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A Better Approach to Quantitative Courses - Part 2: Solving Problems

Math and science are learned by doing

Practice problems are the primary means through which you will learn course content in quantitative courses.  Making the best use of problems will help you learn as quickly as possible and be well prepared for tests.

Misusing practice problems is a waste of study time and can lead to a false sense of mastery and/or confidence.

 

Start with the problems that were done in class

(Ideally) without looking at the solution in your notes, re-do any problems that were demonstrated in class.  Do this within 24 hours of lecture to prevent forgetting and store what you learned in class in your long term memory.

 

Study in short, frequent sessions

You will learn most by taking short breaks every hour and studying a little every day.  Cramming is always a bad idea, but it is especially ineffective for quantitative courses.

 

Stop solving easy problems

If you start working on a problem and see that it’s easy for you, STOP.  Go on to a harder problem.

 

Don’t re-do problems!

Students who do the same problems over and over memorize the problems’ solutions, even if they don’t intend to.  This can lead to false confidence.

Sadly, getting 100% on a problem set the fifth time you do it doesn’t usually mean you’re going to get anything close to 100% doing unfamiliar problems for the first time in the high pressure setting of a test.

If you had trouble solving a problem the first time, try it again (without aids) after a few days of practice.  This can consolidate what you’ve learned and be a confidence booster, but you should use this technique very sparingly. Most of your study time should be spent solving questions for the first time, since that’s the skill you’ll need on the test.

 

Do lots and lots of problems

Learning university-level math and science is hard work and takes a long time.  Many students need to do more than the assigned homework to master the concepts taught in class.

Only you can judge whether you’ve truly mastered a concept – don’t assume that just because you’ve done the assigned problems you’re necessarily ready for the test.

 

Do problems from different sources

Just like writers of novels, problem authors have different ‘styles’.  Solving problems from lots of different sources introduces you to different styles, so you won’t be thrown off when the midterm problems have a different author than the textbook problems.

Find extra problems in previous or practice exams, other textbooks (look at the library, SFU bookstore or other college/university libraries), or web sites (e.g.: the Khan Academy or MIT Open Courseware).

 

Don’t practice a skill that will never be tested!

Lots of students start problems by looking at the solution in the answer key and then figure out how to start the problem from the answer.

Every time they do this, they are teaching themselves the skill of solving problems from a known solution.  This skill will almost never be tested.

If you’re stuck on a problem, find similar examples in your notes or textbooks, look online for help or ask a classmate, TA or prof.  Hints that give you the first step teach you how to get started on problems – a skill that most definitely WILL be tested.