“What’s on the exam wasn’t what was covered in class.” (Or, equivalently, “The exam
was nothing like the homework.”)
The problems on the exam are over the same concepts that were taught in class. The key
is to properly organize the information in your mind so that it is recognizable in a
different framework.
Many times, students don’t recognize when questions on a test are the same as those
discussed in class or assigned for homework. Knowing when you know something is a
difficult thing. Look over the exam and your homework problems to find similarities.
Then, ask your instructor to look at the exam with you and point out where the concepts
were the same as on the homework. Many instructors give exam objectives, and the
same can be done with those objectives.
It’s helpful to do this then try to figure out why you didn’t realize that the same concepts
from class and homework were on the test.
Doing your homework in an effective manner can help with this a great deal. Here are a
handful of tips:
-Read the problems carefully, making sure you know what is being asked and
what information is given.
-Try to visualize what’s going on (drawing pictures and graphs when appropriate).
-Try to formulate and implement a problem solving strategy. Make sure that you
understand each stage of your reasoning.
-Redo homework problems a few days later to see if the material has “stuck.”
It may also be helpful to use the following guide with each homework problem to see
how much you really understand. Be sure that if you rate your understanding at a Level 3,
4, or 5, you can justify your rating with evidence.
Rating (Rating criteria are cumulative.) 0 I have no idea – I don’t think I’ve seen any problem like it before. 1 I understand the teacher or tutor, but I haven’t done it on my own. 2 I can do the problem, but am not sure why I take some of the steps I do. 3 I can do the problem and have a method for checking so I know my answer is correct. 4 I can explain each step of the problem (how and why) using the correct mathematical language and notation. 5 I understand the underlying concepts well enough to apply them to problems I have never seen before. Students feel a definite security in seeing problems identical to what we did before, but to
emphasize these problems on exams would be to validate rote learning alone. In
mathematics, we do homework for the purpose of learning the material, not the other way
around. Use the class period as a guide to what your teacher thinks is important, and be
sure to read the text. As you work homework problems, try to see the bigger picture: why
am I being given this problem, and how does it reinforce and relate to the theory? Also,
the test problems may be closer to the homework than you recognize, but you may be
falling into a rote mode as you do the homework. If your teacher does not use the precise
wording of the book, or blends several problems, you may then feel lost. Scramble the
order of the problems you work as you study for tests. And browse through other books
in your library, and study with friends so you can verbalize the material as much as
possible, in many different ways.