The use of the arithmetic mean (Wikipedia 2016a) for assess people (in particular students results) is strongly used. But is it the *best*, or at least optimal, assessment function? What do I mean here? Perhaps we could assess students in diferent way, obtain a number (or letter (Wikipedia 2016b)) with different procedure. I’m not discussing here the fair of the assessment function (there are a lot of means (Wikipedia 2016c) there) but the didactic aspect of that.

This is my proposition: use additive function. If you have \(n\) marks, \(p_1, \ldots, p_n\), why instead of calculating arithmetic mean \(\overline{p}\) just add them up. This has a lot of advantages:

- It’s more easy to calculate. In primary school, it’s easy for students to calculate a sum rather than a mean (it involves division)
- It captures better the sense of “league”, the sense of “marathon”: you could know, directly, how long you progress a day (“I add it up 5 points today”. “20 points left to get a C”)
- Students know better the weight of a score (exam for example) in relation to the whole course: if one activity worths 10 points, then if you passed, you get 10 points. But what is the weight of a 10 in an exam if you apply the mean? With additive assessment function, “you have what you get”
- There is an obvious equivalence between calculate arithmetic mean and just sum numbers: if each \(p_i\) has a maximum score of \(m_i\), then you could calculate the mean \((p_1, \ldots, p_n) \mapsto \frac{p_1 + \ldots + p_n}{m_1 + \ldots + m_n}\) or \((p_1, \ldots, p_n) \mapsto p_1 + \ldots + p_n\) (of \(m_1 + \ldots + m_n\)).

The only disavantage I know is that you have to be aware of how many test/activities students will get. Because otherwise you could not say “If you get 50 points, you will pass the course”. If students missed tests, then you/they have to re-escale (Wiktionary 2016) it (perhaps an excuse to talk about proportions ;).

By all these reasons, the additive function will be my next assessment function next course^{1}

# References

Wikipedia. 2016a. “Arithmetic Mean.” https://en.wikipedia.org/wiki/Arithmetic_mean.

———. 2016b. “Grading Systems by Country.” https://en.wikipedia.org/wiki/Grading_systems_by_country.

———. 2016c. “Mean.” https://en.wikipedia.org/wiki/Mean.

Wiktionary. 2016. “Rescale.” https://en.wiktionary.org/wiki/rescale.

Right now I can’t modify the existing rules.↩