Mastering Math: The Importance of Re-reading and Understanding

[Howers]

Is it common to re-read entire sections of math?

Whenever I study advanced math, I always find that I need to read a section two times over two days to understand any of it. This can even require more re-reads if the section is highly theoretical (ie. first exposure to precise limits). I spend about 10 minutes trying to prove each theorem/lemma, and usually fail :)

Then during exam week, a third and final re-read will solidify the material and I will feel I really understand what is going on. Especially since I've already had practice with the exercises. Its really strange how it sort of grows on me.

Great... but requires tremendous amounts of time. I can't help but wonder, are there people out there who can get math after one sitting? It really puzzles me how one can come up with the material that I have great difficulty understanding.

I never have this difficulty in science. In under 1 hour and one reading, I completely understand a chapter. And I know other people in my class who struggle with science. So if they clearly show signs of being weak in science, am I showing signs of being weak in math?

 

[symbolipoint]

Yes.

Studying Mathematics using textbooks (including as used according to classroom instruction) nearly always requires reareading, several times. Ten to fifteen pages of material and exercises assigned from them can take-up ten to twelve hours per week OUTSIDE OF CLASSTIME. All this is often true of sciences, too.

One more important thought: Sometimes, "...twelve hours..." per week is not enough.

 

[tmc]

Two times? Heck, sometimes I have to go 10+ (which is why I like very compact, 'strong' books).

Something that one of our profs kept trying to hammer into our heads was to always keep rereading the material until you understood it. Read it front to back, then back to front. Then start at the middle. Then just read random sections. Then read the whole thing again. Pick up all the small details you might have glanced over, etc.
He definitely was a strong believer in reading over doing (although this was a very theoretical course were there were just a handful of possible exercises to do, so we didn't have a choice but to learn by reading).

 

[Howers]

This is undergrad though. So none can zip through math?

 

[symbolipoint]

Howers, you are missing the characterisation of the kind of effort to succeed in Mathematics. Undergraduate Mathematics courses are difficult to learn, although most of them (for lower division "common core" courses) ARE learnable. Hoping to put in "just enough effort for a C" is a bad general plan. You may very well find that in order to achieve a C grade, you could need 2 or more hours of study every day, outside of classtime, all combining reading, rereading, working example problems, and working on assigned homework exercises, and working a few extra exercises, and often rereading again.! Additionally, if after this kind of effort, you earn less than a C, then you have two choices: You either restudy and officially repeat the course, or you change your educational major-field objective. If you truly do put in the required kind of effort and earn less than a C, then YOU are the person who can best figure out why you are having difficulty; you can not rely on someone else to figure out what your problems are.

If you do choose to repeat course, be sure to figure out what are your weak areas from any prerequisite courses and LEARN THEM WELL; and restudy as much of the course in which you earned the low grade as possible before you enroll the second time. When you officially enroll and attend the second time and you do not earn at least a C (should actually be a B or better this time), then either you (1) have too many course this term, or (2) are not studying properly, or (3) really need to change your major.