I have two questions about fairness and value in relation to achievement. Suppose student A works very hard for his exam results and gets the grades he wanted. Suppose also that student B is much lazier, putting in significantly less effort, but achieves the same results due to their greater "natural" ability. Firstly, which student's achievement, if any, is of greater significance or greater value? Secondly, is it fair that student B achieves the same results as student A without putting in the same level of effort (albeit the same level of effort was not required from student B due to his greater "natural" ability)?

The answer to both questions depends on whether you look at "inputs" or "outputs". If you look at inputs, it is clear that A's achievement is more remarkable, more praiseworthy, and in this sense more significant and valuable. But we must also look at outputs, because an education system is, after all, preparing people for professional roles. Thus think of patients in need of an operation or passengers depending on a pilot's skills. For them, output matters: a better surgeon or pilot is better for them even if another made much greater efforts to reach a slightly lower level of skill. So the best justification for designing exams so that your students A and B do equally well appeal to the interests of the public in having positions filled by people likely to do well in them.

Is it fair to distribute professional opportunities by achievement (output) rather than effort (input)? I think the examples of surgeon and pilot show that we have strong reasons to do this. An additional reason is that effort is very hard to measure, especially when it fetches special rewards that give everyone an incentive to pretend to make great efforts (so, if effort were rewarded, your B might pretend to be poorly endowed and to be working very hard). Nevertheless, I agree that the focus on outputs is unfair. But, since it's difficult to reward effort reliably (as I have said), the best way I see for mitigating the unfairness is to reduce socioeconomic inequalities. This would not be a gain in fairness in your comparison of A and B. But it would mitigate the unfairness of gifted people earning hugely more, with equal effort, than less gifted ones.

The answers to your interesting questions depend on how we understand 'value' and 'fairness'. In some contexts we value outcomes more than efforts. So, if our goal is to target students who are most likely to understand difficult material, we may value the one who can understand it without too much effort (your Student B), especially if we think we can motivate her to work harder in the future. If we have reason to think that your Student A will be unlikely to understand quantum physics or Kant, no matter how much effort he puts in, and if, say, a graduate program is looking for students who can advance physics or philosophy, we will value B's abilities more than A's, and our grades may reflect that assessment of their respective value in these terms. Clearly, we will value student C, who has the capacity to understand these subjects and the hard work-ethic required to succeed more than A or C. But (perhaps mistakenly--see below) we tend to think that people can increase their work-ethic more readily than their 'natural' intelligence. (Similarly, in sports we tend to value both ability and hard-work ethic, but in the end we tend to value the outcome of who performs best, so we may not care that much about how the athlete got there.)

If our goal is to target students who are most likely to work hard, then we may value A over B, and our grades should reflect our assessment of that value. Perhaps willingness to work hard at an early age is more predictive of success than assessment of knowledge, in which case grades that assess willingness to work hard will be more appropriate to assess that value.

Whether the grades are fair then turns on whether they assess what they are meant to assess (what we target as our "currency" of value), and more importantly, whether the students and those who see the grades are explicitly informed about what the grades are actually assessing. Most teachers (e.g., me) are not explicit enough about what their grades are meant to assess, or which of their assignments and grades are meant to assess effort vs. understanding vs. both. But in the end, most grades probably assess how much the student understands the topic or demonstrates the skills the course seeks to hone. As such, they do not differentiate between whether the student demonstrated that understanding or skill based on her previous knowledge of the topic or her 'natural' abilities or based on her hard work or based on some combination. But fairness here seems to be largely a matter of being explicit and open about what grades are designed to assess.

One thing that might be more fair is for teachers to reward improvement based on hard work by making their final grade an indication of what the students are capable of doing at the end of the course, rather than an indication of their grades averaged over the entire course. If your student A got C's at the beginning of the term but A's at the end, whereas your student B got A's throughout, most teachers will give a higher final grade to student B. But perhaps that is neither fair, nor an accurate assessment of their current abilities. Indeed, it might be more fair to indicate in some way that student A seems to have more potential.

Finally, your questions get more philosophical when we think about how much control people have over how hard they work. We tend to bifurcate things the way you have--natural abilities (and perhaps limitations) vs. effort (hard-work ethic)--and think that the natural abilities, like physical beauty, are largely beyond our control and sets some limitations on us, whereas effort is entirely within our control and hence limited only by how much we freely choose to exert it. But things are surely more complicated than this. It is very hard to know what comes naturally to people, and one thing that may come more naturally to some than others is hard-work ethic (not to mention luck in finding some activity they enjoy in a way that makes them want to work hard at it).

Although the question is framed in terms of justice, fairness, and value, I would like to consider it in terms of attitudes towards knowledge and learning.

According to the psychologist William Perry's "Scheme of Intellectual and Ethical Development", students who have what he called an "early multiplistic" attitude towards knowledge believe that all questions have answers and that all problems have solutions, but that there are two kinds of questions or problems: those whose answers or solutions we know, and those whose answers or solutions we don't know yet. Such students see their task as learning how to find the "correct" solutions. And students who have what Perry called a "late multiplistic" attitude believe either that most problems are of the second kind (hence, everyone has a right to their own opinion) or that some problems are unsolvable (hence, it doesn't matter which--if any--solution you choose). (What I've summarized here is a vast oversimplification for present purposes.)

Such "multiplistic" students believe that teachers don't have all the answers any more than the students do. Hence, they also believe thatit is only fair for teachers to grade them on the basis of the amount of work they have put in, rather than on the results they obtain. So, in the questioner's scenario, student A is seen as deserving at least as high a grade as student B.

It then becomes the task of the teacher to help such students realize that merely working hard (especially if such work does not result in solving the problem) is not sufficient. Instead, the student must work efficiently (or effectively) so as to solve the problem: The problem may be solvable in different ways, and the value of the solution may be relative to the context in which it was solved (Perry calls this the perspective of "contextual relativism").

In various courses I've taught in which students have complained that the amount of effort they put in should be worth something in terms of their grade (even if they failed to solve the problem), I have offered them the following option in future assignments: If they have put in a lot of effort without solving the problem, then they could turn in a document spelling out how they went about trying to solve the problem, analyzing why they thought their methods didn't work, and suggesting other techniques they could have tried had they only had more time to work on it. I can then give them credit, not merely for working hard, but for working more efficiently.

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