What will be my next assessment function

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

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 ) 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 course1

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

 Wikipedia. Grading systems by country. 2016. https://en.wikipedia.org/wiki/Grading_systems_by_country.

 Wikipedia. Mean. 2016. https://en.wikipedia.org/wiki/Mean.

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

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