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Blog posts about maths being reported in the news

Christmas Lectures 2019

Every year at Christmas, The Royal Institution Christmas Lectures are  a series of lectures aimed at older children, perhaps aged 11 to 14. Each year these lectures are on a different Scientific theme. When I was at the target age, they were an important part of my own Christmas experience. There was a break from televising them, but they reappeared on the schedules a few years ago. Now they are part of my tradition again.  This year I was excited to learn they were on

a maths theme, and the lecturer was to be one of my favourite YouTube Mathematician, Dr Hannah Fry.



Do the current lectures match my memories as a kid?

Well, there are ways in which they can’t! For me they were an intrinsic part of visiting my Grandparents after Christmas, and of course, I’ll never watch them as part of the target audience again.  There are now only  three lectures each year, compared to six in my youth. 

I give that as background, so that my initial impression makes more sense, which was that this year’s lectures seemed to cover a lot of ground. There was a dizzying pace from one example, experiment  or set piece to the next, with the Mathematics explained only at a surface level.

Rewatching for this post, I found I enjoyed the lectures more second time round.  Dr Fry’s purpose for her talks was, I think, to show what Maths can do rather than how it could do it. I think the lecturers in my Christmas memories went deeper, but perhaps that was a trick of perspective.

The Hidden Power of Maths

The subtitle of this year’s talks was ‘The Hidden Power of Maths, and if my concern was that a lot of the Maths did stay hidden, Dr Fry did give a lot of examples of how maths effects our lives today.

I think her greatest success was to encourage her audience to appreciate that Maths isn’t just about numbers. As she says early in the first lecture, “Maths can offer a new way of looking at almost anything.”  She gives many interesting examples of where Maths can be used. Like  Crowd control, weather forecasting, disease control and football tactics. That was all in the first lecture. 

The idea of an algorithm was explained well

In the middle episode, Fry made a good job of explaining the idea of an algorithm. They are good at solving a Rubik’s cube. They are less good at recognising a dog as a dog, and in making a cup of tea. Instructions to a machine have to be very specific in definitions and what to include

I thought the final talk was the better for not trying to cover so many examples. It opened with a spectacular cycling stunt, and closed with some examples of how maths can be used to fool us with fake news and fake music. I confess I found it very hard to tell the fake music from the real.

Despite my reservations on the breakneck speed,  I would still recommend The Royal Institution Christmas lectures to any Maths student. They are available on YouTube. 

A look at some new style questions

This is an article I wrote for my profile on Tutor Pages.

Some of this I may have covered in posts here before

As you are likely to know if you are reading this, the grading for GCSE has been changing, with the new method phased in between 2017 and 2019. Maths, my subject, was one of the first to ‘move over’ to the grades from 9 to 1 from A to G.
Unless a tutor has worked in schools during this period and so picked up on training there, he or she needs to do some homework on the changes. I don’t claim to have done all the work I need to on this, but I thought I would share some observations on how exam questions have changed, specifically in Maths.
The change from letters to numbers is not just cosmetic. The distribution of the grades will be different. Under the old system, grades A to C were considered as the old fashioned ‘pass’. When I took my GCSE course in the 1980s, this was shortly after the GCSE qualification had been created from a merger of GCE and CSE. My lecturers on that course were keen to say that all ‘letters’ were a sign of attainment – a student who gained a D had found some level of success – but the idea that one should ‘pass’ – and that A, B and C were the pass grades – persisted. It’s commonly held that you ‘have a GCSE’ if you attained C or higher.  I’m not saying that is good or bad, but I was sure this would happen even while being told otherwise by my lecturers.

A notable feature of the 9 to 1 system is there are more pass grades.  A grade 4 or above will be considered a ‘pass’ – which is not to say that a pass will be easier to achieve.  A 4 will be roughly equivalent to a C, though the grade boundaries are not exactly the same.  It’s at the top end that the change is greatest, with a 7, 8 or 9 all corresponding to an A/A* grade, and differentiation between the brighter students that provides the reasoning behind the change.

For this to be achieved there needs to be an increase in the number of truly challenging questions on exam papers. There will be more questions that students targeting a respectable 4, 5 or 6 will find it difficult to attempt. There is also a different style of question even in the 4/5/6 range of question that will reward not only hard working ‘book workers’ but encourage a depth of understanding and problem solving skills.

Does this make the exams harder? Arguably so.  But if prepared for properly by educators, will raise the level of ability as related to grade.

I’d like to look at a few examples to support my point – though I’ll add here as an aside, for the non school based tutor, the change has the unwanted side effect that we won’t have the bank of old paper to use. This will of course, improve with time. Exams tend to be made available 15 months or so after they are ‘live’, and some boards have published free samples.

This is a favourite question of mine for working with students is this one – taken from AQA’s sample


Calculation of surface area and volume isn’t the simplest subject area on the GCSE Maths syllabus, but neither is it the most complex. But this question really tests the exam takers reasoning powers. On the old A-G papers, this might have been ‘Find the volume of a cube with surface area 150cm2’. This question puts the student in a new role, which might be unfamiliar if their tutor has not prepared well.

Actually, role playing aside, I wouldn’t recommend any but the brightest student not to just solve the problem themselves first, and compare their approach with Steph’s. She has made a mistake, and one becomes clear when one has worked out one’s own method. But it’s essential to stress that the answer to the question is ‘Steph is wrong because….’ – not the students own answer to the underlying problem

This is another question designed to strech the student. The three marks for part a can be earnt by understanding how to estimate.  The extra mark requires an understanding of exactly what they did in part a. It’s a deeper level of knowledge, and shows that grades 8 and 9 are there if one is truly at home with numbers.

Its not all reasoning questions that make the new exams more challenging.; I have noticed an extension of the syllabus. I don’t remember any question using the language of functions when I taught GCSE in 2013-14, but this question is on the same sample as Hannah above

I have found my able Year 10 student lapped this up – but for a student aiming for a 4 to 6 grade, I’d probably leave this alone.

Are GCSE’s getting harder – An answer

OK so that title is misleading. I am not going to say if I think for sure GCSEs are getting harder, though I do think the maths exams of the last couple of years are making more demands of Students.

But I will give the answer to the question I posted two days ago.


I think what is interesting about this question is that its unlikely the student has seen a question quite like this before.


Its hard to know how to prepare for the question. What it is looking for is a ‘feel’ for the situation. I think the new 9-1 exams are designed so that this ‘feel’ is required to get top grades.

So how do we answer it?  Well, we are given the common factorisation of a2 – b2.   We are told for the values of a and b this is a prime number.

But we also are given a multiply sum (a + b)(a – b) with this as the answer.  And what is the only multiply sum that has a given prime number p as the answer?

Its p x 1 !   So either a + b = 1 or a – b = 1.  A + b can’t = 1 because we can’t have two positive whole numbers adding up to 1.

so a – b = 1,  or a = b + 1. In other words they are consecutive numbers, as the question says.

And that’s it – It is only two marks after all. A knowledge of what prime numbers are, but in an unfamiliar context, is what is required for these marks.

And that’s what I mean by, an ability, a confidence, of recognising skills and facts learnt when seen in unfamiliar surroundings is what is required to get an 8 or 9 in the new GCSE. It will reward true understanding.



Women in Maths;

The advantages of my paid work being in the afternoon is that I can listen to the radio in the morning – in bed!  This morning that meant I caught an interview I wasn’t expecting, on Radio 4’s Life Scientific, with Mathematician Eugenia Cheng..  I’ll include a link to this show here, though unfortunately you’ll need to be in the UK – and to be reading this in the next 4 weeks – for this to works (I Think).


Please listen to the programme, its fascinating.

The first thing that moved me was her discussion of finding Maths a male world. I am slightly irritated that the first half dozen students in my ‘stable’ are all male. There was a possibility of one female student but she preferred a female tutor. I could understand that, but it worries me that parents might be seeing a need to push their son’s but not their daughters towards further achievement in Maths. This isn’t a critique of the parents currently hiring me..  I’m not sure there are any daughters in those families.

But understanding Maths is for everyone. Ones gender does not restrict you from being a real achiever in Maths.  Later blog posts will celebrate the women who have contributed.


Its all linked y’know

 When I was at school, there was some kind of assumption that students heading for A-level would be ‘Scientists’ or ‘Artists’  and it was generally assumed that I would be a ‘Scientist’…  and so I was…

But with the wisdom of age* comes the realisation that there really isn’t that much to choose between them. Maths is the language of Science  and Algebra is the language of Maths(as I say in one of the videos on this website) . Its all about communication of ideas and to limit oneself to one method is to be half the person you could be.

When teaching, particularly exam technique, I do strongly encourage students to write their answers in full sentences. Its about communicating your full idea, and it helps the person reading it (who is in a position to hand out marks!) to be more sympathetic to you.

[*I have age, I leave it to the reader to decide if I have wisdom)

In one of my favourite YouTube clips, Australian actor Tim Minchin gives the graduation address as his University. I’ll post a link below if anyone one wants to watch the whole thing, but in my favourite part of the speech, he talks about the distinction between Science and Arts…  Here are some quotes

“Please don’t make the mistake of thinking the Arts and Science are at odds with one another”

“You don’t have to be unscientific to make beautiful art”

“Science is not a body of knowledge or a belief system, Science is just a term that describes humankind’s incremental acquisition of understanding through Observation
Science* is Awesome”

“The Arts and sciences need to work together to improve how knowledge is communicated”

that includes Maths!