Know Your Workings

I have been fortunate that in the last ten years I haven't worked in a school that requires me to mark classwork. I always get students to mark their own answers in lessons, and I give them time to ask me for help if they find they have incorrect answers. I don't believe it is necessary for teachers to mark the practice that students do in class every lesson - and I can't imagine the horrific workload involved in such a thing. For years my students have received feedback in five main ways:

1. Verbal feedback during lessons, where I look over their shoulder and comment on their work - correcting misconceptions, suggesting alternative approaches, advising on layout etc. I'm not great at using mini-whiteboards, but that's a brilliant way to give feedback and is done very effectively by my colleagues.

2. Feedback through Hegarty Maths - instant marking of homework is very helpful for students and a huge time-saver for me.

3. Feedback from regular low stakes quizzes - I mark these myself, but it only takes about 10 minutes to mark a whole class set and gives me a good idea of common misconceptions, so I see this as time well spent.

4. Feedback from 'formal' assessments. When I taught Year 11 this was two sets of mock exams a year - at 240 marks per student per set, this was a large chunk of marking and feedback. For big classes it was a gargantuan workload.

5. Feedback from written homeworks. This is something I do very little of at Key Stage 3 and 4, but did a lot of when I taught A level. By giving big questions to complete on lined paper at the end of a topic, it gave me the opportunity to give feedback not just on students' understanding of the maths, but also on how they lay out their answers. In long A level questions it's important to be able to follow workings in order to spot where they've gone wrong. This is something that most Year 12s need to be trained in because they probably haven't answered many long questions before. This can be done by sharing examples of good work under a visualiser (I wrote about this here).

In my new school we only have Year 7 and 8 and we do two big MAT-wide assessments per year. I find marking these very informative. However, the nature of Key Stage 3 maths assessments means that the questions are typically one or two marks, and an allocated space is provided for workings. What this means is - if I never mark classwork and all homework is done on Hegarty Maths - I never really get an idea how my students set their work out, and I never get the chance to start preparing them for setting out those big A level questions that they will meet in the future.

Just before half-term I decided to take ten minutes of my Year 7 lesson to have my students complete a task on lined paper. I told them that I would mark these in detail and provide feedback. We'd just finished a unit on percentages and I took the questions from an OCR topic check-in. It was intentionally a relatively short and straightforward assessment, and I emphasised the importance of showing clear workings.

Marking these has been very revealing. I'm a bit embarrassed that it has taken me until halfway through the school year to become aware that some of my students don't really know how to set their workings out. Next year I will do a 'blank page assessment' in the first half term so I can address these things much earlier.

I have categorised the workings I saw when I marked these tests into three main types of student: the separators, the minimum possibles, and the one-liners. I have known all three types of student in the past so I guess they must be fairly common. I wonder whether you recognise them too.

1. The Separator
This student has done all of her workings down the side of the page and has written her answers seperately. Note that the workings aren't numbered, though I am able to work out which set of workings goes with each question.

Here's another one where the answers are separate from the questions, but this one is worse because the workings are in a big unnumbered jumble at the bottom of the page. This reminds me of one of those GCSE questions that are impossible to mark because there are numbers and random calculations dotted all over the page (there's an example of a question like this in AQA's recent publication).

Here's another one like that. It took me by surprise to see this separation of workings so many times.

Here's an even more extreme example. I thought this boy had done no workings at all...

... but then I found them on the back. I never told him to do this, promise!

2.  The Minimum Possible
This student has done the minimum possible amount of workings. He finished the test in about three minutes and loudly put his pencil down and turned his paper over so that everyone knew it. This student prizes speed over all else. If it wasn't for the fact I told him he had to write some workings, he wouldn't have written any at all. He doesn't (yet) see the value in them.

3. The One Liner
I know we're trying to save trees, but there's no need to limit every question to a single line. The maths here is mostly good but I will encourage this student to use a new line for each step of working. I once saw a Year 12 try to answer a six mark quadratics questions in one line. It wasn't pretty.

Thankfully this is all easily fixed. For a start I can show them some good examples using my visualiser. There are some good examples below, and each has a positive feature that I want to highlight to the class. These aren't perfect, but for the most part the workings in these examples are clear and well laid out. The maths isn't all correct, but it's easy for me to follow their thinking, which means I can give them helpful feedback and I can understand misconceptions better.

The last one here made me happy because I am constantly nagging this boy about how messy his classwork is - in fact he's probably the only student I regularly talk to about workings - and this piece of work shows a huge improvement. He has even underlined his answers like I do. It's nice when you realise that someone has been paying attention...

I know my readers probably do this kind of activity all the time, but if you haven't looked at your students' written work in a while, why not ask them to answer some questions on paper like I've done here. It was a very short test so it wasn't a huge workload for me. And given how surprised I was by what I saw, I think it was worthwhile...