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Comment by HKH2 | Hacker News Reader

In Math, you can tell students to show you how they got the answer to a problem.

I think the bigger problem is that '100%' is often the goal, yet it is far from optimal; get students out of the 'all or nothing' mindset, so they don't become cynical.

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In my English schooling system (GCSE and A Levels), if a math question was worth ten points, the correct final answer would be worth exactly one point.

The other nine points were for the steps, and, indeed, were a hint that there were probably ten distinct steps (although usually you could combine several steps and still get full marks so long as it was clear).

Among other things, this also allowed for error-carried-forward: if you made a stupid arithmetic error on step 3, and all your subsequent steps had the wrong values, you would only lose one point, though your final answer was completely wrong.

This always amazed the Americans I speak to, for whom it seems there's just a random point or two for "showing your work."

I would love to see this approach used in more schools.

Back in the 2000s, a variation on this was used in the US navy's technical schools. Correct answer? Full points, regardless of showing work. Incorrect answer with work shown? Points off for the error, but allowance for errors carried forward. Didn't show work? No points for you!

This was also the 80s and 90s approach (at least in Catholic schools when I was a student)

this reminds me of the error biased marking scheme

get an answer right = +1 point

get an answer wrong = -2 point via subtracting the number of wrong answers from the right answers.

so the plan that was advised is if you are not 100% sure of the answer then dont answer, and you only lose 1 point for not answering

This is the same as my experience growing up in Australia - right the way from primary school up to university-level subjects, mathematics working is marked and you get almost full points if you solve the problem correctly but just make some clerical error somewhere. Even if you can show progress towards a solution but can’t quite get the last bit, you’ll often get 7 or 8 out of 10.

At Caltech you'd get partial credit for getting partway to the correct solution. But, if you got a nonsense result (like negative energy), you'd get negative credit unless you included a note:

   I know the answer is absurd, but I don't know where I went wrong.

Negative credit? You mean you lost marks vs not answering the question at all?

Yup. That was institute policy, not the professor's discretion. They were pretty clear about thinking whether the answer was reasonable or not.

Makes sense, with the situation that if the student includes the note then they are not penalized.

It's pretty important to be able to recognize if you fat-fingered a calculator and got something ridiculous or not.

I think this is a good policy, and have often been annoyed that I can’t (rules of the university) mark my students down for such absurd answers.

> This always amazed the Americans I speak to, for whom it seems there's just a random point or two for "showing your work."

Random point or two? As an American I think it was usually worth most of the points for the math I did...

But this is still aiming for 100%. Being challenged is dangerous to your grade.

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