you feel good that you solved it without help, that's how I feel at least when I do a hard problem that I solved myself. Haha.

Ben Niehoff, thanks a lot for your input, I think it helps me more getting sort of a guide to go by, instead of just blindly going through the book. What I mean by guide is that you told me to do the Chain Rule (which is what I'm doing in the next unit), and then Implicit Differentiation. I looked at implicit differentiation but didnt bother reading, I was just scanning through the chapters.


Does anybody know where I could get a high school calculus book? Since I have to wait 2 years to take calculus (hopefully less if I can convince my counselor to let me take 3 maths in 1 year), so I don't have access to one anytime soon. That is, unless the school let's me 'borrow' one for a little while. I think by the first semester of next year I should have the calculus books I'm reading done and have a pretty good grip on differential and beginning integral calculus, but the reason I ask is because I don't know how far into calculus you get in high school. I was guessing high school doesn't go very far beyond logarithms because some of the college textbooks I've read have logarithms half way or so through the first chapter. I am sure it depends on your high school, of course but does anybody have a general idea of how far high school gets into calculus? How far into it did you go when you were in high school? Did you take calculus AP?

 

[moe darklight]

yea, I understand why they would do it in principle... but to me it seems like the detailed solutions provided are always of things that are pretty self evident and obvious in the first place... questions for which I don't need the explanation because I got it in the first place.

you could say that with the harder questions there'll be the temptation to look at the steps and not come up with an answer oneself... but at the same time the whole point of a textbook is to explain stuff. so if I become stuck in a hard question It'd be nice to be able to see exactly where I went wrong, or look at the next step as a hint... I guess they count on there being a teacher should one get stuck.

 

[The_Z_Factor]

Yeah that's true I suppose. I know when I get the wrong answer there's no way to tell where I went wrong because my books don't explain it. I get the answer then check in the back of the book to see if I get it right. But the back of the book there's no explanation. Gets annoying sometimes. I guess its a good thing I usually don't get the answers wrong huh? Ha..ha..ha.

 

[moe darklight]

I guess its a good thing I usually don't get the answers wrong huh? Ha..ha..ha.

touché. yea I usually get a few wrong... why are the smilies not working! ... how did people communicate before smilies!

 

[Integral]

Perhaps you should post some of the problems you are doing, and your solutions in the homework help forum, just so we can verify that you are not missing something.

Show us all of your work.

 

[moe darklight]

most of the time it ends up involving having made a stupid mistake (like writing "1" where a "1x" should be and not noticing, and it ends up throwing off the whole thing) and I end up figuring it out.

but sometimes the mistakes do involve actually misunderstanding the lesson, so I do a search here or on google to see if there's a similar problem... I've only made 2 or 3 posts here on math questions. one last week on precalculus and one on calculus a month or so ago... both of which were on easy questions, which made me suspect that the problem was me not understanding something, in which case I do need help.

I don't really like asking questions on specific problems unless the problem is that I don't understand something conceptually, because otherwise it just involves a mistake from my part that I should figure out on my own.

(I know calculus and then precalculus sounds backwards, and it is: I started the book on calculus [I think around August or June] not even knowing there was stuff that you're supposed to know before it... I'd always fall on something confusing and when searching the internet find an explanation.
until I learned that all those things fall under something called "PREcalculus" :-O that makes sense. so I put off calculus and got the college precalculus book now; some of it is review of things I learned while looking for what I was doing wrong in calculus, but some of it is new... I didn't know where to start, and that really confused things and wasted time— hence my frustration at not having taken math in school).

 

[Integral]

Moe,
My comment was meant for the OP.

 

[moe darklight]

oops sorry. since he said he rarely got wrong answers I figured it was directed at me.

 

[Integral]

I get concerned when somebody says "I am self learning calculus, it is to easy"

I would really like to see that he has indeed got the right idea. He may have missed something major, and not even know. We can give feedback to ensure that he is on the right path.

 

[Moonbear]

Am I the only one noticing that the OP talks about being really interested in learning this material and skipping ahead, but then claims to be getting bored and lacking motivation? If the only motivation to do the work in a class is good grades, are you REALLY sure you're interested enough to be skipping ahead on your own?

I'm also noticing that you're saying the material is easy, but then comment that you're memorizing it and sometimes missing steps. That doesn't really sound to me like you're really understanding the concepts and finding it easy. Maybe the lack of motivation and the reason you're finding it boring right now is that you've jumped too far too soon and actually aren't understanding it but just memorizing it. Memorization can be tedious, boring, and very unfulfilling, not to mention sets you up to struggle later when you don't really have solid conceptual understanding, not to mention you'll be even more tempted to skip that when you have to do it AGAIN for an actual calculus class.

I don't want to discourage you from satisfying your curiosity about more advanced subjects, but if you haven't yet taken algebra 2 or geometry, maybe you're just biting off a bit too much too soon, and should set aside the calculus book for a while, and just let yourself get excited looking forward to taking a calculus course in the future so you're more motivated to do well with a more structured learning environment.

Nonetheless, as others have mentioned, if you want to keep pushing ahead, use the HW help forums to check if your understanding is where it should be before moving on.

 

[The_Z_Factor]

I get concerned when somebody says "I am self learning calculus, it is to easy"

I would really like to see that he has indeed got the right idea. He may have missed something major, and not even know. We can give feedback to ensure that he is on the right path.

Right now I find it quite easy especially easy for what a lot of my friends make it out to be. But anyways, if you want to know some of my work I've been doing, the first bunch of problems I started doing were along the lines of

Differentiate x^5, which is 5x^4

Then itd get a bit more complex, into

Differentiate 5x^5, which is 25x^4,

Then it could get into

Differentiate 3x^3+8x^2+x+10

which would be 9x^2+16x+1

then I got into marginal analysis, and Id get problems like,

Find the cost of producing x units using the equation C(x)=x^3+5 (or something like that, don't remember the problems I kinda went through the marginal stuff fast)
and have x=2 x>0

Which would be 8+5=13 so 13 dollars to produce 2 units

Then I would do marginal revenue, so Id get an equation something like R(x)=3x^2+5

And x=3 x>0

So it'd be 27+5=32 dollars

Then it got into marginal profit and actually I believe I am going to have to look that back up because I've forgotten how to do some parts of it..

Anyway it was something like revenue minus the cost to produce, and I believe you could differentiate the two functions or differentiate the new function after subtracting one function from the last but I don't exactly remember...


Anyways.. now I am doing the product/quotient/power, and about to start on the chain rule.

So the product rule is I believe say I have two functions the first one F(x) and the second one S(x). It goes F(x)*S'(x)+S(x)*F'(x).
So if the function for F(x)=x^2
and the second S(x)=3x^2+x

Running out of time right now, but I'll surely be back later and post some answers for the product quotient and power rules a bit later.

 

[Integral]

Did I not say homework fourm? Please