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The Battle over Homework: Marking in Mathematics

Within five minutes of any teaching inspection from OFSTED, the inspector will be leafing through students’ exercise books in search of evidence of regular and meaningful marking. If it’s not there then they will probably already be penciling in the “requires improvement” column. With no-notice inspections now in the UK, and with such high stakes for Senior Management, there is ever greater pressure and expectation on UK teachers for “OFSTED ready” marking – with all the significant increase in workload that this entails. Yet, how much discussion ever takes place as to how effective such marking is for mathematics?

Dr Harris Cooper of Duke University, one of the few academics to really research homework policies in depth, provides compelling evidence of the need to rethink marking strategies through a meta-analysis of research on the subject. He cites 47 studies which demonstrate that the act of setting homework itself, regardless of whether grading or comments were provided has a positive benefit for students.

There are much fewer studies specifically looking at grading strategies – but here again they run contrary to accepted norms. Three studies which looked at different homework grading strategies – marking every problem, marking a random sample, marking for accuracy or marking for completeness were found to have no difference in student attainment. Five more studies meanwhile suggest there is little difference in attainment when students are provided with comments as a pose to grades.

One study cited was that by J Austin looking at whether comments on homework affected student performance. Researchers found that in 7 of the 9 classes in the study, there was no significance in raised mathematical performance between students who received comments instead of simple grades.

This probably makes sense to anyone who has ever marked maths homework before – either students will get everything correct, or most students will get the same question wrong. Rather than spending 40 minutes writing out 20 explanations of how to use Pythagoras’ rule correctly, surely it makes more sense to spend 2 minutes at the start of the next lesson explaining (or getting a student to explain) it to the whole class?

Mathematics marking is also an area which computer programs can provide huge benefits. Websites like MyMaths allow students to be set targeted homework, which they can have marked in real time. These homework tasks are accompanied by lesson content so that students who do get questions wrong can then go back to the lesson, review the material and then resubmit their homework again. The evidence clearly shows that specific, immediate feedback raises attainment – and such programs not only do this, but also encourage students to become self-learners in the process.

A couple of recent studies looking at the effectiveness of web-based marking versus traditionally graded marking in university students found no significant difference in overall student performance between different approaches – and found that web-based homework both increased the students’ time spent on the task and provided greater opportunities for them to recognise and correct errors.

Given such evidence it is depressing that so many school leaders and OFSTED inspectorate remain wedded to the importance of using comments in exercise books as a core method of assessing teaching.

Central to this discussion should instead be the concept of greatest teaching efficiency – i.e. what is the most effective use of teaching time to maximise student attainment. Current policies effectively ignore this question completely, and work on the assumption that there is no upper limit to working hours in a day and that all new strategies will have no detrimental effect on other ones. The reality is the reverse, new strategies squeeze out old ones, overwork leads to increased stress and an overall drop in both student-teacher relations and teaching standards.

A more honest approach would be to start with a fixed idea for the number of hours per week staff members should be expected to work – whether that be 45 hours, 50 hours or more. Once that figure is fixed then it simply becomes a case of working backwards – filling in those hours with various teaching responsibilities. Doing this then forces a genuine debate as to what is the most effective use of teaching time – 5 hours a week marking books or an extra 5 hours a week planning lessons, organising gifted and talented events, or holding after school revision sessions. Which strategy actually has the greatest impact on attainment?

Immediate, targeted verbal feedback within the classroom setting has been shown to to have one of the greatest impacts on attainment. Comments for maths homework do little to raise attainment over simple grading, and web based programs offer both immediate feedback and the opportunity for students to become self-learners. None of these appear as evidence in a two minute flick through of a student book – but what evidence does this actually provide? Maybe it’s time to challenge the existing marking paradigm.