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In Chile, we score from 1 to 7 (this is a legal normative), where 4 is the minimum grade to pass. Thus, the passing grade corresponds to halfway point (50%) of the grade span (from 1 to 7). However, it is common practice to require a minimum score of 60% to pass (e.g. 6 points of 10). This creates a dissonance between the minimum grade and the minimum score to pass.

If we use a minimum score of 50% (4) to pass, we use a linear function to assign grades. However, if we use a minimum score of 60%, we need two functions to calculate grades from scores. In other words, the function breaks at the minimum grade to pass, such that points at the bottom (below 4.0) are worth less than the points at the top (above 4.0).

Having two functions to assess the performance troubles me. In other words, people that have more troubles in the course are being evaluated with harder standards than the ones with better performance.

One solution to this problem would be to change the grading scale. Unfortunately, this is not legally an option in the short term. A second solution would be just to drop the minimum passing score of 60%. But I think sometimes you may need to increase the grading difficulty because of the importance of the content you are teaching.

Under those circumstances, what is the better solution in this case: a single linear function or two different functions to grade scores?

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    I've tried to tighten the grammar/wording a bit. Please feel free to edit/roll back changes if I accidentally changed the meaning of anything! – tonysdg May 29 '17 at 19:30
  • I think your math is wrong. If 60% (of 7) is 4.2, 50% is 3.5, not 4.0. – Glorfindel May 29 '17 at 20:13
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    @niklai in English, approve is to accept something. The translation of "aprobar" is to pass. – Davidmh May 29 '17 at 21:23
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    "people that have more troubles in the course are being evaluated with harder standards than the ones with better performance." Surely the two segments meet at the cut-over point, resulting in a different marginal return, but not a different slope across the whole range. Which implies that everyone is held to the same standard on the easy questions. Then in practice the harder questions (which the poor students likely won't even attempt) are worth more, although due to sloppiness some of the better students might lose a few points on easy questions. – Ben Voigt May 29 '17 at 21:25
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    Many courses end up having whatever curve results in separation of failing, merely acquainted, competent, expert, and outstanding students into the corresponding grade ranges. Whether you do this by changing the curve or changing the difficulty variation matters little; the end result is quite similar. – Ben Voigt May 29 '17 at 21:28
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You should focus on getting the grading correct for students who do much better than just passing, who score within the range where you would personally draw the line between who is an expert who has completely mastered the subject and who is good but needs to study a bit more to be considered to be an expert. This line is not usually at 100% because you can make minor errors even if you are an expert, it's more typically somewhere between 80% and 100%. You then want to assign some grade, say 7 to students who are at or just above that boundary, which mans that the boundary percentage should be mapped to 6.5.

The goal of teaching is to assist students who do their best and may go on to embark on an academic career, it's not about catering to students who for whatever reasons end up not doing well. The students who are not doing well risk getting into problems; if they score sufficiently low they'll not "pass the course" but it's just a total waste of efforts to figure out how to draw the line for that.

Your attitude should be that someone who scores well below, say, 85% has de-facto failed the course, but in the gray area between, say, 60% and that 85%, they are not going to be deprived of a diploma just because they didn't do well on your exam. Whether that 60% becomes 50% or 65% should not be of any concern to you. That uncertainty should make your students who are not studying hard enough worry a bit more so that they end up studying harder.

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I would tend to just follow the prescribed rule and call 50% (or 4) passing. My students generally have trouble enough meeting that threshold.

On the other hand, you don't need "two functions" (nor a piecewise function) to do the task of transforming 60% -> 4. For example, y = 2.5x^2 + 3.5x + 1 does the job.

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