…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.
Performance always degenerates under stress. One way to mitigate that is by overtraining, so that whatever’s left after stress takes its toll is still enough to get the job done. In the case of your students, if their level of ability with metric conversions is “I can figure this out by counting on paper when I’m not pressured”, then sufficient overtraining might be “I can see an exponent and immediately tell you how many decimal places it’s going to be”.
Another mitigation technique is to practice under stress, but that’s probably not very useful in a classroom situation where you need the time to just teach them the material in the first place.
I think the underlying problem is that tests are stressful.
Also, looking at the exponents should be considered proper procedure, not “overtraining”.
State-dependent memory — retrieval of memory is easiest when the internal state that you’re in when you’re remembering something matches the state you were in when you learned or rehearsed it.
http://dailypsychologylesson.wordpress.com/2011/07/21/context-dependent-and-state-dependent-memory/
Some darts players claim to only be able to play drunk. That’s likely because they learned and practiced drunk.
IME, even if you can’t actually learn in the appropriate context, you can imagine that situation and, in your mind, rehearse performing or remembering as you need to. I’ve had teachers who simply said “Now, when you get to this question ON THE MIDTERM, what are you going to do?” which sure evokes the context for me!