With our Y13s gone and our Y12s doing internal exams last week, it’s been a good opportunity for some reflective thinking within our department. This is my first year as HoD (and boy, what a year…) but now I feel settled enough to think about much longer term goals for the department. One of these is to try ‘nudging’ the students’ performance – I guess in a value-added sense – so that students who might be close to grade boundaries can end up on the better side of the fence for example.
Obviously this means identifying some elements of our practice where there is room for further work and improvement. I feel fortunate to have a team who are open to such discussions in department meetings and, individually, enjoy engaging in longer conversations with me whenever we find the time. Whilst I have a scribbled list of half a dozen ideas, here are our (current) top 3. In no particular order…
Corrections
We have (what we believe to be) an effective system in place that includes a relatively hefty weekly homework assignment and also a weekly class test. The homework is very much a formative task and students can access departmental support throughout the week. Indeed, they are also given numerical answers to all the questions and are expected to check, mark and correct their work before the due date. There is no ‘marking’ in the traditional sense – we look to see that students have invested appropriate time and energy in the work and offer constructive feedback on aspects of the work that could improve or, for example, if they’ve used inefficient methods or drawn inadequate diagrams.
With our tests it’s the opposite – these are marked and graded, but we write only the briefest feedback on them. The expectation is that students then follow this up with corrective work (and potentially re-study some aspects of a topic) but we don’t currently have a regular process in place to ensure such follow-up work has happened. We are currently discussing a number of options: should students be asked to resubmit their test at a later date? Should students do all their tests in some kind of exercise book so they and we can always look back and see a longer term picture? Should students keep some kind of reflective list of their errors and misconceptions?
Communication
This idea has already been through several iterations in our discussions. We frequently bemoan the poor presentation, less than logical flow, and generally not quite ‘up to scratch’ nature of our students’ solutions. However, we realise we perhaps don’t have sufficient focus on explicitly teaching our core standards and expectations and then holding students to them.
We are considering a framework for solutions along the lines of “Inputs / Argument / Conclusion”. These names are still evolving but we’re aiming for a common department vocabulary. In brief:
- Inputs: this can mean many things in many situations, so some examples might be best. It could be as simple as just copying a pair of simultaneous equations given in a question, adding numbers to them. It could mean a force diagram in Mechanics, summarising all the information presented textually. It could mean a summary of facts about the terms of a sequence, again interpreted from the text of the problem
- Argument: this is then the logical flow of the solution with good, correct, clear mathematical communication
- Conclusion: this can be the final ‘answer’ (with appropriate rounding and units), a summary statement of what was asked for (eg a clear statement of a binomial approximation, or partial fractions decomposition) etc
Not all of these elements are necessarily present for every question, nor perhaps will they always be clearly disjoint (that isn’t ultimately necessary). But our belief is that clear, careful communication in solutions helps improve students’ prospects of solving a problem fully and correctly.
We are also considering including specific marks in our weekly tests for appropriately meeting these expectations (and thus not simply applying exam-standard mark schemes, that do nothing for improving the quality of students’ responses).
Random revision questions
How often do you present your students with a totally unseen, unrehearsed question on an unexpected topic? For us it is seldom until, for example, we are in revision mode much closer to exams. We are considering a model that perhaps changes from year 12 to 13:
- In Year 12… students could be given such a ‘surprise’ exam question once every week or two, as an activity in the classroom. They would try it in exam conditions, but then have the immediate full support of discussion, feedback and correction without any stakes attached. We hope this would highlight to them the need to keep on top of past topics, refreshing their memories every now and again.
- In Year 13… such questions could be an element of their weekly test (which is typically rather topic-focussed on recent work). This raises the stakes – weekly test results mean a lot to our students! – but they are that much closer to the end of their course, so we feel it is reasonable to increase the demand.
sxpmaths - the PROcrastinator 