I've written two posts about curriculum - this is the second.

My first post was about how to shoehorn an oversized curriculum into a limited number of lessons. Dan Draper summed it up nicely: "

*you can’t win but you can pick how you lose*”.In today's post I've written more generally about curriculum reform and some opportunities to make changes in maths when the time comes.

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The main concern in both primary and secondary schools is that the curriculum is way too crowded with content. This creates a suboptimal experience for children. I believe the rationale for increasing content levels was to raise the level of challenge across the curriculum, but there are better ways to challenge students.

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I can't imagine how difficult it must be to agree on what topics to include on a national curriculum. I suspect that numerous interested parties argue passionately for the inclusion of the topics they personally value, and as a result too many topics end up on the shortlist. An example of this is the Royal Statistical Society's involvement in the decision to include the Large Data Set when the A Level Maths curriculum was last rewritten.

- The maths curriculum is so vast we don't currently have the opportunity to teach its content in depth.
- Skimming the surface of a broad range of mathematical ideas at Key Stage 4 doesn't allow us to develop strong 'A level ready' mathematicians.
- We can't increase the time allocated to maths because schools need to timetable other subjects.
- Teaching maths 'in a rush' is frustrating for teachers, leading to further dissatisfaction with the profession.
- Making the maths curriculum smaller, and therefore allowing schools to reduce maths contact time, is one strategy for dealing with the severe shortage of maths teachers. It may be one of our only options at this stage.

*top ten topics to consider axing from Higher GCSE*'. Please note that this is meant to be a bit tongue-in-cheek so don't rant at me if I've listed your favourite topic!

**1. Systematic Listing and Multiplicative Counting**. As much as counting ice cream flavours makes for an engaging lesson, I doubt anyone would miss this if we removed it.

**2. Loci and Constructions.**I'll be very happy if I never have to see a pair of compasses again in my life. I know some people think we should teach constructions because they deepen students' understanding of geometry but come on, guys. Seriously. It's not 1850.

**3. Plans and Elevations.**I can't even think of anything interesting to say about plans and elevations.

**4. Negative Enlargements.**I think you could make a case for axing all of shape transformations, and this would save a large amount of Key Stage 3 curriculum time. But I get that people would be unhappy with this! Transformations run through from Key Stage 2 to Key Stage 5. But I do struggle to see what's to be gained by the existence of negative enlargements.

**5. Iteration.**As much as I enjoy the fun with calculators, I don't know what the rationale was for adding this to GCSE, and I don't think any of us will lose any sleep if it's dropped.

**6. Factorising non-monics.**Teachers from other countries think it's weird that we make such a fuss about how to teach factorising non-monic quadratics like 2x

^{2}+ 5x + 3. They ask why we don't just use the formula to solve quadratics like this. And our answer is: because sometimes GCSE exams ask students just to factorise an expression, not to solve an equation. Which is silly. The whole point in factorising is that it allows us to solve, so why separate the two? Don't get me wrong, I love factorising non-monics. I'd happily enter a speed-non-monic-factorising competition and I reckon I'd do pretty well. But come on, do we really need to teach this particular skill?

**7. Quadratic Sequences.**Knowing how to find the nth term of a quadratic sequence takes us nowhere. It doesn't even come up at A level.

**8. Pie Charts.**They have the advantage of linking together other topics: angles, proportion, percentages, interpreting statistical graphs... but we all know that pie charts are a rubbish representation and people should just stop using them. As legend John Tukey said, “There is no data that can be displayed in a pie chart that cannot be displayed better in some other type of chart.”

**9. Exact Trig Values.**I'm not convinced these help deepen understanding of trigonometry. We all know that most students just cram them into their memory the day before the non-calculator exam. I haven't met many teachers who think that the addition of exact trig values to GCSE was a good idea.

**10. Vectors.**This one pains me because I love teaching vectors. But it's a pretty chunky topic that's feels a bit stand-alone. I'm just not sure it's entirely necessary to teach vectors at GCSE.

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While we're at it, how about removing some of the topics that are doubled up? Our lovely colleagues in science teach scatter graphs, standard form, kinematic graphs, speed, density and pressure. Do we really have to teach and assess them in maths as well? We could cut these from maths to win back some time. They'd still be taught in science, so students won't miss out on these topics.

And there are more topics on the maths curriculum that need serious discussion...

Triangle congruency reasons? Hmm.

Trigonometric graphs before A level? Necessary?

Graphical inequalities? Yuck.

Histograms? I'm not a fan.

I know many of you want to remove circle theorems...! I get it. But I will cry if they cut them. I bloody love circle theorems. All that beautiful reasoning...

**Does anything need to be added?**

Every time I teach quadratics I think it's weird that the discriminant isn't on the GCSE curriculum. It's on the equivalent qualification in Scotland. It fits well and helps students make sense of quadratic graphs. It's fine to leave it until Year 12, I just find it weird that when they were deciding what to move from A level to GCSE, they moved some random stuff like tangent to a circle, quadratic inequalities and composite functions, but they didn't move the discriminant. I would love to have been a fly on the wall in the last round of curriculum discussions so I could hear the rationales.

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I agree i love circle theorems and have great activities for discovering them etc, but students really do find them difficult out of all proportion to the skills required to solve them, and as for “give reasons” well ……

ReplyDeleteI too am a circle theorems fan but fully understand why the students don’t share my enthusiasm. I do struggle to answer their “when will I need this” questions (which come up far too regularly!)

ReplyDeleteI got taught plans and elevations, enlargements and anything that requires drawing including Pythagoras and Trig via technical drawing as part of design technology. We never did much in maths. Left school in 1996 (year 11)

ReplyDeleteInteresting that 6.5 out of 10 of these are not actually in the IGCSE qualification. And pie charts I think are technically but I can’t remember when they last came up. And while your thoughts on pie charts are absolutely correct, it is not wholly obvious to most people, including many maths teachers. Or perhaps it is because I have only taught IGCSE where, we do so little stats, that people are not aware of Tukey as I am from my previous job as a data analyst. Part of the reason I decided to retrain as a maths teacher was because they had a PIE CHART IN 3D on the recruitment poster for becoming a maths teacher. I will just repeat: IN 3D. I had to try to be change I wanted to see ðŸ˜‚

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