How to evaluate students in a “do all you can” exercise?

Question

Imagine a math problem that consists in doing all sum operations you can in 2 minutes.

And then imagine these are the correct operations each student has done (each list entry represents a different student, it is ordered to keep it simple):

1. 4 correct
2. 7 correct
3. 10 correct
4. 11 correct
5. 12 correct
6. 12 correct
7. 15 correct
8. 15 correct
9. 17 correct
10. 22 correct

One way of evaluating it would be based on the overall students performance (maybe < 10 not passed, > 16 excellent). But I don't see fair evaluating a student based on another student performance.

Another way I though would be to set each "milestone" myself. For example > 6 passed, > 18 excellent but I was not the test author and students didn't know about that "milestones".

So, do you have any idea of what could be a fair option to evaluate students in an exercise of this kind? (It is a real case.)

Thanks!

Answer 1

You should try to have a feel for what level of skill you want. Now, this is not an easy problem. Much more exploratory and Bayesian. (But actual teaching/pedagogy is different than Euclidean if-then logic of math itself.) There are ways to estimate this. Previous class performance. What you think they need for the next lesson or year. Your own performance. Or the excellent suggestion of having another teacher try the task (could just try a few numerate, but non teacher adults also).

It would help a bit if you told us what sorts of addition, you gave. But assuming they were no longer than two digit problems, I would say something like 20 is reasonable. Kids can learn speed at easy operations. But first try it yourself and see how fast you can do it. Just the act of actually doing the test will give you insights, different than purely observing.

Answer 2

I find it unfair to give the student a task where they don't know what they need to achieve to get the best grade.

I would ask another colleague(s) to do the task. These colleagues should be expert but haven't seen the task before. Then I take their average to be equivalent to the full grade.

On the exam sheets, I inform the students how many correct operations they need to do to get the full grade.

Answer 3

If your students are 7 years old, I believe you are asking the wrong question. At this age I would not try to be fair, but try to motivate them. To me this has much to do with evaluating each student with respect to their efforts. So (to me) the question is not "how much does student A know compared to student B", but rather "how much effort did student A put into learning the current subject". Since math exams at the age of 7 are unable to achieve this goal, I would try to be generous. In addition I would ask myself: Do I motivate my student by telling them, that the marks are given w.r.t. the other students? If you are not telling them this fact, then it really doesn't matter.

I'm teaching at the university level. Unfortunately, the classes are too large to know every student personally, so at first sight it seams to be hard to judge on an "effort scale". However, my students have to work on problem sheets and use an online platform to hand in their solutions. These "problem sheet grades" partially add to the grade achieved in the final exam. However, what the students don't know is that I use these "problem sheet grades" to estimate their effort. In every exam there are extra points, which could be argued either side. Either I am generous and give half a point for a partial solution, or the solution is insufficient. Thus, even at this stage (20+ years old) I do not try to be fair, but rather try to motivate them by judging them on an "effort scale".