A large number of students failed a statistics exam that I gave recently. Comparing their grades to previous times I’ve taught the course, I noticed that students typically do the worst on this exam. Because a few students needed to take makeup exams, I had a few extra days between grading and giving the exams back to consider what had gone wrong. To me, the exam seemed fairly simple and straightforward. To my students, it seemed nearly impossible. Thinking about this led me to what I have decided to call the divergence of memory and understanding.
I am fairly certain that the courses students deem “difficult” are the courses that require them to retain knowledge and build on it as the semester progresses. Foreign language, natural science, and statistics courses all require an understanding of the information discussed in week one for success in week nine. Unfortunately, students tend to postpone studying until the last possible moment, which privileges memory over understanding and prevents them from building a foundation of knowledge that they can use later in the semester. As I’ve said before, this is like waiting until the night before a dentist appointment to start brushing your teeth. For most students, the results will not be pretty.
On earlier statistics exams, then, students were able to remember the required steps of calculating, say, standard deviation when studying, which allowed them to do fairly well on the exams without ever developing a knowledge of how standard deviation works. Toward the end of the semester, however, the amount of information that they would need to remember includes information stretching back to the beginning. For a student who understands the basic concepts, doing well is like adding a few bricks to the top of the house they have been building all semester. For a student without this understanding, though, doing well is like remembering the instructions for building a complete house and then trying to build that house during an hour and twenty minutes. Their memory is no longer able to make up for their lack of understanding and the task itself seems incredibly daunting.
As an instructor, the most frustrating aspect of this realization is that it is difficult to gauge real understanding in a statistics course using standard statistics-type assignments. If students do well on assignments and exams early in the semester, it seems like they are understanding when they may simply be remembering. I have always thought of statistics courses as a bit of respite from the long-hours spent grading papers and essay exams. It seems, though, that I might need to change my own approach in order to help students change theirs.