Wednesday, December 6, 2006

An Answer is not Always a Solution

Students benefit from the whole concept of part marks. There is of course a tension that immediately develops concerning the nature of a correct response to a question. Does the question require that a final correct answer is the key objective or does the question imply that the student should follow a path to the correct answer and that the path may in fact be more important than the destination itself. In my mind I have always distinguished between the answer and the solution of a question. This has everything to do with part marks.

The answer to a question is brief to the point of a single number with units. A solution describes a complete path from the question to the final answer.

If students expect part marks for solutions that have incorrect final answers then they must also be willing to accept only part marks if the solution is incomplete even if the final answer is correct. The problem of course is assessing where on the path did the student make a mistake and does that demonstrate a simple slip or actual lack of knowledge. On the other hand, does an incomplete solution indicate a quick mind that recognized a step as trivial or does it mean that when asked a different question where the step is not trivial they will fail to get a correct answer?

A solution may be brilliantly set up and sweep majestically to the wrong answer or a solution may be a crooked wreck of a thing that tails across the page as a yard of toilet paper stuck to your shoe but still gets to the correct answer.

In math the rigour is very high and it is assumed that all steps will be explicitly shown. A good solution at the end of a long path in math is therefore followed with the majestic Latin acronym Q.E.D. (quod erat demonstrandum "that which was to be demonstrated"). In physics, the handmaid of mathematics, it is expected that a solution will consist of a number of parts including a suitable diagram that establishes the frame of reference with the relative positions and magnitudes of the elements of the problem. This is followed by stating the relevant given information (converted if necessary to the form required for the solution). The standard form of the relevant equation is then given followed by the form that isolates the unknown variable. The symbols are then substituted with the numbers from the problem and the math completed to give a final answer. In Physics it is usual for the solution to be completed with a very brief statement of the final answer to the problem.

Chemistry is the wayward child of Physics and thus follows the intent, if not the complete form, for a solution as that in Physics. The structure is the same but usually a diagram is not required and a completing statement is generally not necessary as long as the solution sequence gives a clear final answer.

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For a while it was all about research and then it was all about teaching and now it's all about trying to find a balance while teaching at a small liberal arts and science university.