## AS Levels

We are now fully into “Exam season”, Year 11 have their GCSE exams, and Year 13 have their A Levels. Then Year 12 have AS Levels.

AS levels are a weird thing. They are no longer a component part of the A Level, they are very early in the exam session and it seems to me an unnecessary added pressure.

Last year we took a decision as an academy not to enter pur maths students for the AS exams. We did this to maximise pur teaching time and avoid unnecessary stress. This year the decision was taken at trust level to enter them in all subjects.

I can now see two sides of the argument. Last year our students focussed heavily on their other subjects and not maths as they had external exams for those subjects. This meant we lost teaching time and their homework suffered during exam season. This year we have not finished all the content early enough to really focus the revision. I really dont know whats best. I do think, however, that it is important to have a decision made for all subjects.

*Are you entering your students for AS Levels? I’d love to know if you are or not and why you made that decision. You can answer in thw comments or on social media.*

## Single exam board?

*This post was written prior to Michael Gove being knocked out of the leadership contest. It was first published here, on Labour Teacher on 8th July 2016.*

Way way back in the days of the ConDem coalition, we had an education secretary named Michael Gove – a man who very soon could be our prime minister. Give polarised opinion within tele profession. Many chastised everything he did, and other rushed to defend his ideals. There were some, like me, who took each idea on its merits, chastised some and celebrated others. (You can read some of my thoughts on his tenure here.)

One of the ideas he had that I liked was the idea of a single exam board. We had a situation where it.was considerably easier to gain a C in maths on some boards than other and that, to me, seemed quite ridiculous. This idea was quashed before it started due to “EU monopoly laws”.

Last week after a long campaign I was left heartbroken by the decision taken by the (slim) majority of the country for the UK to leave the EU. I had looked at the pros and cons and am certain that remaining would have been the better option. I tried to find positives, but there were few. People celebrated the fact we would no longer have Cameron (a man who I generally detest) in number 10, but even this was a negative as the names I the frame to replace him make him look a much more reasonable option. Some of the folk in the running make him look positively Marxist.

So I continued to look for positives, and I remembered the idea of a single exam board. Surely this would now be back in the table? Especially if, as I suspect will happen, Gove wins his parties leadership?

This would mean students from around the country were all sitting the same exams and we sold have a situation where you knew exactly what each grade means. I’ve got my fingers crossed.

## Examinations, Examinations, Examinations

*This post was first published on the 3rd May 2016 here, on Labour Teachers. *

Sometimes it feels like the government’s main three priorities are examinations, examinations and examinations, and this fact has certainly led to many people involved in education to express their disagreement and disappointment with the system.

Most recently, a large number of people with children of a primary school age have chosen to keep their children off school in protest against the new SATs test their children will sit. This has caused me to spend some time thinking about this, and try to put together some views.

**Exam factories**

One of the leading criticism of these tests is that it drives schools to shrink their curriculum and focus heavily on the content which will be examined – meaning subjects like art, music, history etc get widely ignored and children miss out on an important part of their education. I can certainly find agreement with this, however I think this is already an issue with the SATs as they stood, so it doesn’t seem to warrant the furore of the new tests, which can only compound an already prevalent problem.

**What are they for?**

This is a key question, and I think that a different answer to it would lead to a different outcome. The tests as a marker for informing future teachers of a students ability are very helpful. The tear that SATs were boycotted we saw real problems with the grades reported by primary schools as there were massive inconsistencies from school to school. However, this argument alone seems to be silly, as what we see often is that students primed and drilled from the test from September to May achieve well, but then do no more maths from May to September and often regress. If this was to be the sole reason then surely they could be abolished totally and secondary schools could complete diagnostic tests on entry?

The other answer to this question is to measure school performance, and this is a real can of worms. It is this exact fact that leads to the exam factory conditions and the gaming the system and as such causes a load of problems. The other side of it is, however, that there needs to be some way of ensuring that schools are doing what we expect them to do. I don’t know what the answer is, but I tend to think high stakes testing is not the answer.

**Is it just a problem with SATS?**

No, all the issues outlined above are transferable to GCSE and A level exams. Again, I don’t have an answer, but I think that there must be a better way to treat 16 and 18 year olds than to make them sit high pressure, high stakes, examinations at a time of increased hormones knowing that if they go wrong that could seriously affect their life chances.

I don’t have the answers, but I do feel that there are answers and our job in opposition is to find them and present them to the public, showing that if they vote differently in 2020 we can give them a better way.

## Dumbed down markschemes?

Today I was working through the June 2014 Edexcel M1 paper for my year 13s, noting down thought processes etc and I arrived at this question:

It’s quite a nice, general bouncing ball question that takes into account many of the rules of mechanics. When I finished the question I checked it against the markscheme so I could jot down where each mark came from and on part E I received a bit if a shock.

The weight of the ball is given as is the distance it’s dropped from and the distance it bounces to. In earlier parts of the question you have been asked to calculate the final speed of the bit before the first bounce and the initial speed after. Part E asks for the time between the ball being dropped and the second bounce. I split it into to, used s = ut + (1/2)at^2 (u=0, s=2,a=9.8) to find the time it took to drop, then the same equation for the time between bounces (this time s=0, u= the value already calculated, a=(-9.8)). A simple question, a simple solution and a nice answer. The markscheme, however, says this:

I don’t understand why they have felt the need to work out the time between the first bounce and the top then double it. It’s a valid mrthod, granted, but surely looking at the whole motion is sensible as acceleration is constant?

Worryingly, in the notes there’s no other solutions offered and I was left wondering if examiner’s might miss that thus method is not only correct,, but actually more sensible.

*Which way would you have done it? Do you think I’m correct thinking mines the mire logical sensible way?*

## Did they meet their targets?

Manifesto’s are due to be launched imminently, I thought about last time round and wondered how much of the conservatives manifesto actually came to fruition. I dug out the 2010 manifesto to take a look. The section on schools starts with some bold claims:

They were going to “Improve standards for all”, “Close the attainment gap”, “Enhance the prestige and quality of the teaching profession”, “Give heads and teachers tough new powers of discipline,” “restore rigour to the curriculum and exam system,” and “give every parent access to a good school”.

Did they manage it?

*“Improve standards for all”*

This is a noble aim, and one I hope all politicians have at their core. I certainly think the tories were trying to improve standards. This is fairly unmeasurable though. They cut money for school buildings, which means some schools are housed in less than brilliant accommodation, but some schools were improved. Let’s hope we all, in the education sector, have been, and continue to, improving standards fore all.

*“Close the attainment gap”*

In 2010 the reported attainment gap was 27.5% in 2014 it was 26.6%, this is certainly a drop. A drop which one would assume owes at least some thanks to the Lib Dems pupil premium payment.

It is great that the gap has dropped, although it is still far too high. And the measure itself is crude, as it’s based on FSM which is self nominated and misses a large amount of the most deprived in our communities.

*“Enhance the prestige and quality of the teaching profession”*

This is a great aim, the highest performing school systems have prestigious status for teachers. It is unclear, however, why Michael Gove thought an all out war with the teaching unions in which he repeatedly demonised teachers was the best way to do this. The constant teacher bashing and dismissing opposing views to his own was certainly not a way to achieve an enhanced status for the profession, quite the opposite in fact.

Teach first (love it or hate it) has certainly brought in more top end graduates, and as one of the largest graduate recruiters it would seem that at least with final year students some prestige has increased. Although that’s certainly not something the government can take credit for as it’s a charity and existed before they came to power. Their manifesto included the idea to expand it to “Teach Now” and “Troops to teachers” neither of which I’ve heard much about since?

*“Give heads and teachers tough new powers of discipline”*

This one was mainly lip service I think, and hasn’t really impacted anything. Legally schools can now keep pupils for detention for up to two hours without prior notice, but I don’t know any schools that have moved away from a policy of informing parents. There was also the “reasonable force” measure, that was pretty much exactly the same as the law it replaced.

*“Restore rigour to the curriculum and exam system”*

This one remains to be seen. I’m certainly in favour of the new maths curriculum, all the way from KS1-5, it certainly has more rigour, although I’d personally have liked even more (ie calculus on the GCSE, you can read more of my views here). I’ve not really looked in depth at the other subjects, I don’t have enough knowledge to discuss them – I’d love to hear your views if you have any in the new curricula in your subject.

The exam reforms are another matter, we won’t know whether they are an improvement until they start, they have a lot of potential but it certainly seems to be a little rushed. The new maths GCSE is due to be examined in 2017, the course contains more content and as such it will take more than two years to cover, yet we have no sample assessment materials as yet to base a decision on which exam board to choose. That said I do think it will be an improvement, I just wish it had been thought out and introduced better and more quickly.

*“Give every parent access to a good school”*

Like the others, a very noble aim, and one which we should be applauded. However, the decision to allow Free Schools to be built where people fancied, rather than building schools where there were a shortage of places, has led to some areas still having a shortage of school places and some having a surplus. This means that some parents struggle to access any school, never mind a good one. The investment in new schools had been evident, but it’s been too often in the wrong place.

*So, they have closed the gap, and they have increased rigour in the curriculum. They haven’t improved the prestige of the profession, they’ve failed to build schools in the correct places and they’ve not increased power to discipline. Some hits, some misses. They did, of course, have other education policies over their tenure (I discussed some here) but these are the ones mentioned in their 2010 manifesto.*

## Maths Conference 2014

Yesterday I attended the Maths teachers conference in Kettering. Here I intend to share some thoughts on the day, and on the workshops I attended. I won’t go into too much depth, and will come bacTo k to these topics in later posts.

The event was hosted by Mark McCourt (@EmathsUK) of La Salle Education (@LaSalleEd) which, to my disappointment, has nothing to do with Dr Benton from ER. The event was in Kettering, and due to an overestimate of my travelling time I arrived an hour before the start. Luckily I wasn’t the only one, and found some similarly early maths teachers to chat with.

The event started with coffee, pastries and an exhibition of stalls from examboards, book suppliers and other such folk. This was another nice opportunity to chat and to learn more about the specs for the new GCSE. It was then off to the theatre where Mark give an intro to the day, and then Andrew Taylor from main sponsor AQA (@AQA) give a short speech to kick us off. It set the tone well and had us all ready for the first main headliner.

*Vanessa Pittard (@vanessapittard) – Department of Education*

Vanessa gave a great overview of the current changes in maths education policy, and the rationale behind it. She touched on many topics that would be met again throughout the day, such as the importance of mastery and curriculum design. She gave me many starting points from which I hope to learn more and gave me a better understanding of the China/England maths exchange which seems to have been majorly misreported by the press. She spoke about the Maths curricula in the highest performing countries, and something that surprised me was to hear that pupils progress through at the same pace, regardless of ability. She neglected to include the status than in high performing countries teacher spend 30% of their time teacher, with the rest spent planning, preparing and assessing as well as working on improving their practice. Compared to the UK, where it’s 90%.

*Mark McCourt – A maths teacher’s network *

Next it was our host, setting out his utopian vision for a better world for all maths teachers. This vision is encompassed in his new product “Complete Maths”. It’s an online resource that aims to help with lesson planning and sharing resources. It’s a big idea. It allows a personalised curriculum and the part of it that builds assessments looks particularly interesting, but I have my concerns. Mark said that when you upload a resource it goes to the design team who vamp it up and publish it with your name on it, that worries me. What if I don’t like the way they make it look, or if they make a mistake on it, and then there’s a resource with my name on it that I’m not happy with. Also, if every maths teacher in the world does get on this programme, can you imagine how many resources would be available for each lesson? It would take forever to wade through them to find the good stuff. It’s a product that has masses of potential, but it also has a massive price tag and it currently unproven. I shall look forward to hearing reviews of it once it’s been up and running a while, to see which way it goes.

*Mel and Seater from Just Maths (@Just_Maths)- KS4 intervention.*

This was the first of the workshops I picked. Like all the choices it was tough, and I had to miss out on seeing a lot of people throughout the day who I would have loved to see. I chose this one because I feel that it could benefit my pupils.

Mel and Seager form the perfect double act, they’ve worked together for a long time, and they bounce of each other superbly, it was a thoroughly entertaining presentation. They spoke about the intervention policies they’d put in place in their previous school, and what they’re doing now. Some of the things they do, we do, but some were ideas I’d not heard, so will feedback to my department and discuss whether we can get any benefit from them. I was particularly interested by the one to one tuition they were offering, and the strategic take on early identification of those in need of support.

They also highlighted some of the resources on their website. Some I knew about, and some I didn’t, so I left the workshop with plenty of new info to work with. I am especially excited by oops sheets, and the bread and butter sheets.

*Johnny Ball*

I won’t lie, my decision to choose this workshop may have had more to do with my childhood memories, than a belief I would gain much out of it. And to be fair, that’s what I got. A charismatic entertainer who made me laugh and told me some interesting facts about maths, some I already knew, and some I didn’t.

*Bruno Reddy (@MrReddyMaths) – The King Solomon Story*

I have been following the fortunes of Bruno and his colleagues at KSA for a while now, and was excited to learn more about the school who hit 93% 5 A*-C including English and Maths with 75% of the intake Pupil Premium.

Bruno presented very well, I learned a lot about KSA and their strategies, that he calls the 1% things. The principal ones being that culture is king and consistency is queen. I think there are a few things I can take away from this session and a few that are common sense, but there was also a lot that may work in a 60 pupil intake where pupils are in lessons from 7:15-4:30 everyday, but logistically couldn’t be transferred to a larger school with a more normal school day. There were also things I don’t think I could buy into, such as the finger clicking and chanting! The latter of which has a real cultish feel to it.

He briefly touched on the mastery curriculum that they use in maths, which is something I’m extremely interested in. I’ve been advocating mastery for a while, and the results from KSA suggest that that advocacy may well be correct.

*Kris Boulton (@Kris_Boulton) – Curriculum Design*

Kris is one of Bruno’s (now former) colleagues at KSA and he spoke in much more depth on the mastery curriculum that they have pioneered there.

For me, this was the session I most enjoyed and found most interesting. He delved into the theory behind mastery well and used it to explain why they had decided to back it at KSA. This was intriguing, and I hope to look further into the studies he mentioned myself.

He also gave an overview of the curriculum itself, which helped me understand what it is in more depth. It’s incredibly simply, but makes a ton of sense. Cover less topics in more depth, separate minimally different concepts and build in opportunites to practice and embed knowledge.

*I enjoyed each session, and enjoyed the day immensely. I have written this from memory, and without notes. I have made notes and I will, at some point in the future, be reading through them and looking deeper into each parts. When I do, I will share more on this blog.*

*It was great to meet so many new people at the conference too. Some who I’d already spoken to on twitter, and some entirely new. Unfortunately, there were some I didn’t get to meet, so maybe next time. If you went, and have written your reflections, please let me have a link, I’d love to hear what others thoughts are on these issues, and to hear in detail about the workshops I didn’t manage to attend.*

## Passivity in the maths classroom

Today I managed to find a few minutes to browse the latest issue of Maths Teaching, the ATM journal. One article that caught my eye was the “from the archive” section, where Danny Brown (@dannytybrown) introduced an article that was first published in 1957. The article was written by Ruben Schramm and is entitled “The student’s passive attitude towards mathematics and his activities.”

The article discusses mathematics teaching, particularly the nature of students who often, for whatever reason try to find an algorithmic method to follow to solve a problem, looking to recognise the problem and answer it in a similar way to how they have answered questions before. This is a problem that was obviously prevalent in the 1950s, as evidenced in the paper, but it is still prevalent now, and I feel the nature of our exam system must at least hold a portion of the blame. The questions on exams tend to be very similar and students will learn methods to answer them whether the teachers like it or not. This is one issue I hope will be dampened a little with the upcoming changes to the exams.

Schaum suggests that this passivity in maths, this tendency to look for algorithms, is in part down to how students see mathematics. He suggests that when they see teachers solve problems on the board by delivering a slick, scripted solution they can get a feeling that it is via “witchcraft” and see the whole process of uncoordinated steps, rather than a series of interconnected mathematical ideas. The latter would encourage the students to drive the mathematics from their internal ideas, and this would lead to them being more able to apply their knowledge in new contexts. If we can develop this at all levels then I feel we really would be educating mathematicians – ie giving students the skills to be able to apply their knowledge in new contexts, rather than teaching them to follow a recipe to answer a question.

Schaum goes on to discuss authority, the infallible authority that students see in their teachers and in the mathematical theorems and formulae. It is suggested that students see these theorems as infallible, and as such they reach out for them in their memories and try to apply them to problems. This can mean that the problem they are applying them too is only vaguely similar to the problem the theorem or method is actually there to solve. Schaum calls these “analogy mistakes”, and suggests that it is down to how comfortable with the content students feel that mean they revert to them. I feel that this is true in part, but that also the pressure of exams can lead students to confuse things in their head if they have opted to learn algorithms rather than looking to develop a deeper understanding.

I’ve had a couple of examples of these “analogy mistakes” in lessons and exams recently. A year 12 student came to an afterschool elective as she was trying to solve some coordinate geometry problems involving tangents. She had gotten herself really confused because in her notes she had written tangent gradient is perpendicular (when discussing circles) but she didn’t think it should be perpendicular because a tangent at a point should have the same gradient as the curve. I spend a little time discussing where her misconception had come from (her notes should have said “perpendicular to the radius”) and discussed how she could remember this more easily if she has thought about the graphs and sketched them.

Another example was in a recent exam one of my students had answered part of a question on alternative from incorrectly, she had done the alternative form bit well and the answer was 25 Sin(x + a), but it then asked her for the maximum she had written -25. When I questioned her about this after it seems she had fallen victim to an “analogy mistake”, she had remembered that “maximum is positive” when discussing second derivatives and in the pressure of the exam this memory had taken over, rather than the rational thought process that should have flagged up that the maximum or the function would be 25, which is definitely bigger than -25.

In his preface Danny Brown suggested that one way to counteract this would be by questioning and discussion, if we remove the authority from the discussion and don’t validate the answers by issuing statements saying they are correct or incorrect, but rather open them as conjecture to the class who then can discuss this, then we can allow students to develop their own mathematical ideas. Lampert (2001) also discussed this idea and suggests that as teachers we need to be striking the right balance between allowing students to discuss and conjecture and ensuring they understand what is important and aren’t making mistakes. This is something I strive for in my own classroom, and something I am currently working on trying to improve.

This post was cross posted to Betterqs here.## Share this via:

## Like this: