Grading and designing test are probably what I like the least in my work (with the discipline part). Not because of the time spend on it. I can spent hour correcting exams without problem as long as I was not the one designing them, I am given a clear mark scheme and I am preferably not grading my student (as well I am being paid for the grunt job) . It is more for the feeling it implies linked with the difficulties of matching a grade to the work.
I am not grading essay. So far, I am only giving "classical" tests consisting of many exercises for which I can make a mark-scheme to apply. I count the number of mark for each exercise, add them up and give a resulting grade. Still grading always comes with its share of hesitation,s going back and forth, comparing students' similar solutions, modifying a mark-scheme that looked so natural at first, ending up introducing half or even quarter of marks... Still not being satisfied at the end of the day.
Having read recently the Bean's Engaging Ideas Chapter 14 – “Develop and Apply Grading Criteria” – I started reflecting about grading not only math test. Honestly, I have difficulties to understand how one can grade an essay. Grading criteria can be a good way to see / show what the grader is looking for in an essay. Even if this way of grading is appealing for the Cartesian me, it is clear that the quality of an essay is more than the sum of some achievement in given criteria.
Actually, I think I understand (at least one) reason why grading is and will remain artificial as long as a task is more complex that checking a multiple choice questionnaire. This has to do with topology. If we consider all the possible essays / answers to a given (complex) question. Suppose we can provide this space with a "natural" topology based on "quality". The more complex the question is, the more continuous the space becomes. The possible answers to a yes/no question will look like the set {0,1} but the set of all possible essay to answer a question is infinite and far more complex. To me it compares more to Q or R (or a product of them) than to N. As I haven't defined a clear topology and studied the space, all this remains heuristic ;). And what is grading? This is an attempt to match this infinite set of possible essays to a simple finite discrete set of grades. It is impossible to have a one-to-one function between them. And if the set of all possible essays end up being continuous, even a continuous function is impossible. to cut a long story short, grading is and will remain an approximation, a rounding of the actual "value" of the essay.... Therefor will always remains unsatisfying to me.
I am not grading essay. So far, I am only giving "classical" tests consisting of many exercises for which I can make a mark-scheme to apply. I count the number of mark for each exercise, add them up and give a resulting grade. Still grading always comes with its share of hesitation,s going back and forth, comparing students' similar solutions, modifying a mark-scheme that looked so natural at first, ending up introducing half or even quarter of marks... Still not being satisfied at the end of the day.
Having read recently the Bean's Engaging Ideas Chapter 14 – “Develop and Apply Grading Criteria” – I started reflecting about grading not only math test. Honestly, I have difficulties to understand how one can grade an essay. Grading criteria can be a good way to see / show what the grader is looking for in an essay. Even if this way of grading is appealing for the Cartesian me, it is clear that the quality of an essay is more than the sum of some achievement in given criteria.
Actually, I think I understand (at least one) reason why grading is and will remain artificial as long as a task is more complex that checking a multiple choice questionnaire. This has to do with topology. If we consider all the possible essays / answers to a given (complex) question. Suppose we can provide this space with a "natural" topology based on "quality". The more complex the question is, the more continuous the space becomes. The possible answers to a yes/no question will look like the set {0,1} but the set of all possible essay to answer a question is infinite and far more complex. To me it compares more to Q or R (or a product of them) than to N. As I haven't defined a clear topology and studied the space, all this remains heuristic ;). And what is grading? This is an attempt to match this infinite set of possible essays to a simple finite discrete set of grades. It is impossible to have a one-to-one function between them. And if the set of all possible essays end up being continuous, even a continuous function is impossible. to cut a long story short, grading is and will remain an approximation, a rounding of the actual "value" of the essay.... Therefor will always remains unsatisfying to me.