If a student gets it wrong are they confused or underprepared, or did they choke or panic.
When I’m working with new teachers and we’re discussing making up items for a test, I like to ask them, about a problem they are proposing, ‘What do you learn if they get it wrong?’ This is usually in reference to a problem that has some extra complexity that will most likely prevent many students from getting to the point of the problem. For example, for a problem that is supposed to test a student’s understanding of the Quotient Rule, but is so algebraically complex, that if the student has weaker algebra skills, they will get beat up by the algebra before they even get to the QR.
So if a problem is written well, I expect that if a student gets it wrong then he or she was either confused about the underlying material or didn’t prepare well for the test.
I’ve gained a new perspective on this question after reading an essay by Malcolm Gladwell, from What the Dog Saw. In this he discusses the difference between choking and panicking, as other possible situations of ‘getting it wrong’, and it has some interesting things to say about student failures.
In panicking, a person forgets what to do, or tries to do things that are totally inappropriate. In a testing, this would be the case where a student makes up a (non-working) technique to solve a problem, or the case when they just go totally blank. The basic solution to panicking, is preparation through practice. There are also issues related to relaxation/anti-anxiety. Through practice and some exam assistance, if needed, most students can be helped to overcome panicking.
In choking, a person forgets the sort of fluency that they have developed and revert to an approach based on just using basic skills. This would be like the student who solves a complex Chain Rule problem by actually expanding out the function before taking the derivative. It seems that choking is harder to control because becoming aware that you are choking or even fear that you will choke can often make you choke. I don’t really know if you can help someone with choking without deep involvement.
Understanding these new possibilities gives me a new basis for thinking about assessment and the issues that students might face.