Like many teachers it’s often disappointed me the way students mostly seem to overlook the careful corrections and comments we write on tests and other assessments before we give them back. They want the mark and once they’ve got it they are pleased or disappointed and then it’s over for them. I want them to read those comments, consider their mistakes, think about where they went wrong and to build their understanding. I have always encouraged my students to have what is now called a growth mindset, but when I started teaching 35 years ago, was just encouraging students to believe that they could ‘do it’. Yet has always been an important word I use with my students. If they say “I can’t do it”, I have always replied, “maybe you can’t do it yet, but you’ll get there if you work hard and ask questions.”

So, today I implemented a blend of ideas that I have been reading, trialling and thinking a lot about over the last couple of years in particular: a combination of Number Talk (Making Number Talks Matter: Ruth Parker and Cathy Humphries), Sense Making and Growth Minset(Jo Boaler: Mathematical Mindsets),   Highlighted marking (Leah Alcala) and ‘My Favourite No’ (Leah Alcala).

I am job sharing this year, so my colleague and I planned together what we would do. She gave the test, collected it and went through and highlighted the mistakes. We then met and she showed me the two common errors that students had made. It was a test on surds: the first common error was students incorrectly cancelling and the second was incorrect expansion when rationalising the denominator.

I started the lesson with placing 2 similar questions on the board and telling them that these represented our ‘favourite mistakes’ on the test, because several people made them and because they highlighted misunderstandings that we wanted to address. I can’t remember the actual questions, but they were something like:

I asked the students to work these out. They could discuss if they liked. I then basically ran a Number Talk. I asked for suggested answers to the first question. They were hesitant at first – this is an ‘advanced’ group and they fear being wrong and ridiculed, but I stressed that even if they weren’t correct it would be really helpful to everyone. After a short while a student that I had taught 2 years ago, May, offered her answer, I then asked for others. Eight different solutions were presented which certainly sent a murmur around the class. After a bit of discussion they realised that some of the answers were the same, as they either weren’t simplified, or the denominator hadn’t been rationalised. That got us down to three. I then asked if anyone was prepared to defend one of the answers. May responded, she explained her method and solution and I wrote down what she said on the board so everyone could keep track. At no point did I say whether it was correct. I then asked if anyone else wanted to offer a defence, maybe with an different approach. We ended up with three. I then moved on to the second answer (the third – with no surds involved had been ruled out by the students by this time). Campbell, said that he got the second answer but was now doubting that what he had done was ‘allowed’. I asked him to tell us what he had done (cancelling √3, from each of the three terms, treating it as if the terms in the numerator were added, not multiplied). Several other students then agreed that this is what they had done. Again, I recorded the steps of his solution on the board, again without making a judgement. The class agreed that these were not the same answer, so only one could be correct. A short discussion followed on whether this second method was or was not accurate. Someone had pulled out their CAS calculator by now and had confirmed that the first solution was correct, so it came down to making sense of why, which involved me providing some simpler, whole number examples for some students who struggled with the reasoning at first. The error in the second case was identified quite quickly.

At this point I was ready to hand back their tests. I had decided on groupings earlier. Four to a group, not the usual people they sat with, and a mix of student ‘abilities’. Their task was to discuss the errors highlighted and between them to identify why these were errors. Most groups engaged in the task very well and only occasionally was I called on because the group couldn’t quite decide what the error was.

I then collected the tests. Our school has moved to continuous reporting, so after each test, comprehensive worded comments about what students could, and couldn’t yet, do on the assessment task is required. Now that the students have looked closely at the tests themselves, those comments will be published for them and their parents to see and will hopefully have more meaning. Finally, when we have given them time to read the feedback, we will publish the actual test mark.

Only time will tell if this strategy will help students become more focussed on improvement, but even in one lesson today, I was really pleased to see students relaxing and willing to share mistakes they had made and confusions they had. That’s a great start I think.