Eric Sasson asks: > I have found it to be the case that the best way to test my understanding > of something is to discuss it, or even better try teaching it to somebody > else. What > are other ways in which we can test whether or not a student has learned > something? > > It seems to me that the method used most often now is to give written > examinations. Exams however tend to test a student's ability to DO > similar (if not essentially identical) problems. It was rare in my > education that I was forced to discuss concepts in math class.
While I agree that being able to explain, discuss, and teach a concept is one of the best ways to test one's understanding and that most written exams merely ask students to recall and repeat problems done in class, it seems to me that another way to test understanding is to apply a concept in a novel situation. My high school calculus exams always presented problems we had never seen before, although they used the same concepts we had covered. In this way my teacher could tell whether we had grasped the concepts or just the calculations. In a subject such as high school mathematics, whose primary value is in application, how can we balance the use of discussion to promote learning and written exams to test ability to apply the learned concepts? Andrea Hall AndiHall@aol.com