Recently I have found myself having one discussion repeated again and again, and it goes a little like this:
“Sir, why was I told I only needed a C in Maths at GCSE but now I’m applying for unis I need a B?”
“I never said that, and I’m pretty sure none of the rest of the department said that either.”
“No, but you’re maths teachers, it’s the whole world ain’t it. It’s all about A* to C. As long as you get a C in Maths and English you’re fine!”
Now I know for a fact that no maths teachers still at our school perpetuated this myth, and I would like to think that none of our former colleagues would have. I’m also pretty certain that none of our colleagues in other departments would. So it leaves us with the clear fact that the source of this feeling is external to the school. It is society, it is the media, it is the league tables.
We have build a system in Britain of ranking schools by their “5 A*-C including maths and English”, and this is what has given rise to the feeling. Pupils see this focus on the news, on other tv programs and in other media. They are hammered with it. It is no wonder that when some achieve grade c on early entry they feel secure with that, feel like they have the golden ticket, and place their revision eggs in other baskets.
This is why I’m spending my frees tutoring year 13’s who should have gotten As two years ago. I don’t mind doing it, they are all pupils I have a lot of time for and I want them to succeed. I just feel this could have been avoided if the country wasn’t so “C grade focussed”. I’ve already had approaches from year 12 pupils asking if I can help them get a B this summer, so I feel it is still a problem.
On the plus side, they’ve been in to explain the importance to my year 11s!
The issue is two fold really, firstly the heavy focus on Cs needs addressing. It schools were judged on levels of progress, rather than C grades, pupils wouldn’t feel that a C was the B all and end all.
Secondly, there is the early entry issue. Should pupils be put in for early entry? I think that this issue is hugely complex. I feel that some schools were abusing the early entry system and I can understand where Mr Gove was coming from when he changed the rules, but it isn’t as simple as that. Some pupils don’t make it to then end of year 11 for a variety of reasons varying from Illness, pregnancy etc to bereavement or being unable to cope. Without early entry these pupils leave with nothing, but with it they could leave with some qualifications. Also, what about your top sets, those working at a high level by the end of year ten should be able to sit it and move onto another maths qualification in year 11 (AQA offer a good L2 one and OCR a L3 one). I worry the new rules will mean schools won’t allow this incase they have an off day.
I could go on, but I’ll save that for another day. The bottom line is there needs to be reform, reform on the reporting of results, of the “headline measures” and of the early entry system.
I’d like to see some early entry allowed, but with things in place to stop the abuse (schools should not be sitting 4 different modular and linear courses simultaneously to see which gets the best grade). And I’d like the headline measure to be on progress. Remove the C obsession, and remove the stigma attached to those who don’t get it.
Calculus. A word which excites me, probably more than most people. I’m amazed by it. It’s conceptual brilliance, it’s abstract nature and it’s real life application. Not just that though, but it’s history too.
From the earliest visualizations of Archimedes and Diophantus, through the work of Fermat, to the amazing work the student Newton did to really bring forward the calculus we know today. Leibniz and the plagiarism battle. Then the rest, Newtons further work: the product, quotient and chain rules, integration by parts, multivariable calculus. All of it.
Calculus sits alongside complex analysis as my favourite areas of maths. With that in mind, it is probably no surprise that I lost a few hours on Friday to planning a course of lessons entitled “Introduction to calculus” for my year 12 class. (I will share when finished!) In fact, I was so excited by it I ended up dreaming about calculus. (Not for the first time…. I remember while in my second year at uni cramming for an exam on a tensors module and dreaming I was floating through space surrounded by integral signs….)
Then on Saturday I perused the new proposals for A-Levels (Not maths, we’re getting our own review later). The science A-levels have a decent amount of maths in them, it was good to see. However, I noticed there was mention of rates of change and graphs and calculating them by drawing tangents and using them to approximate the gradient. This reminded me of something that I’ve long thought: “Calculus should be on the GCSE specification”. Calculus is the mathematics if change. It can tell us exactly what the gradient of the curve is at a given point and it cab tell us exactly the area. It doesn’t get used in science A-levels as it doesn’t appear until maths A-Level and we need these to stand alone. So why not solve it and teach it to those in compulsory education? Basic calculus is no harder to grasp than circle theorems. Why should it be kept solely for a level? Why shouldn’t it be the spark that inspires more to study maths A-Level? It was on the old O-level when my parents were at school, it didn’t do their generation any harm. In fact their generation produced some amazing mathematicians such as Andrew Wiles.
When I heard about the coalition government’s review of maths GCSE I had high hopes for it. I hoped calculus would make the cut. I was disappointed.
There are other things missing too. Take Standard Deviation, for example. It is the building block for most of the statistical analysis that goes on in psychology, biology and other areas, but is not taught as standard to those in compulsory maths educational.
I would like to see group theory on the GCSE, set theory too. Perhaps a little bit of matrices. Matrices and critical path analysis were then when I did it, and I’ll never know why they went. They are fun and hold far more meaning than some things we teach today, such as trial and improvement!
Are there any topics you’d like to see in there? Or any you’d like to cut? I’d live to hear them and your reasoning.
I’m keen to discover how maths is taught around the world. Both in respect of the curriculum, and in respect of pedagogy.
I’d like to know at what age certain topics at introduced. (When is algebra first touched on? When do you introduce calculus? What do you teach about angles and when? What age do you introduce qiadratics, cubics and quartics? What about complex numbers?)
I’d like to know structures. We have 4 hours a week, which is about standard in the UK. How much teaching time is given to maths elsewhere? Do you teach algebra and geometry as distinct subjects? Do students have to pass a phase (unit; topic; etc) to move on, or do you move through regardless and fill the gaps later? Is data handling (surveys and charts) seen as part of maths?
Is there a preferred pedagogical approach to maths where you are? If so, what is it and do you agree it is the best approach?
I know some countries teach certain subjects in languages other than their native tongue, is maths taught this way anywhere?
I’d love to know these, and many more things. If you have time to answer any of the above, or have a link to a site I can visit myself, I’d be grateful to know!
Here are my new classes latest attempts at the mathematical concept cards!
It seems like an age since I’ve done any concept cards, so I ran some as starters with a few classes last week. Here are some from the sixth form:
My favourite is the BIDMAS effort!
Some from year ten:
These two (above) are my favourites!
Then there’s these from year 8:
And my favourite:
Hope you enjoy them, you can read more on these here and see previous entries by exploring this virtual display! Please let me know your favourites.
This week I was “tweeted” at by one of my “followers” (@bt2bn) with the “hashtag” #MTBOS. I thought, “I wonder what that stands for?” and promptly looked it up. It stands for “Math(s) Twitter BlogO Sphere” and I thought “that sounds like something I’d be into.” So I signed up. (Sorry for the unworldly amount of quotation marks in that opening stanza…)
On further inspection, the #MTBoS seems to be a maths based #blogsync. This week’s prompt was to choose a tweet you’ve favourited and write about it. And this tweet arrived in my feed today and fits the bill entirely.
I retweeted this, and it turns out that quite a few people did already know about it and teach it this way. I’ve never encountered this method before, but given that the preferred multiplication method for most of my pupils is the grid method, it would seem to make sense to offer this as an option next time it comes up.
I was intrigued to see this new method, and I was also intrigued to know so many were using it. If you do, I’d be interested to here your views, and if there are any draw backs. I’ve got a while before it comes up this year, so I’m going to play around with it and get a real feel for any positive or negative points, and to see which method I feel is better for understanding.–
Today has been a good day, 3 of my lessons went fantastically well, one went quite well and the other was a mock (not my favourite things, but certainly things that are useful to measure the progress of the class and inform future planning). Then after work I attend a seminar at Leeds University with a particularly inspirational speaker.
The seminar was nominally around the future of Vocational education at post 16, but in reality it was much wider and focused around the bigger issues of engagement, pedagogy and education policy.
The starting point for the seminar was the 1963 Newsom Report: Half Our Future. At the start of the seminar the summary of the report (as displayed here) and I was immediately stricken by the amount of the suggestions in the summary which were entirely relevant today.
Equality of education
The report and the seminar both look at the importance of education, and how a fair society would incorporate and equality in education. Equality is something I feel extremely passionate about equality in education (I have written before on this subject here and here). I feel that as a society we are failing if we allow the future if our children to be mapped out by the postcode they are born in, or any other reason for that matter. During the seminar the reasons for inequality were broached and It was suggested that the reason for this was political, and rooted in the class system in the UK. This really got me thinking, I have written briefly about this before, but I have never thought about it on this level. On my way home I ran into traffic, and I had many of the issues raised running round my head. I couldn’t help but wonder how different the country would be if people like Kier Hardie hadn’t fought for an equal education. Would we still be born into lives which were fully mapped our? Would I be hard at work in a manufacturing plant because I am a Yorkshireman? These are the questions I was left with and I’m pretty sure that the answers would be yes. For these reasons I feel that we are in a situation where our education policy is too closely linked to political ideology. This gives rise to vast changes which are not given a proper chance. The role of Education Secretary has been something of a revolving door, and as such the changes have been fast and frequent. This worries me. I feel that policy decisions should be made in the best interests of all the young people in the country, not to make political points, and I see a need for a review of the structures involved, if we are to see an improvement.
During the seminar I found out some interesting facts about vocational education and the different approaches that different countries take on it. I was interested to hear that those with the most success are those who offer a wide range of general education, along with the vocational training. This made me think of the recent policy discussions in the UK around new core maths qualifications at post 16 level. I think there is a need for further maths study past the GCSE grade C, but I think it should be focussed around numeracy and functional maths, as opposed to the abstract, and technical, maths covered at A Level. A Level maths should prepare those who do it for further academic study (preferably in maths, but equally in economics, one of the sciences or the such). This new qualification should prepare students for the rest of their lives. It should enhance their opportunities academically and in future careers. I’ve yet to see anything concrete about the New qualification, but I’m looking forward to finding out about it when it arrives.
Engagement is something that is a problem for many in the country, and something that everyone has a say in. A portion of the seminar was around reengaging the disengaged, and this is something I’m keen to know more about. The figures around those who are classified as NEET are quite worrying, but they are improving. The fact that these figures are higher in areas where there is more poverty is a sign that we still have a long way to go before we find a truly equal society, with an education system offering true equality.
I spent some time on the drive home thinking about engagement. Thinking about my classes specifically and the levels of engagement in them. The persistent absentees who disengage from school entirely, and the disengaged pupils who come to school, but avoid work. As teachers we need to recognise that these pupils are as worthy of our time than all the others, and we must endeavour to give them an equal shot at success. I don’t have the answer to how. I feel every pupil is different, every class is different, and we need to keep trying new things until we can achieve this goal. (You can see other post on engagement here, here, here and here).
Hattie, my current reading list (which is quite long) includes this name a few times, because almost every blog or article I read, and inset or MA training I attend or any conversation I have involves him. I’m yet to read any of his meta analyses, but I’m led to believe that his findings suggest that the most important factor to improve outcomes is that teachers see themselves as learners. And this is something I can fully understand. I love learning, and would like to continue to be a learner for my whole life, this learning mindset is important, I hope it will rub off and inspire my pupils to look at continued education and to raise their aspirations. I can also see that being a learner will help me teach, my brain will be in learning mode and I will find it easier to think like a learner, thus will aid my planning and help me ensure pupils are making the best progress. Finally, my MA is in Education and Professional Enquiry, I will be analysis and conducting research and applying it to my own practice, thus keeping my practice in a state of constant reflection, renewal and hopefully improvement.
Now, I just need to find some time to knock some titles off this reading list….
Recently I was at university for a day of lectures towards my MA. During one of the sessions the professor posed the question: “what does progress look like in your subject?” and this really started me thinking about progress, and perceived progress.
Mostly, when folk talk about progress they are talking in quantitative terms. They are talking about progress from one level to the next via performance on a predetermined exam. This is an idea that worries me.
Last summer, edexcel threw us a curveball with a c3 paper that (shock horror) not only failed to ask the same questions in the same order, but that tested some assumed prior knowledge (i.e. That speed = distance /time and that sin a = cos (90-a) ). (You can read Colin Beveridge aka @icecolbeveridge ‘s post on the exam here .)This threw up a rather interesting result in my year 13 class. Pupil a who normally scored the highest scored lowest on this test, scoring lower than his others, where as pupil b who normally scored lowest scored the highest and his marks were not as significantly affected as the rest. The most remarkable thing was that this was exactly as I expected. Pupil A was top through solid hard work, he wasn’t as naturally mathematical as the rest, but put his all in all the time. Pupil b was by far and away the most naturally gifted mathematician in the class, but didn’t work anything like as hard. If I look at the paper results, over the course of the a level pupil a had made more progress (not a full grades worth, but quite a few UMS points), but I feel pupil b has a much better mathematical understanding and is much better placed to study maths further at university. Surely then, pupil b has made more progress?
This isn’t limited towards a level, across the board examining bodies have consistently set paper after paper using the same formulaic questions, which has encouraged a culture of teaching to the exam. This isn’t the way it should be. I (and many others I might add) believe that we should teach for understanding, rather than teaching “this question means type… Into your calculator.”
I would favour a world where exams where unpredictably diverse in their questions. Where they examined a deeper understanding of the subject. I feel this is what is needed to improve the quality of our future mathematicians, and those who go on to study other areas! (Dave Gale, aka @reflectivemaths, has this to say on the future of maths exams, and I’ve written on the topic previously here)
In short: what does progress in maths look like? A greater mathematical understanding, and as such, a greater ability to make sense of the world.
See my previous post on progress here.