I’ve spent a good few hours this weekend marking Level 4-6 SATs papers that our year 7s did as end of year exams.

As I was marking, I found depressing patterns amongst the papers. Without looking at the name on the front, I could tell you whether the paper was from a kid in my top set , or a kid in my middle set based on just a couple of questions.

These weren’t the level 5 and 6 questions at the back of the paper. The children did surprisingly similarly on those.

The difference was on questions like these:

This answer makes me want to bang my head against a brick wall.

The kids’ lack of number sense and understanding of operations is scary – and scarily easy to miss. They got the magic level 4 in year 6. They’re continuing to progress in year 7 in line with targets. They can do the woolier parts of the curriculum like data handling, and they have a modicum of logic. This carries them through. They’re not flagged up. As far as the government, the school, and parents are concerned, these kids are *good enough* at maths.

The kids unstable foundations in arithmetic will probably plague them for the rest of their school days. They’ll correctly apply an algorithm in algebra until they encounter a negative number when they’ll freeze. Their confusion over times tables means they’ll always utter “I hate fractions”, but they’ll give finding the LCM a go, and get enough answers correct to escape special attention. They will forever confuse perimeter and area, but the teacher will put it down to silly mistake in the test and move on. They’ve got so much material they need to cover before Easter!

Always moving on, moving on, moving on. Never mastering the mathematics properly.

Why? Because the system at my school is set up for that to be the case.

Take a look at the expensive market-leading textbooks my school spent thousands on this year. They dictate our scheme of work but are horrifically sequenced, jumping from topic to topic. The unit on data handling I’m due to teach the kids next goes like this: a lesson on pie charts, a lesson on averages, a lesson on questionnaires, a lesson on probability. Then – oooh kids, data’s over for now, it’s time for some shape and space!

The obsession with progress and levels means it’s a death trap to be teaching basic numeracy when an SLT member might be around: “why are you teaching level 4 work when they’re predicted level 5s?”

Time spent cementing the basics is considered strange by colleagues. Those SATS type questions don’t come up in the GCSE. Just teach them how to draw a box plot under a cumulative frequency graph. That’s an easy few marks that even Tabitha can manage.

There is no focus on mastery. Got over half? That’s OK. It’ll do. We’ve got to move on to the next topic anyway.

Pleasingly, the tide seems to be turning. Michael Wilshaw praised block by block maths teaching. ARK’s maths mastery pilot is the envy of many a maths teacher I speak to nowadays. There is hope. But ultimately, too many children are still being fobbed off with the “good enough” approach. That’s not right. For me, the tide can’t turn fast enough.

teachingbattlegroundReblogged this on The Echo Chamber.

Geraldine CarterBrilliant post, thanks. This is exactly the situation with foundations of reading. Poor readers may guess their way or learn by ‘look and say’, and mixed and muddled strategies until they are 7-8, then they fail. A plethora of dumbed down reading material is provided. Sad and shaming and costs the gov. a bomb.

Michael TiddSadly, no amount of textbook changes will make a difference. Most of those elements of mastery should be embedded by 11, but why would a successful primary with high test results take a risk on an apparently slow approach to mastery when progress and attainment is so narrowly judged by Ofsted, etc.

As an individual teacher, I know that the risk of thorough mastery is that my progress data suffers and in future therefore so might my pay! Messrs Gove and Wilshaw are as culpable as any.

Tom SherringtonI understand the frustration here. I’ve written in one of my posts that the number line is the most important diagram in the universe. OTT perhaps but sense of number is such an under-rated issue. Is 3/4 bigger than 0.7? Knowing that 5x 5 will be bigger than 4×6; Why £3.99 x 6 is easier to work out by taking 6p away from £24 etc. Next in a sequence….10,6,2,..-2, All these things should be revisited continually. However, having taught maths, I do feel you need release time.. if students are stuck on the basics, it can pay to go on a detour via softer areas before going back in. The levels issue is of course another nonsense. L5 Shape and Space vs L5 Algebra- it’s just a made-up comparison.

carmenMmmm…call me stupid but I never did learn my times table because nobody bothered explaining how they worked. When I finally figured it out, I had the best metal maths in the year (you try adding up 7 nines quickly enough to please the teacher!). So explaining stuff is well worth the time and effort ..and if the same concept can be covered in a different way by a different person in a different subject area (be it Music, Art or PE) then so much the better…

JamesI think the best approach would be spending 2-3 weeks at the start of the school year thoroughly embedding written and mental methods for all four operations in the way you wish children to use them – they have been taught such a range of methods since early primary that there is huge variety. Then we should be able to circle back to these methods easily throughout the year.

Things like decimal ordering, counting in decimal sequences, number bonds to hundreds and thousands, times tables etc could be taught as mental/oral in any unit of work.

marvinsuggsThe pursuit of target levels have come at the expense of fundamental understanding of concepts. In Science, most of my students pride themselves on the level they got in their test but there’s no value placed on understanding a topic or practical skills themselves. We’ve been discussing a similar approach re practical skills – a concerted attempt to teach something that isn’t specifically on the curriculum but that we all know is essential. We’re planning a two/three week practical SOW at the start of Yr 7 and maybe even 8. It won’t solve the big picture problem though. Great post

EllieI’m a year 6 maths leader and totally agree – an enormous proportion of time (including by me) is spent working out how children can get to the next level in a test, and teaching these ‘gaps’. As part of my MaST course, I’m currently doing some school based research on how we can give children those mental models with which to calculate (and stop them thinking numberlines are for little uns). Happy to share findings, and hopefully some successes.

Ellie

Matt McKee (@matt_mckeeSA)Well put – I think we have a similar issue in much of science, especially given the ground to cover, even more so in triple science. I worry a little that the suituation may get worse with the use of 2yr KS3. No mastery and consolidation and lots of ‘when the question says this’, ‘do this’.

KatyI find the same in Science, too much content and too little time. Scientific skills are taught implicitly, rather than explicitly and Oh, Im sorry, James – did you not quite get this lesson on microbe transmission? Sorry, I have to move on – no time, no time, no time! Argh!!

chestnutI think teachers of all subjects have the same problem and I think at the heart of it lies the fact that NC levels are not a tool to measure progression.

Matt McKee (@matt_mckeeSA)I think you’re right chestnut, but without trying to ‘compete on trickyness’, some subjects that may be more conceptual, counter intuitive or have a lot of subject specific terms or need to cover a lot of ground in a relatively short space of time will have difficulties with deeper understanding etc… The NC levels are not a tool to measure progress either and as you probably know the sub levels don’t even really ‘exist’. (I think I’ve overdone my quotes marks quota…..

HeatherFI have helped my own children with maths and found it really frustrating that they quickly forgot a topic once they moved on. I ended up trying to find materials that practised a range of topics each session to ensure mastery was achievec. That meant ordering Zig Englemann’s materials from America. They work a treat but I can’t get over the fact you can’t find materials that build in regular practice of what has already been learnt. It is the same issue with my daughter’s French learning. I cannot understand why no account is taken of memory in curriculum planning.

srcavMastery is an issue, and with basic number it should be embedded by the time pupils leave primary. Unfortunately this is rarely the case. We are introducing literacy based starters across KS3 for every lesson to embed these skills and increase mastery. Tgere are 4 worded questions on the board when pupils arrive and these are answered by the pupils. The weakest are “add seven to fourteen”, etc where are the top sets will be more complicated. This allows gradual introduction of vocabulary and can be easily personalised depending on the ability level of each set. We’ve trialled it this year with some low and middle ability classes and received good results, so we are hoping to replicate this across tge key stage and embed skills required for KS4.

The sequencing of the SoW issue should be easily tackled. You shouldn’t let a textbook dictate the order you teach something in. You are a department full of professionals, you should get together and write a new SoW. You can still use the textbooks if you like (although I generally dislike them myself), but you don’t need to do it in a specific order.

Teacher_PYou mention it’s a “death trap” to be found teaching L4 topics to kids with L5 targets if SLT find out.

Well, SLT aren’t the worst problem. The kids are! (To be fair to them, it’s something they pick up from other subjects.)

A couple of years ago, I was helping a colleague with some after school GCSE revision sessions. She’d already done a load of diagnostic tests to find out which kids were weak with which topics.

The topics I was supporting were all E/D grade. All good so far!

But the problem was the kids had C/B targets. As far as they were concerned, there was no point in them “wasting time on E/D topics”. They believed they needed to be doing C/B grade work and simply would not spend any time on basics – basics that were letting them down throughout the paper.