Grading exams: need ideas

Dionysus

Hi,

I set a paper for one of my classes and they all found it difficult. As a result kids who would usually get in the 90s will now get in the 50s. I accept the questions were too time-consuming and this slowed them all down.

So, I'm wondering is there any grading system that I could use where instead of marking students out of the available marks I can mark them against each other?
I think that might be fairer, but any better ideas on this issue will be welcome.

Thanks.

MathsManiac

Of course there is. You simply transform the scores in whatever way you see fit.

If you're happy with the spread of the marks, then you just need to add a fixed number to everything. if you're not happy with the spread, then you can multiply by something and then add something.

e.g. Suppose your raw scores have mean 45 and standard deviation 10, and you believe the students deserve marks that would have a mean of 60 and standard deviation 15. The you could do the following:

First multiply the scores by 1.5 (which is 15 / 10). These scores would have mean 67.5 and standard deviation 15. So then you subtract 7.5 marks, and Bob's your uncle.

This kind of transformation from a raw score to a scaled score is relatively common in a lot of assessment contexts.

If you're operating in the context of a transparent system (scripts being returned and mark schemes available,) then you need to include the details of the transformation in the mark scheme, so everyone can see what's been done.

There are lots of different methods for deciding what the transformation should be. One common way is to consider some samples of what you consider to be borderline candidates between particular grades, and create the transformation that maps their raw scores accordingly.

Dionysus

MathsManiac wrote: »

Of course there is.

Great. (this is the easy bit )

MathsManiac wrote: »

You simply transform the scores in whatever way you see fit. If you're happy with the spread of the marks, then you just need to add a fixed number to everything. if you're not happy with the spread, then you can multiply by something and then add something.

e.g. Suppose your raw scores have mean 45 and standard deviation 10, and you believe the students deserve marks that would have a mean of 60 and standard deviation 15. The you could do the following:

First multiply the scores by 1.5 (which is 15 / 10). These scores would have mean 67.5 and standard deviation 15. So then you subtract 7.5 marks, and Bob's your uncle.

This kind of transformation from a raw score to a scaled score is relatively common in a lot of assessment contexts.

OK. What do you mean by 'spread of the marks'? And 'raw scores'? One of my students has a mark of 94/180, which at the moment is 52%. I presume the "raw score" here is 94? But how does that translate into a mean and standard deviation figure? I don't know/remember what the mean and standard deviation is either but say, for example, I have 3 students and they got 95/180, 60/180 and 100/180, the mean would be the three raw scores added (255) divided by 3, giving me a mean of 85? Right or wrong? And what is the standard deviation of this?
(sorry about this; obviously I'm not a Maths teacher!:o)

pathway33

Don't be getting bogged down. Add 30 to every score and don't give hard exams again . No matter how hard the exam was if a student got less than 10% then they failed.

or

I had a geography teacher who used to give us exams with 140 marks available. Nobody ever got over 100/140 so whatever mark we got he called a percentage. i got 70/140 once which was changed from 50% to 70%.

implausible

I've sometimes done this - overestimated their ability or overestimated the time available. Just mark the questions as per usual e.g. out of 50 and then at the end when you're totting up, give the final mark out of a lesser number to get a higher percentage. So if you have 4 X 50 mark questions, just use a final mark of less than 200 to get a decent percentage.

I also tell the students if I've done this, to shatter their delusions of my infallibility:cool:

spurious

You can always add (say) 20 marks for homework and 20 marks for 'effort' which can bring them up a bit. It helps to encourage the weaker ones to keep trying so that eventually their marks can come up in the exam.

MathsManiac

My apologies.

I agree with all of the above suggestions.

If you don't think you're going to have to do this again, it's not worth trying to get your head around the stats if you didn't follow them.

The easiest way is to just add a fixed number to everyone's score. The more complicated stuff I suggested is only necessary if you want to have a more sophisticated level of control over where everyone finishes up.

The alternative suggestions offered, such as marking it out of a number other than 100 and then just pretending it's a percentage, are basically the same as multiplying everyone's score by some number (e.g. Pathway33's geography teacher was effectively multiplying everyone's percentage score by 1.4, and Deemark's suggestion is similar).

Dionysus

Thanks everybody. I went for the really complicated - ahem - solution of adding 30 to each score as I figure it's more transparent/easier for them to understand that way even though the Geography teacher idea of Pathway's is otherwise probably better.

Note to self: must not give hard exams again to the whippersnappers.;)

forestfruits

Sometimes its no harm to give a time consuming test it prepares them for real exam situations!