…is better than the devil you don’t.
I just finished correcting the end-of-quarter exams for my honors physics students. While they did quite well and will be pleased with their grades, I did notice a trend that was noteworthy: several of them learned a skill or technique and applied it on a homework assignment, but reverted back to their prior knowledge and skills on the test.
One of the questions dealt with metric conversions. In their biology classes, they learned to write out all of the prefixes from milli to kilo and count the number of steps to determine how many places to move the decimal point. Of course, this only works for the range from milli to kilo, where they have a prefix for each step. Outside that range, the steps are 103 each and the trick doesn’t work. I taught them to look up the actual powers of ten, but I didn’t point out to them explicitly where and why the “count the steps” method fails. Almost all of them did the conversions correctly on the homework assignment, but several of them reverted back to the “count the steps” method for the test.
Another question involved arithmetic operations on numbers in scientific notation, specifically a formula that had numbers in scientific notation in both the numerator and denominator. I had taught them explicitly to use the “EE” function on their calculators in order to store the numbers directly rather than calculate them. I pointed out that if they didn’t do this, they needed to put the denominator in parentheses. Again, the students did the calculation correctly on the homework assignment (with most of them using the “EE” function). On the test, they reverted back to the algebraic expression, and several of them forgot to use parentheses and got a wrong answer.
I’m sure there’s a good psychological explanation for why this happens. If so, I’d love to know what it is.