how useful are exercises in textbooks for self-teaching?

March 9, 2009 4:43 PM

in your experience, how useful is it to go thru all the exercises in a textbook to learn a subject, when teaching oneself? and how many/which ones would you pick?

this is sort of a followup/rephrasing of a previous question of mine (http://ask.metafilter.com/80954/Research-on-effectiveness-of-exercises-in-learning). i was really asking the wrong question given my intent back then. i find that some exercises are absolutely useful to solve, but others don't really teach me much of anything and take lots of time. i want to spend as little time as possible on the exercises, but i do really want to learn the subject thoroughly, and that is much more important than speeding thru for me.

posted by tehgeekmeister to Education (9 answers total)

Here's a link for the lazy.

In regards to your question: it all depends on what you want to learn, how much you know about the subject already, what you want to do with the material, and how you learn. Some people can read something once, it will make sense, and they can apply it. Others need to study it, try it out, review it, and try again.
posted by filthy light thief at 4:47 PM on March 9, 2009 [1 favorite]

Best answer: Do the exercises that challenge you and skim the one's that you assume you can answer without a doubt, but make a note of them. Then check the answers that you worked out, and your notes for the skipped questions. Then, and this is important, pay attention to what skipped and attempted questions you got wrong, figure out the underlying idea each was meant to teach and study that. Then compare the skimmed, but correctly answered questions to the correctly answered questions you worked out and find your weaknesses. Do this for 2-3 chapters/lessons and you'll learn how important ideas are presented, how the authors write, and what you are or are not picking up.
posted by Science! at 5:02 PM on March 9, 2009 [2 favorites]

When I was studying engineering, there were some courses that I simply never attended. I read the textbook and did every exercise, both the ones inline in the section (solved for you) and also those at the end of the section. I'm sure I would not have as well if I had skipped some questions.

i want to spend as little time as possible on the exercises

is in direct conflict with

i do really want to learn the subject thoroughly.

I suggest you do every single one, even if it's repetitive or tedious. Repetition is a great way to learn.

Caveat: If you don't have the answers, and have no hope of ever knowing if you were right, forget about the exercises. It's too frustrating to never know if you got the right answer.
posted by Simon Barclay at 6:42 PM on March 9, 2009

* ...not have done as well if...

I wasn't studying English, evidently.
posted by Simon Barclay at 6:44 PM on March 9, 2009

Even better is working them in a group. If you have been well educated, plan to work similarly hard in the future, and can find someone else there is nothing to lose by helping each other learn the tricks. Because the problems always have a trick, and that trick will be used over and over once you get into the field. There is something to say for having the creativity to solve new types of problems, but that is not the same thing as you are asking here. [The best colleges usually encourage collaboration on problem sets, but require individually handed in papers.]
posted by gensubuser at 6:47 PM on March 9, 2009

Lots, and lots of them. My method for calculus, physics and linear algebra at uni was: do all of the exercises in my textbook, then borrow textbooks from different authors from the library, and do more exercising.

Having a large base of material to choose from, and assuming exercises are sorted in growing order of difficulty, my time would be split more or less as follows: start with a few exercises from the beginning, skip quickly to mid-chapter, marking the skipped exercises, proceed to full blast, then resume in reverse order (harder to easier) with the skipped exercises to cool off. Harder exercises would be taken on several times, possibily with different approaches.

18 years later, d(x^xx)/dx still eludes me, though.
posted by _dario at 7:21 PM on March 9, 2009

Also, read the introduction to the text. Often, there is an answer key for even-numbered exercises, which may be more or less difficult than odd-numbered ones.

And do not let yourself get over-stuck. It is ok to do all the easiest ones first, then go back.

and with ^ standing for exponentiation
d (x^(x^x))/dx
= d exp(log(x)*(exp(log(x)*x))) / dx
= exp(log(x)*(exp(log(x)*x))) * d ( log(x) *(exp(log(x)*x) )/dx
= exp(log(x)*(exp(log(x)*x))) * (exp(log(x)*x)/x + log(x) * exp(log(x)*x) d( log(x)*x) /dx)
= exp(log(x)*(exp(log(x)*x))) * (exp(log(x)*x)/x + log(x) * exp(lox(x)*x)* (1 + log(x)))

= (x^(x^x)) ( (x^x) ( (x^x)/x + log(x)* ((x^x) + (1+log(x)))
posted by hexatron at 8:06 PM on March 9, 2009 [1 favorite]

...I think that was correct till the last line, which should be

= (x^(x^x)) (x^x) (1/x + log(x) * (1+log(x)))

(I just had to work it out myself... it's been a while.)
posted by alexei at 12:40 AM on March 10, 2009

Well, I wrote one too many (x^x) on the final line of my solution -- (the line above it is correct except for substituting one lox for a log and not including a bagel & cream cheese)

But I was really more impressed with dario. I never knew you could stack subs and sups.
Like A^BCD_EFG or A_BCD^EFG

or X^XXX^X(1/x + log(x)*(1+log(x)))

and for lunch _meatball^minestone
posted by hexatron at 5:30 PM on March 10, 2009