Covering the maths curriculum?

The GCSE maths curriculum is huge, and it’s split by tier, so immediately there is an understanding that some students won’t be able to access it all by the end of year 11, but that does leave us as teachers with a dilemma. How much do we actually cover with our students.

In particular, if you have a group of students who are realistically only going to get a grade 1/2 on foundation, or 5/6 on higher, do you aim to cover all of the content with them, including the stuff they are really unlikely to grasp? If you do want to, how much depth can you actually achieve with them, especially on those more challenging topics. If you don’t want to cover it all, what gets left behind?

The reality is at the outset of their secondary journey you have three choices:

  1. Cover everything in depth.
  2. Cover everything, but for some topics you will only skim the surface.
  3. Don’t teach it all.

Let’s break them down:

Everything in depth

For most people this would be the ideal, cover all the curriculum fully and in depth so that all students get it, and can think and act mathematically even in the face of tricky exam questions.

The problem is it would require huge flexibility in the amount of time we have to spend with students. Some need far more time to develop their understanding than others.  That isn’t possible when you’re trying to mass educate every child in the country with class sizes of 30, staff shortages, and an overloaded curriculum in most subjects.

We simply don’t have the hours necessary to get all students to learn all the maths by the time they are 16, and also have time to cover the curriculum in all of their other subjects.

Skim the surface

This does sound better right? Students still get that full curriculum experience, they still have a chance at answering all the exam questions, and if they find one topic tricky they might pick marks up elsewhere so it’s not such a bit deal.

The reality is this does sort of work with many students, particularly as you near exams in year 11, because you can teach them some vaguely memorable tricks to help them solve problems. Maths is crammed full of handy mnemonics for students to recite when faced with standard maths questions.

The downside now is that those students often haven’t got the faintest idea what they’re actually doing, so if you ask them anything non-standard they will be hopelessly lost. You might have the time to do this, but that time is being spent racing through material which is swiftly forgotten because there was no depth.

To really understand maths you need to build on your prior understanding, make connections with other ideas, grasp the structure of the problems you are tackling rather that just the surface number crunching. Those helpful memory tricks are more likely to be mis-remembered than useful if there is no deeper understanding to pin them to.

Sure, it might mean they sit in an exam and there is nothing “unfamiliar”, but that isn’t the same as being able to answer the questions.

Don’t cover it all

The third approach is to deliberately not teach everything. To teachers in other subjects this probably sounds like blasphemy. How could you even think of sending students into an exam knowing that they won’t have a clue how to even start on some of the questions?

This path is generally taken by staff who know (or at least think they know) in advance that certain topics will be inaccessible to their class, so time is better spent elsewhere securing the foundations. There are some clear pitfalls to this approach.

If you’ve never taught a topic, students have an immediate ceiling on their potential in an exam. If (when) those topics show up on the paper, they have no choice but to skip them (or guess, but that’s not likely to bear any fruit). And how do you choose what to skip? How do you know this class won’t cope with that idea? What if you skip the topic that your class would have absolutely nailed in a couple of lessons?

Deliberately avoiding topics in the curriculum is a complex business, but it does adequately solve the time problem. You just teach what you have the time to cover properly and don’t worry about the rest.

In conclusion

Do I have a preference? Well of course I do, but I’ll save that for the next post…

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Results do matter

It’s that time of year again when well-known public figures proudly proclaim that they flunked their exams, or that exam results just don’t matter.

Don’t be fooled, they are completely wrong.

Back in 2017 an accounting firm commissioned an infographic detailing all the UK billionaires without a university degree.

It’s compelling, you can be a success without university, so forget those A-level results, and don’t waste your time studying.

It’s utter rubbish though.  Their list included a grand total of 13 individuals.  The times rich list in 2017 named 134 billionaires.

Taken as face value, that means you are 9 times more likely to become a billionaire if you have a degree than if you don’t.

Of course, that’s rubbish as well, the vast majority of that list have their massive wealth not because of qualifications, but because of good fortune (luck).  They were born in the right family or they fell upon the right opportunity at just the right time.

And the same goes for other successful figures (for the sake of brevity let’s call them all celebrities).  Sure, some of them did very well in school, and others didn’t.  Most of those recognisable characters were beginning to become successful before they even started A-levels.

Their talent was spotted early, they were already on the path, so why would they bother with academic studies?  How much of their success could be attributed to those exam results anyway?  Again, a healthy dose of luck is at play here, being talent spotted, getting the right mentor to develop your skill during those formative years, and having skill in a field which enables you to become a celebrity (can you name a famous project manager?).

Here’s the really important part though:

Celebrities are the minority.  There are so very few of them compared to everyone else.  Almost everyone I’ve ever taught will not be famous, they will just get a “normal” job like everyone else.  Their family and friends will know them, but no one else will ever recognise their name.

Those “ordinary” people are far from it, they are amazing individuals, with incredible capacity to do extraordinary things with their lives.  Those things probably won’t make them famous beyond their close circle of friends though.

For those ordinary people, exam results matter.  They are the key that opens the door for whatever is next in their lives.  Sometimes they open a different door than was expected of planned.  That’s fine, no one really knows where they will be in 5 – 10 years, we just plod on with the next step.

But to pretend the exam results are irrelevant is foolishness.  Those results are often the first thing a prospective school, university or employer will look at.  In a wide field they are the first step in narrowing down candidates, and that really does matter.

To claim that “poor” (by which I mean lower than you wanted) results are the end of the world is also foolish.  But that isn’t because they don’t matter, it’s because there are always alternate paths to take.

Missed your offer grades?  You could go through clearing to find a different course at a different university.  You could opt to retake year 13.  You could look at a foundation year course.  You could take a gap year and reapply with your results in hand next year.  You could shift gear entirely and explore apprenticeships.  There are so many choices, they just look a little different from the plan in your head before you opened the results envelope.

There’s no denying the disappointment you will feel though, and being told by celebrities that it doesn’t matter is going to cause more hurt than relief.

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#ClassicBlogWeek roundup

I will be adding some summary posts when I’ve managed to collect my thoughts, but it will take a while as there is so much to read here.

In the meantime, here is a simple table of all the blog posts shared during the week (that I found, if I missed any please let me know!)

Blog PostAuthorShared By
Snake Oil@oldandrewuk@CFarman1
At what cost?@jo_facer@bennewmark
Hornets and Butterflies: How to reduce workload@joe__kirby@MrAHarrisonCS
Mode A + Mode B = Effective teaching and a rich enacted curriculum@teacherhead@Pete_Bonn
Achieving coherence in primary science@Mr_AlmondED@Mr_N_Wood
What did I mean by ‘the curriculum is the progression model’?@mfordhamhistory@isaacmoore7
Genericism’s children@Counsell_C@Ruth_Ashbee
This much I know about…why putting your family first matters@johntomsett@meganbows
Beyond knowledge organisers; building the best curriculum in the world.@jon_hutchinson_@teacherhead
Why teach?@bennewmark@MrEFinch
Retrieval Strength Vs. Storage Strength@EdScientists@Benneypenyrheol
E. Coli and Quality First Teaching@Ruth_Ashbee@sharperpencils
Sequencing and coherence: what are we really talking about?@VallanceTeach@MrAWGordon_
Organising an event: a toolkit@Penny_Ten@TeachLeadAAli
The 3D curriculum that promotes remembering@ClareSealy@coejooper
Marking and feedback are not the same@jdurran@coejooper
Teach Like Nobody’s Watching@EnserMark@MrPattisonTeach
Why we’ve got planning and marking all wrong (part 1)@MichaelT1979@TomRees_77
Simplifying Cognitive Load Theory@adamboxer1@Dr_Castelino
Why Target Grades Miss Their Mark@bennewmark@PaulCline_psy
On Eudaimonia: Simply Outstanding Is Not The Best@Trivium21c@onechriswhite
What if we cannot measure pupil progress?@profbeckyallen@HistoryKss
Careering towards a curriculum crash?@profbeckyallen@head_teach
The Slow Practical@adamboxer1@MBDscience
Marking is a hornet@joe__kirby@MrThorntonTeach
Structured revision lessons using retrieval, spacing & interleaving@missdcox@MrThorntonTeach
Do they understand this well enough to move on? Introducing hinge questions@HFletcherWood@MrThorntonTeach
Applying Cognitive Load Theory to English part 3: The Problem Completion Effect: An Overview@Tom_Needham_@MrThorntonTeach
The 7 habits of highly effective lesson plans@PepsMccrea@ahmdsahbi
What sorts of substantive knowledge are needed to get better at history?@mfordhamhistory@vickilbarnett
“So that’s what you mean, Miss.” Using multiple-choice statements to model source analysis@PaulaLoboWorth@MrThorntonTeach
Red pill, blue pill@head_teach@CarlyWaterman21
The Extraordinary Case of Mr Yamazaki@solomon_teach@AlexJQuigley
The Science of Science Practicals: Are We Wasting Our Time? Pt. 1@adamboxer1@DrWilkinsonSci
Knowledge: independently necessary or collectively sufficient?@mfordhamhistory@MrMountstevens
Nothing new, it’s a review – on why I killed my starters.@bennewmark@MrAHarrisonCS
End graded observations: this year’s brain gym, and the gorilla in the classroom@joe__kirby@HFletcherWood
I was a teenage progressive: a defence of the debate@JamesTheo@Ruth_Ashbee
The specific things that leaders do@steveadcock81@head_teach
Should we use questions to teach? – Part 2@Kris_Boulton@ahmdsahbi
Tests are inhuman – and that is what is so good about them@daisychristo@JamesTheo
The Progress Myth@jpembroke@primarypercival
The 5 Golden Rules of tracking@jpembroke@primarypercival
How to speak truthfully about what it means to be human: a user’s handbook.@ClareSealy@DynamicDeps
No written marking. Job done.@primarypercival@DynamicDeps
A ‘Mastery-light’ Subject Curriculum Model@atharby@BeckfootTL
Applying Cognitive Load Theory part 1: Overview and The Worked Example Effect@Tom_Needham_@NSMWells
An idiot’s guide to the philosophy of education: part 1@JamesTheo@NSMWells
Can we improve school interviews? Part 1: A brief review of the research@DavidDidau@NSMWells
What is school leadership?@TomRees_77 @Barker_J@NSMWells
What makes checklists transformational?@HFletcherWood@NSMWells
How retrieval practice works part 1@overpractised@NSMWells
Curriculum Series Number One: Curriculum Chaos@Trivium21c@NSMWells
Undiscovering the mountains of kong@JamesTheo@PaulCline_psy
Pedagogy is overrated@StuartLock@primarypercival
#ClassicBlogWeek AfL In Science: A SymposiumCheater, lol@TChillimamp
Education is an end in itself not a preparation for the workplace@C_Hendrick@JamesTheo
Progressive vs Traditionalist vs Professional@EmathsUK@ahmdsahbi
Clear Teacher Explanations I: examples & non-examples@Mr_Raichura@Dr_Castelino
World building: What can history teachers learn from imaginary realms?@michaeldoron@VallanceTeach
Memory not memories – teaching for long term learning@ClareSealy@primarypercival
A lesson is the wrong unit of time@BodilUK@primarypercival
The Secret of Happiness and Virtue: behaviour and sanctions@danicquinn@HFletcherWood
Why Fads and Gimmicks Should be Resisted in the Classroom@C_Hendrick@stoneman_claire
To wish impossible things@head_teach@chrisdysonHT

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