# Should I use a linear function or two linear functions to grade scores?

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?

• 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
• @niklai in English, approve is to accept something. The translation of "aprobar" is to pass. – Davidmh May 29 '17 at 21:23
• "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
• 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