Yesterday I introduced a session on curriculum sequencing at #mathsconf27 in Ashford. Thanks to everybody who attended. On this submit I’ll summarise the details and supply a hyperlink to the slides.
I began by speaking concerning the nationwide curriculum. It is statutory for all local-authority-maintained colleges in England to show the Division for Schooling’s programmes of examine. In actuality the overwhelming majority of non-local-authority-maintained colleges (e.g. academies) train them too. I talked about how closely prescribed the content material is for maths. Apart from science (which can also be closely prescribed), all different topics have a good quantity of artistic scope over the content material they train. When you’re a Head of English you would possibly select to show Macbeth, and should you’re a Head of Historical past you would possibly select to show the Black Dying. When you’re a Head of Maths you could have just about no say over what you set in your faculty’s curriculum (by way of the content material), aside from maybe a little bit of enrichment that goes past the nationwide curriculum.
However that is to not say we now have no management over curriculum in any respect. We will management the sequencing of the curriculum and we are able to management our pedagogy, sources, strategies and approaches. Mainly we are able to management the implementation of the curriculum. This implementation varies extensively by faculty.
I talked about how odd it’s that we do not all observe the identical sequence, and that there is no such thing as a agreed ‘greatest order’ for the subjects we train. In some international locations (I talked a few particular instance from Shanghai) a substantial amount of analysis is finished on getting the order proper, all the way down to the minutia of ‘is it more practical to introduce space first, or perimeter first?’. But in England our choices about curriculum sequencing (that are usually made in isolation by every Head of Maths in over three thousand completely different secondary colleges) are usually not research-informed. I additionally talked concerning the massively completely different approaches to curriculum sequencing seen in the USA, the place college students spend a whole 12 months on algebra and a complete 12 months on geometry. To us this appears uncommon, and to them our strategy appears uncommon. I shared some photos from Ben Orlin’s very humorous submit about this. And the query I requested is, ‘Has anybody truly researched which of those approaches is more practical? Which strategy optimises pupil expertise and progress?’.
I talked about why Heads of Maths and lecturers must be thinking about curriculum sequencing. It isn’t simply because Ofsted would possibly ask them about it! I additionally talked about an fascinating level made by White Rose of their submit Order, Order! The Significance of Sequencing – though our sequencing choices are primarily decided by stipulations (i.e. you’ll be able to’t examine this subject till you’ve got carried out that one), there are additionally concerns referring to pupil expertise.
After this lengthy introduction about why we should always take into consideration curriculum sequencing, the remainder of my presentation was damaged down into three elements: stipulations, interweaving and customary apply.
Conditions
Lecturers ought to take into consideration the stipulations for each subject they train. That goes with out saying. Once I begin instructing Pythagoras, the very first thing I ought to do is ask myself the query ‘what maths do my college students have to know to entry this subject?’. That is carried out by Heads of Maths when creating their scheme of labor, and it is also carried out by lecturers when planning their very own lesson sequences. Conditions have a big half to play within the order of our curriculum. For instance I would not put space of a circle as the primary subject in Yr 7, as a result of with a purpose to entry that subject I have to first make sure that my college students are fluent in rounding, calculator use and squaring.
I mirrored on the truth that college students at my faculty do rounding in January of Yr 7 however then do not truly use rounding in any subject till January of Yr 8. So maybe it is smart to maneuver rounding to Yr 8, when it may be taught after which instantly utilized in subjects like Pythagoras, circles and quantity.
Interweaving
I confirmed examples of subjects that may be interwoven and the way the order of our curriculum can create alternatives for interweaving. For instance, I feel it is actually necessary that angles ought to observe equations in Yr 7. If angles is finished first, it may find yourself being a repeat of major faculty angles. But when angles is taught second then lecturers can take advantage of alternatives to interweave equations and angles. This provides depth and problem to the subject of angles, in addition to giving college students the chance to utilize their newly acquired equation fixing abilities.
I gave the instance of how I just lately taught index legal guidelines to Yr 8 after which increasing brackets with the identical class, so was in a position to make use of index legal guidelines inside my classes on increasing brackets. It is necessary that college students perceive that every little bit of maths they be taught takes them to the following step, and permits them to entry extra complicated maths. We need not reply ‘Why are we doing this?’ questions from college students with tenuous real-life utility nonsense. “All roads result in calculus”, and they’re on a journey heading in that path.
Widespread Apply
Within the final a part of my workshop I shared examples of schemes of labor. Though all of us train the identical curriculum, there may be little or no consistency in curriculum sequencing throughout colleges. And regardless that Heads of Maths put numerous time into designing their schemes of labor, once you have a look at all of the completely different orders side-by-side, it nearly appears random.
In my latest survey of just about 800 Key Stage Three maths lecturers, I discovered enormous inconsistency in when subjects are taught. Search for instance on the subjects with few stipulations (form transformations and constructions) that are unfold throughout Yr 7, 8 and 9.
I talked concerning the concept behind spiralling with a purpose to construct depth of information. I really feel like spiral curriculums are generally seen as the alternative of mastery curriculums, however that is not essentially the case. The worst sort of spiral curriculum touches on subjects at a floor degree and returns to them yearly. Issues are rushed fairly than mastered, that means annually it is like ranging from scratch once more. A greater type of spiral curriculum takes a strand of maths in its entirety (e.g. angle geometry) and every subject inside that strand provides a chunk to the jigsaw, constructing on prior information and deepening understanding of the strand as a complete. Angles might be taken as 5 subjects: ‘fundamentals’, parallel traces, polygons, bearings and circle theorems. Every year we train considered one of these subjects, and every time we accomplish that we not solely add a brand new piece to the jigsaw but additionally construct depth of understanding of the strand as a complete.
The strategy taken within the new DfE/NCETM curriculum sequence appears to vary to this. This has challenged my pondering, and I might love to listen to the NCETM staff converse concerning the rationale for his or her proposed order. I do know the staff behind this are very skilled and educated and may have given it numerous thought, so this deserves our consideration.
Within the final a part of my presentation I shared my very own 5 12 months curriculum sequence. I made it for instance for the aim of this presentation, actually simply to see how tough it was to do, and it is due to this fact merely based mostly alone ideas and expertise. The primary problem was time: we simply do not have sufficient of it. It is irritating. I’ve stated it for years and I will say it once more: we merely have an excessive amount of prescribed content material in our nationwide curriculum. If we’re going to have any hope of instructing this content material correctly – truly in depth, with out simply skimming the floor of all of it – then the content material must be diminished. They might begin by eradicating constructions… 🙃
I ended with the message that curriculum sequencing is fascinating, and it is one thing maths lecturers ought to take into consideration and speak about.
In order that’s a quick abstract of my speak. There was much more in it, however that is the gist. I hope that individuals who attended discovered it useful.
I spoke extra about all this in my latest podcast with Craig Barton.
You possibly can obtain the slides from my workshop to be used with your personal division.
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Lastly, I simply need to say an enormous thanks to La Salle for organising this convention. As a lot as I just like the digital conferences, they’re nothing in comparison with the in-person ones. Being in a room filled with maths lecturers and having impromptu conversations about colleges and instructing is simply so highly effective. I loved all of the periods I attended, and I feel Kris Boulton’s workshop was among the best I’ve ever been to. And on condition that I’ve been going to La Salle’s conferences since 2014, that is saying one thing.
I additionally need to say thanks to those that joined me at my drinks on Friday night time. At work on Friday I used to be stressing that I might booked a desk for ten individuals however would possibly find yourself sitting at all of it on my own, however in the long run I used to be joined by Chris, David, Sudeep, Nathan, Nathalie and Rachel, after which later within the night by many extra conference-goers. I ended up dancing in a membership till the early hours. I can rely on one hand the variety of instances I have been out dancing like that since I grew to become a mum a decade in the past! It was a lot enjoyable. After my first massive night time out in my forties, I used to be a bit worse for put on on the convention – however it was price it.
See you all on the subsequent one.
