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.
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.