Testing Cumulative Knowledge

"Education is what survives
when what has been learned
has been forgotten"

B. F. Skinner, Behaviourist

In the liberal arts it is assumed that the intent of both the student and the institution is the development of an educated worldview. A worldview that will be useful to the student in developing an attitude towards new knowledge and contextualizing life experiences. There is also an expectation that the education will be "useful" right out of the box. That expresses the hope that a graduate will have developed a mastery both of content (direct knowledge) and process (how to learn and teach).

In chemistry, knowledge is cumulative. Just as in a language, progress can only occur when the student has remembered the previous lesson(s). In fact, the language of science is mathematics (or more correctly the mystical symbols that we use to capture our thoughts about mathematical truths). In math, knowledge and content and progress are intimately linked in an upward spiral. As we fall way from the maths into the physical sciences and then the natural sciences or more observational sciences we begin to see the disciplines becoming so chopped up that it is possible to develop courses that are completely self-contained and there are no expectations of knowledge prior to the course and indeed no consequences to forgetting, after the course.

Into this tension between the global goals of the liberal arts education, usefulness and continuity of knowledge comes the physical sciences professor. When I started out, I taught at three different universities in four years and at each university they had me attend their "Teaching Essentials for New University Professors" full day symposium thingy. I went for the brownie points, free lunch and the chance to escape diaper duty for a full Saturday. Anyhoo, in all of the presentations it was made clear to us that a fair test only tested topics that had been clearly covered in the course and were completely covered in the supporting readings for the course.

In my courses, where there is a clear link to the content of a previous course (for example second year organic chemistry and first year general chemistry) it is my habit to have a mid-term test in the second week of classes. This mid-term will only test material from the previous course that is directly related to topics that will be taught in this course). In my opinion it gets all the students walking in the same direction, cleans up any differences between in-house and transfer students and it forces them to realize that there are some principles so fundamental that they form connections between prior knowledge and the current course.

For this I am constantly harassed by the students and my fellow faculty. In response, I voice the ideals that I used to begin this post. We have enough of a liberal arts tradition in our university that the ability to invoke the ideals means that I have thought this through and people will leave me alone. The only concession that I have made over the years is that I will have three mid-tern tests and will allow the student to have the lowest test mark dropped. Personally I think I caved on the ideal but there is a direct link between how a student does on the first mid-term and the final exam.