e-assessment (f)or learning

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.

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.

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 (more…)

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.