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!

This time I am mostly excited by…..the youth of tomorrow | pmcbride2014March 19, 2017 at 12:20 pm[…] wasn’t going to post this today but having seen Mel @justmaths’ latest blog it seems somewhat […]

Jon HinchliffeMarch 19, 2017 at 1:17 pmIsn’t what is being test the ability to take a complex problem and use strategies to make it easier until you get an insight into finding a solution? An important skill in the real world.

I have found student don’t know the calculation to make in this question from Collins

“A typical adult has about 20 000 000 000 000 red corpuscles. Each red corpuscle weighs about

0.000 000 000 1 gram. Write both of these numbers in standard form and work out the total mass of

red corpuscles in a typical adult.”

So I had to teach them to change the numbers to simple numbers such as

“A typical adult has about 20 red corpuscles. Each red corpuscle weighs about

1 gram. Write both of these numbers in standard form and work out the total mass of

red corpuscles in a typical adult.”

Then they could just “see” what the calculation should be and were able to do the standard form part.

We just have to keep training students to change the numbers in a question until they have the concept with simple numbers and then go back to the original numbers.

Perhaps we should also stop having so many questions with integer answers too.

I do feel the new exam is the correct way to go despite the headaches it causes me as a teacher.

How we break student from wanting to do everything in their heads and wanting neat presentations in their books is the next big step. Maths should not be the clinically neat subject many students think it is. It is sometimes about going across a pond on stepping stones and finding the occasional dead end. Being a fairly new teacher to Maths I still hit problems and am not sure how I will get to the end. I just have to try things until suddenly I realise I can see the way to the end. Every time this happens in class I point this out because this is what students need to learn.

Janet (@mathsJanet)March 19, 2017 at 1:41 pmRamblings it may be, but useful thinking when it comes to the resit which is what I am teaching. I see this barrier all the time & hands to go right back to basics for me grade resit students. I have to teach then strategies throughout the year, whilst applying then to exam type questions in the hours they won’t skip them in the exam.

AnneMarch 19, 2017 at 1:46 pmAre these alternative questions you refer to available somewhere?

adminMarch 19, 2017 at 2:27 pmIf i ask Graham Cumming nicely he may let me share them … send me an email mel@justmaths.co.uk

adminMarch 19, 2017 at 2:29 pmYes but my point is that IMO this new GCSE requires numerosity beyond what the current year 11s have. Lower down the ages I see that it will be fab but in the mean time we have teachers and students having to deal with it. We should have waited for the new ks1&ks2 students to work their way up the school before inflicting such a big change on them.

Atul RanaMarch 19, 2017 at 3:43 pmHow small is the small minority? I wonder if some of them have Dyscalculia. Around 5% of the population has Dyscalculia; and causes a real disconnect with any feel for numbers and the basic operations. If they haven’t got a feel for what multiplying by 1.1, 1.25, 1.5 actually means it’s simply going to cause a disconnect with them. Nice questions on the idea of having fixed rates (callout charge for a plumber for example) alongside variable rates though.

Janine BMarch 19, 2017 at 5:08 pmAs a tutor I work with all sorts of students and I am certainly aware that an average year 6 student I teach has a far better grasp of using fractions, decimals and percentages than many I have worked with in recent years for GCSE. Many of the year 8 and above students have little grasp of multiplication or division and certainly don’t know tables or ways of working them out.

Stephen GodwinMarch 19, 2017 at 7:36 pmHearing your pupils are struggling with these issues is oddly comforting, as we have experienced exactly the same issues (I never delight in anyone’s struggles, so hope you understand what I mean).

Two areas to comment on.

Firstly, for quite a while we have been saying that they know what is required on simple questions (algebraic substitution, is the number if n a sequence etc), but their basic numeracy means they fail to complete the task. Back to basics at KS3 (and even KS4) to try and ensure this problem is eradicated going forward.

The second issue are multi step questions and as you describe and how it overwhelms pupils. Like you I have used simpler numbers in modelled examples and questions and this is something I have advocated for all topics. For example, when looking at angle rules I have always suggested that initially the number bonds should be easy (multiples of ten) as we are testing spatial awareness, angle rules etc, not addition or subtraction. Complicating the question with “horrible” numbers can come later.

I have also advocated breaking down these questions down in to their constituent parts, before reassembling them. For example pupils really struggled on a question that asked “what percentage of the shape is shaded” and from memory the question was a trapezium with a circle inside.

On one board, I posed the following individual questions (they were all written separately with no apparent link between them).

1) area of a rectangle

2) area of a triangle

3) addition with two numbers

4) area of a circle

5) subtraction with two numbers

6) write one number as a percentage of the other

Questions 1,2,3 & 5 were easily answered. Thanks to the “Circle Song”, question 4 had much success and it was only question 6 that needed support, but we got there.

I then put the exam question up on the board and was met by a sea of helpless faces! We started to break the question down and it wasn’t long before they twigged it was the same processes (and answers) as the six questions they had just done. Cue much relief.

I have repeated this a number of times just to get them to give it ago and try and gain some marks.

JustMathsMelMarch 20, 2017 at 12:49 amGreat response! and yes I understand it being oddly comforting … we are after all in the same boat to more or less of an extent.

This is a great idea for breaking down these multi step questions … thank you!

JoMarch 20, 2017 at 5:09 pmMel I totally agree with this and am very concernexd about KS4 especially this year. I am really pleased someone has vocalised it!