The government has just released the new GCSE Maths programme of study for first teaching in 2015. There are significant changes we need to engage with right away to ensure that our current Year 8s are fully prepared by the time they get to KS4.

### Changes to grades and tiers

New grades will be numbered 1-9, where 9 is the highest. Falling below the standard required for a 1 will result in a U grade. This means there will be a total of ten possible outcomes, unlike the nine grades of A* to U at present – so a correspondence between the old and new systems is not immediate.

Maths will continue to be tiered, though the split will be different and **we cannot assume that the same profile of students should enter for Higher and Foundation** as at present. The Foundation Tier will give access to grades 1-5, and the Higher Tier 4-9.

There are currently no grade descriptors, nor any indication of what “expected progress” will look like for students with different starting points. Instead, we will be held to account over our value added against an unpredictable “cohort average”.

@jamesgurung 1/2 The progress measure will show whether pupils do better or worse than average given their starting point.

— DfE (@educationgovuk) November 1, 2013

So forget moving goalposts – now there are no goalposts at all. Gone are our instruments for self-evaluation: “3 levels”, FFT, A*-C. We’re on our own to determine the right targets (and tiers of entry) for each student.

### Changes to the assessment objectives

The three objectives AO1, AO2 and AO3 have not changed but they are weighted differently, with AO3 now accounting for the same proportion of marks as AO2. At Higher Tier, only 40% will be set aside for AO1, placing even greater emphasis on students’ problem-solving skills.

### Changes to the provision of formulae

Some formulae previously given in the front of the exam paper will no longer be listed. Students will need to memorise them.

- Area of a trapezium
- Volume of a prism
- Quadratic formula (Higher Tier)
- Triangle sine, cosine and area rules (Higher Tier)

The cone and sphere formulae will continue to be given, and now also the SUVAT equations – presumably only for rearranging and substitution.

### Changes to the course content

The new syllabus is greatly expanded with completely new topics making an appearance at both tiers. But while there are some substantial new challenges for Higher Tier candidates, the greatest shake-up is **a vast shift of content from the Higher to the Foundation Tier**. It looks like even to secure a Grade 5, concepts will have to be mastered which today’s students targeting A and B grades are struggling to contend with.

The following changes are in comparison with the current AQA Linear specification. Some topics are already tested by other exam boards and these are indicated with an asterisk (*).

#### Skills to be assessed at Foundation that are currently Higher only

- Calculate exactly with multiples of π
- Use standard form
- Round to any number of significant figures (currently 1 s.f. only)
- Expand double brackets
- Factorise quadratics including the difference of two squares
- Solve quadratic equations by factorising
- Know the difference between an equation and identity
- Use y = mx + c to identify parallel lines
- Sketch quadratic, cubic and reciprocal functions
- Derive simultaneous equations from real-life situations
- Solve linear simultaneous equations algebraically and graphically
- Perform calculations with density, mass and volume
- Solve problems involving percentage change and reverse percentages
- Use direct and inverse proportion graphically and algebraically
- Solve problems involving compound interest
- Find corresponding lengths in similar shapes
- Use the congruence criteria for triangles (SSS, SAS, ASA, RHS)
- Enlarge shapes with fractional scale factors
- Find the areas and perimeters of compound shapes involving circles, and calculate arc lengths and areas of sectors
- Use the sin, cos and tan trigonometric ratios for right-angled triangles
- Use tree diagrams to solve probability questions
- Infer properties of a population from a sample, while knowing the limitations of sampling

#### New skills assessed at Foundation and Higher

- Find the equation of a line through two points or through one point with given gradient
- Recognise and use sequences of triangular, square and cube numbers, Fibonacci type sequences, quadratic sequences and geometric sequences
- Calculate compound measures including pressure in numerical and algebraic contexts
- Express a multiplicative relationship between two quantities as a ratio or a fraction
- Write a ratio as a linear function
- Set up, solve and interpret growth and decay problems
- Use inequality notation to specify error intervals due to rounding
- Understand the ≠ symbol (not equal)
- Use the standard convention for labelling sides and angles of polygons
- Derive the sum of angles in a triangle
- Know the exact values of sin, cos and tan at key angles (0, 30, 45, 60, 90 degrees)
- Use Venn diagrams
- Consider outliers when calculating the range of a distribution
- Know that correlation does not imply causation

#### New skills assessed at Higher only

- Recognise and use the equation of a circle centred at the origin *
- Find the equation of a tangent to a circle at a given point, using the fact that it is perpendicular to the radius
- Find approximate solutions using iteration (is this just trial & improvement?)
- Solve quadratic inequalities
- Find the nth term of a quadratic sequence
- Recognise and use geometric sequences where the common ratio may be a surd
- Apply the concepts of instantaneous and average rates of change by looking at the gradients of tangents and chords to a curve
- Prove the circle theorems
- Use the probability “AND” and “OR” rules *
- Change recurring decimals into their corresponding fractions and vice versa *
- Find inverse and composite functions
- Locate turning points of quadratic functions by completing the square *
- Sketch y = tan x (in addition to sin and cos)
- Interpret areas under graphs and gradients of graphs in real-life contexts (e.g. recognise that the area under a velocity-time graph represents displacement)

#### Skills no longer required

- Design a survey question and identify sources of bias
- Convert between metric and imperial units
- Draw and interpret frequency polygons and stem and leaf diagrams
- Solve equations using trial and improvement (no longer in Foundation Tier)

### We’re all in the same boat

It’s worth noting that there will be no alternative mainstream courses. In their guidance on the 2016 performance tables, the DfE explains that qualifications such as iGCSEs will soon stop counting alongside the new, more demanding GCSEs.

[We] will seek evidence that any qualification being proposed for inclusion in performance tables does not have significant overlap with reformed GCSEs. … In time, this will result in the phasing out of academic qualifications from the annual list of non-GCSE qualifications counting towards performance tables.

### Next steps

I’m still in the early stages of processing these changes and considering what they mean for our provision at Key Stages 3 and 4. It’s clear that our schemes of work will need to be revised and for Years 7 and 8 this probably can’t wait until next academic year.

I look forward to forming a working group with colleagues at school to engage fully with this information and also with the new Key Stage 3 curriculum which comes into play from 2014. Our first task will be to establish a much clearer picture of how learning can be built up across the five years – responding to the challenge of a deeper syllabus while also avoiding the temptation to “cover” content in an instrumental way.

Another key action will be to explore with SLT the possibility of increased curriculum time. It probably isn’t true that the stakes are raised. From 2016, maths will be double weighted to count for 20% of the Progress 8 floor standard – just as it currently makes up 20% of 5A*CEM. But with one commentator estimating that the syllabus has increased in size by a third, we’ll have lot more learning to fit in. The secretary of state has suggested that schools set aside 7 hours per fortnight for maths, though it isn’t clear for which year groups this advice applies. We return once more to the issue of judging against a cohort average: as soon as some schools change their timetable allocation, we all need to. As a shortage subject though, I suspect it will pay to be a leader in this particular pack.

### Key questions

**What are the implications of the overwhelming shift in content from Higher to Foundation Tier?****How need we adapt our KS3 schemes of work to ensure the 2017 cohort are fully prepared for the new course?**

**Please share your thoughts in the comments or tweet me at @jamesgurung.**

To support faculty leaders in communicating these changes to their teams, I have created a summary presentation which you are welcome to use.

Excellent post James, many thanks…

Just to confirm, the following 2 points for higher:

– Find the equation of a tangent to a circle at a given point

– Interpret areas under graphs and gradients of graphs in real-life contexts

Imply we’re hitting out Y10/11 students with Calculus? Or am I misinterpreting this?

Thanks Chris. I thought that too when I first read the programme of study, but it turns out calculus doesn’t come into it. You can find the equation of a tangent to a circle by using the fact that it’s perpendicular to the radius. The “areas and gradients” bit is more ambiguous – but I think it just means interpreting the area under a speed-time graph as distance, and so on. I’ll update the blog post to clarify.

Aah. Makes sense, but lots of intermediate information to get wrong if calculating gradient of radius before working out equation of tangent.

Was also looking at page 9 – interpret the gradient at a point on a curve as the instantaneous rate of change;

My instant thought was basic differentiation. Esp when mentioning quadratic and non-linear graphs on page 7

Thanks for clarification though. I can breathe easier now I hope!

Fantastic post. Thanks.

I too am looking forward to getting stuck into this one!

Re: calculus, it isn’t there as a requirement unfortunately. I would have liked to see it in.

I disagree – “calculate gradients of graphs and the area under a graph, including quadratic” is differentiation and integration and later “interpret the gradient at a point on the curve as the instantaneous rate of change: apply the concepts of average and instantaneous rate of change” all signifies calculus surely?

You’re right that it’s ambiguous, and I guess we will only really know once the exam boards publish their specifications. I have a strong suspicion that calculus will not feature though – mainly because no scope is given in the subject content. If it said “calculate gradients of polynomials” that would be different – but it just says “calculate gradients”. Students will most likely do this by drawing and measuring tangents. I could be wrong!

Calculating gradients of tangents and interpreting areas under curves is currently in the current AQA Linked Pair Pilot Specification.

Great article.

Are Labour up for this?

…how much planning do we have to do before we find out further changes?

Thanks for taking the time to put this together. Much appreciated. There are ‘interesting’ times ahead for Maths departments and for curriculum designers/timetablers. What gets squeezed out for extra Maths?

What a fantastic summary. I have forwarded to my colleagues and management. Something is going to have to give in the timetable, but love the new content. We teach Edexcel IGSCE which includes Calculus and Functions, so would like to see this content included, kids tend to really like the Calculus in particular.

Thanks for the summary it is very useful. Does anyone know if Independent schools will be required to follow this course or will they still be able to do the IGCSE?

good summary

Very helpful – thank you

I worry what all of this will look like for the E/F/G grade students. What will their exam paper look like and how will they feel about their Maths? I am looking forward to the beefed up curriculum for the more able but concerned for those who genuinely struggle with the Maths. Getting the level of challenge right at Y7/8 will be much better as in some schools I feel there is often a “repetitive / stagnant and repetitive” phase. The new curriculum will make us ‘get on with it’ which must be better for all concerned.

Are you aware of the following website:

https://sites.google.com/site/maths2014sow/

We are a group of maths teachers preparing for this with an online scheme of work.

Jon

Hi Jon

Thanks for sharing this. To be honest, I’m rather hoping PiXL will come up with something…

How do I follow this blog please and get hold of the presentation?

Thank you so much for this post! Im starting teacher training this year and this has been so helpful!

Gina

I am a retired teacher but keep my hand in by tutoring. This site was just what I needed as I teach different boards and needed a general change to subject grades. Excellent information easily laid out.

Many thanks

I too am a retired maths teacher doing some private tuition and found this extremely useful. Thank you very much indeed.

May I ask one question? Can someone recommend a good text book for students with good explanations and lots of questions for students?

Thank you once again.

Solving equations by iteration is not just trial and error. See this for example: https://revisionmaths.com/advanced-level-maths-revision/pure-maths/algebra/iteration