The case of units and variables

I’ve talked about students’ difficulties with units before – on 10th and 15th March 2011. In addition to the deeper problems that students encounter, they frequently give the incorrect case when writing abbreviations for units. When they write Kg instead of kg for kilograms in an answer to an iCMA question, I have a certain amount of sympathy (especially since K and k are completely impossible to distinguish in many people’s handwriting – including mine!). However Kg is just plain wrong, so I would be unhappy to give full credit for an answer that included this error. It is really important to give targeted feedback on errors of this type.

Students also get the case wrong when the correct case of a unit is more obvious e.g. they write j instead of J for joules. And they make similar errors in writing the case 0f variables e.g. in answer to a high-stakes question where the correct answer is nRT, more than 1% of responses were only incorret because of case, with many responses of nrt, NRT etc. I find it slightly disappointing that students don’t seem to appreciate that things like this matter (even though we have explained this in the teaching text).

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Errors in finding the gradient of a graph

Consider the simple question shown below:

This question is generally well answered, but when students make a mistake, what do they do wrong? Continue reading

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BODMAS, BIDMAS, BEDMAS

More on simple arithmetic skills that people don’t always understand as well as they think they do, leading to difficulties at a later stage.

In the OU Science Faculty we use the mnemonic BEDMAS (others use BODMAS or BIDMAS) to remind students of the  rules governing the order of precedence for arithmetic operations:

Brackets take precedence over

Exponents. Then

Division and

Multiplication must be done before

Addition and

Subtraction.

When analysing student responses to iCMA questions, lack of understanding of the rules of precedence and related issues, whilst not contributing to as many errors as do problems with fractions and/or units, it’s still up there as a common difficulty. Sometimes the problem can be attributed to poor calculator use e.g. a lot of students interpret 3 6/3 as meaning (3 6)/3,  perhaps because they don’t stop and think before using their calculator.  This misunderstanding (seen in lots of variants of a question in summative use) led to a talk I used to give: ‘Why is the answer always 243?’.  But it goes deeper than that! For example, even after teaching students how to multiply out brackets etc., many think that (x + y) 2 is the same as  x2+ y2. Mistakes of this ilk are completely understandable, but it is nevertheless something to watch out for.

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Throw away the handouts

I was at a meeting in Bristol yesterday ‘Using assessment to engage students and enhance their learning’. Much of the discussion was on the use of peer assessment (and plenty of interesting stuff), with a keynote from Paul Orsmond, considering student and tutor behaviour inside and outside the formal curriculum.

However, what struck me most was something reported in a presentation from Harriet Jones of the Biosciences Department at the University of East Anglia (UEA). They want students to make their own notes so have made a conscious decision to stop giving out lecture notes (though copies of presentations used in lectures are available on their VLE 48 hours before each lecture, for those who want to download a copy and also for students who want to check something later). It’s a brave decision but also, I think, a very sensible one.

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Problems with fractions

I’ve been aware for some time that Open University science students have problems with fractions (and many things that express themselves as difficulties in other areas e.g. working out units, simplifying algebraic expressions, have their origins in poor understanding of the arithmetic of fractions). We’ve improved our teaching all over the place, but I have recently become aware of a problem I hadn’t spotted before. Why do students give the (incorrect) answer shown below?

It’s actually remarkably simple Continue reading

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The significance of rounding and significant figures

I now find myself chairing the production of two new Open University modules, so writing course materials ought to take priority over writing this blog. That’s a pity, because there’s so much assessment-related that I want to reflect on.

As a compromise, I’ve decided to report a few more of the things that I’m finding out from our analysis of student responses to  Maths for Science e-assessment questions (since it’s Maths for Science that I am deep in re-writing at the moment). Some of the findings reinforce what we already know, some are unexpected. However, in each case, if there are mistakes being made by a number of students then it behoves us to look carefully at our teaching in those areas.

As an example – our students seem to be really bad at rounding – they will truncate 1.465 to 1.4 rather than rounding it to 1.5. I still don’t really know why this is, or whether it’s a common problem with students at conventional universities. However, when I looked carefully I realised that so far Maths for Science was concerned, one of the problems was that we didn’t explicitly students how to round (though we did teach rounding in the context of orders of magnitude). Oops! Hopefully the new edition of the book will do better.

Our students are also really bad at quoting numbers to an appropriate number of significant figures. After more than 20 years of teaching OU students, this finding didn’t really surprise me – and it is reasonable that students will more readily quote an answer of 3.4 as being to two significant figures than they will 0.034 or 3.0. I’ve tried to improve our teaching of these points too, but I’m not optimistic as to my chances of success.

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Open-ended and multiple-choice versions of the same test

I’ve just read an excellent paper. It’s rather old, so old indeed that I might have been one of the ‘first year secondary school pupils’ involved in the evaluation! (though I don’t think that I was). The full reference is:

Bishop, A.J., Knapp, T.R. & McIntyre, D.I. (1969) A comparison of the results of open-ended and multiple-choice versions of a mathematics test. International Journal of Educational Science, 3, 147-54.

The first thing they did was to produce a multiple-choice version of a mathematics test by using, as distractors, actual wrong answers, commonly given to the same questions in open-ended form. Continue reading

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The testing effect

This will be my final post that picks up a theme from CAA 2011 , but the potential implications of this one are massive. For the past few weeks I have been trying to get my head around the significance of the ideas I was introduced to by John Kleeman’s presentation ‘Recent cognitive psychology research shows strongly that quizzes help retain learning’. I’m ashamed to admit that the ideas John was presenting were mostly new to me. The ideas echo with a lot of what we do at the UK Open University in encouraging students to learn actively, but they go further. Thank you John! Continue reading

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Are we assessing what we think we are?

In the past week (when I should have been working at Open University summer school, but got sent home ill) I haven’t felt up to doing a great deal, but I have managed quite a lot of reading. I’ve also tried to get a deeper understanding of some of the concepts in assessment which I once thought I understood – but the more I learn the less I feel I know. Validity is one of those concepts. Continue reading

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Poor quality assessment – inescapable and memorable

David Boud famously said ‘Students can, with difficulty, escape from the effects of poor teaching, they cannot (by definition if they want to graduate) escape the effects of poor assessment.’

Boud, D. (1995) Assessment and learning: contradictory or complementary? In P. Knight (ed) Assessment for learning in higher education. Kogan Page in association with SEDA. pg 35.

Poor assessment is also memorable. Continue reading

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