Doing well in math requires students to learn and really understand theory (definitions and theorems) as well as to have a lot of practice (examples and problems). Anyone wanting to succeed cannot do only one of these, and that is true at every level, from basic algebra and geometry to graduate school and beyond. Unfortunately, many students make precisely this mistake. Some (more often non-majors) mainly practice on specific types of problems and hope this will best prepare them for their exams (it usually wonít), while others (more often majors) mainly learn the theory and think that this is sufficient to successfully continue to higher level classes (it usually isnít).

The situation is similar to learning a foreign language, although the latter involves less thinking and more memorization. Definitions are like vocabulary, theorems like grammar, examples like reading and listening, and solving problems like speaking. If you are only exposed to a limited selection of phrases and learn to repeat them but do not know much vocabulary and grammar, your conversations will be very limited. If you only learn grammar and vocabulary but do not practice much, you will also not be able to communicate well. One needs to do all of the above, which requires time, dedication, and hard work. But the benefits, particularly when math is concerned, are definitely worth it!