# What will be my next assessment function

blog, en, assessment, addtitive function, mean, accumulative assessment

The use of the arithmetic mean [1] 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 [2]) with different procedure. I’m not discussing here the fair of the assessment function (there are a lot of means [3] 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 [4] it (perhaps an excuse to talk about proportions ;).

By all these reasons, the additive function will be my next assessment function next course1

## References

[1] Wikipedia. Arithmetic mean. 2016. https://en.wikipedia.org/wiki/Arithmetic_mean.