# What will be my next assessment function

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Abstract

This will be my next assessment function

The use of the arithmetic mean 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](https://en.wikipedia.org/wiki/Grading_systems_by_country “Wikipedia. Grading systems by country. 2016”")) with different procedure. I’m not discussing here the fair of the assessment function (there are a lot of means 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 it (perhaps an excuse to talk about proportions ;).

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

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