Wait! Don’t start solving problems yet!
Many students think that the key to success in math and science classes is solving lots and lots of problems. This is a necessary step, but if you want to get superior marks, you should first consolidate your learning and deepen your understanding before you turn to problem solving. If your knowledge of a concept comes entirely from problems, it will necessarily be limited by the scope of the questions you’ve answered. Broadening your understanding before solving problems means that the details of particular problems are placed within a larger cognitive framework, and the problems become examples rather than everything you know.
When a test introduces unfamiliar problems or new applications, a student with a firm conceptual foundation will be able to think creatively and apply their knowledge in a new way. A student without a broad understanding is more likely to be stumped by the demands of hard problems: “but we never did an example like this in class!” Precisely! That’s why the professor included it on the test – they wanted to test your understanding of the concepts taught in class, not just your ability to mechanically apply problem solving steps.
Build a conceptual framework by summarizing the material from lecture and readings in your own words. Some students use mind-maps, diagrams or note cards. Another good idea is to write a one page concept summary. Name the concept, list the key equations, define the terms, list additional information and write your own example.
But don’t skip the homework - math and science are not spectator sports!
Never assume that you know the content because you understood the problems demonstrated in lecture. There are two big problems with this (very common) assumption.
First, following a demonstration and being able to do something by yourself are not the same thing. Think of how hard it was the first time you drove a car – it looks so easy when someone else is doing it! Understanding lecture is the first step. Being able to solve problems by yourself without any outside aids usually takes hours of practice after the initial demonstration (just like driving).
Second, the problems done in class are meant to introduce concepts, not show the full range of applications. Examples done in class are usually easier than test problems.
Skipping assigned homework is probably the most common error that students who are new to university quantitative courses make. This might have worked for some high school math and science courses, but it’s the “express bus” to failure in university.
Like a good scientist, test your hypothesis (“I understand everything!”) by always doing the homework after lecture.
For more information on concept summaries, see:
- Video: Math – Problem Solving II
- Fleet, J., Goodchild, F. and R. Zajchowski (2006). Learning for Success: Effective Strategies for Students (4th Ed.). Toronto: Thomson Nelson, pages 113-116.