Ramblings of a mad woman probably but I’m trying to get my head around ways to work with our current and future cohorts to overcome issues whereby some students do this:
- Read the question
- Decide they aren’t going to be able to FINISH the question
- Don’t even start having a go … arggggghhhhhhh!!!
I’m going to try to put some context to this first. I am not referring to all students – it’s a very small minority. I just have extremely high standards and am always wanting all students to be able to access the work … I always want “more”. My current year 7 are some of the strongest year 7’s I’ve taught and they are so confident in knowing which “operation” they need to choose to do a “sum” and coupled with the fact that their written formal methods are quite secure they’ll have a go at almost anything. Oh hang on … last week I used some Tangrams with them and some of them found this “hard”. All we were doing was moving bits of paper around the desk … I hadn’t asked them to climb a mountain or do brain surgery so I know we have some work to do on resilience with a couple of them. Regardless of the “few” in this group, in general they are pretty strong in terms of their “numerosity” and I can see that this new GCSE will be easier to access for them. They are getting pretty fluent in “number”.
What concerns me is that some students sitting this new GCSE in the Summer (and for the next few years) just don’t have this level of “numerosity” (I’m talking about the national picture here and not in any specific school!). They haven’t been subject to the new KS1 and KS2 and lots of their time in lower years will have been spent trying to get some of them to a level where they are fluent and confident in their number skills. Nationally , believe it or not, there are year 10 students that still don’t know (I’m not getting into the discussion about rote learning here!) their times tables and by that I mean they don’t even have a method to work them out and haven’t made the link between multiplication and repeated addition (not the only link they could make!) and to some of these “division” is one of the scariest words they could hear! To me, all of this kind of stuff is “sums” and not the “maths” that we are testing at GCSE.
The feedback I’m getting on my travels is that students are finding the papers (whatever board!!) very tough … on both tiers!! I see it as there being a level of numerosity that is required that lots of students just don’t have (yet!). I said something at a “thing” recently that I thought summed it up for me … lots of the questions have some really nice “maths” but they are out of the grasp of lots of students because there is a “sums” barrier that they can’t get over. I genuinely worry that they aren’t being allowed to “show what they know” because they can’t get past the “sums”. As a result of a conversation (I think I talked and he nodded!) with Graham Cumming he put together my very own alternative version of their first secure foundation mock papers and I’ve used them with my high attaining year 9’s with a view to using my findings to shape some future strategies which I thought I’d share.
The below question is one that demonstrates my point … looking at the data that was collected by Edexcel through ResultsPlus for this question it was pretty poorly answered with just over 60% getting zero. I’m not having a dig at Pearson/Edexcel because I could equally likely, have found examples from the other boards too (lots of them!!) but chose this because it was amazing of Graham to spend the time putting the alternatives together for me which allowed me to investigate my chain of thought further.
I wonder what are we testing here? if we are testing the ability to substitute numbers into formula did it really have to be decimals in the formula? To prove the point I asked half of my year 9’s to have a go at the question above and there was lots of “how do I multiply by 1.5/1.1/1,25? I can’t do that!” and half of the group had a go at the below version and all of them nailed it!
Whilst the first group eventually got their answers because they CAN do it. I worry that in exam conditions students will panic and move on to other questions when in fact what we want them to do is write down “1.5 x 30” regardless of the fact that they might not be able to work it out. One of the students, once they had written it down went on to work out “1 x 30” and then “0.5 x 30” but when he was trying to work it out mentally was getting into a right tizz.
I did the same exercise with lots of questions and used it as a learning point to identify strategies to use in an exam following a recent assessment. I’d like to say that I’ve always reviewed any questions I use in class (either for modelling or for students to complete) when I decide the progression of difficulty that I want with a specific group but I know that I haven’t always done this as thoroughly as I’d like. Recently I’ve looked at how I can ‘strip’ out the difficult sums with some topics/groups to show students that they can do the “maths” that they are being taught which is having a positive effect on confidence. I’m not talking about dumbing down because in fact when I’ve made a question easier we have always worked back up to being able to do the original question.
I started this by saying it was the ramblings of a mad woman and it has been … Mel out!
PS: Graham has kindly allowed me to share these documents following the number of requests for copies. You can find them here->
PPS: I’ll be blogging about my visit to Ofqual this evening!! Many are asking me about that too!