Now that I am in my final year as an undergraduate, I have been taking a little time to look back at what classes I have taken, what I was supposed to learn, and what I actually learned. And I am disappointed by the disparity between them. I actually planned on writing about this last semester, but I only had examples of poor and mediocre courses to work with, so I put it off. Now I have an example of what a good test looks like, so that is what I will discuss here. Lest any of you be concerned, I have the professor’s permission to write about this.
Several of the problems with introductory-level classes were discussed in the staff editorial for last week’s issue of The Poly. However, what were not addressed are issues in 4000-level courses. The majority of tests I have taken in upper-level physics and math (those are my two majors) courses have followed the same pattern: to study, memorize the equations; during the test, look at the information given for each problem and use a memorized equation to solve it. Occasionally, I have been asked to apply what I have learned to a new problem. Rarely have I taken tests where more than the necessary information was given. And never have I had a test where I needed to contend with incomplete information.
Up until this semester, I could have done better on every test I have taken if only I had the textbook for the course and a little more time. I realize that sounds like “I could have done better if only I knew all the answers,” but I will give an example. For the class Introduction to Numerical Methods for Differential Equations, many of the test questions amounted to “use a method of your choice to solve this differential equation within the specified accuracy.” The thing is, I could hand someone else at this school the course textbook and they would be able to answer that question without ever taking the course.
So what should I tell companies that I want to work for? That they could, instead of hiring me, buy a $150 textbook? If I had to answer that question, just using my coursework as a justification, that is the answer I would have to give.
Now, let’s take a look at a question from the good test I mentioned above. The task was to identify a pathology involving a specified protein and then to develop a treatment for that pathology. So instead of simply needing to memorize an equation and solve a simplistic problem, the knowledge I must have is how to search databases of primary research articles for relevant papers and then use my knowledge to create a new solution to the disease I choose. The other questions on this exam focus on similarly broad skills such as determining if data given in a research paper supports the conclusions, developing hypotheses, and designing new experiments. My textbook for the course serves the same role as a dictionary or thesaurus would: a place to look up what I don’t know or haven’t memorized.
Now it’s possible that this is something that only biology classes can take advantage of, right? Well, no. Without even thinking about it, I have a question of this caliber that could be asked on a numerical methods exam. “What is the minimum error that can be achieved for a real-time solution to a differential equation?” For instance, if one were to model the regulation or feedback in a biological system, the model would run at the same rate as an experiment testing the same mechanism, allowing real-time comparison of the data.
I hold this question up as a good example because it requires analysis and evaluation of numerical methods, not simply rote memorization. It requires that a student know what questions to ask, better equipping them for when they encounter material they have not seen before.
It seems to me that most of the exams I have taken here were designed for an era when information was not as easily available as it is today. From my experience, the shallow problems that these tests present do not assess the skills needed for current jobs in industry.