There is no cost difference between incarceration and an Ivy League education; the main difference is curriculum.
There’s a lesson I’ve learned in the steadily growing number of years that I’ve been in middle and now senior leadership: quite simply, systems beat ‘stuff’. In other words, you can use what ever materials and ideas you want in teaching and learning, but it’s how they fit together into a system as a whole that truly matters.
Designing and putting together a curriculum is not easy. It’s got to have a breadth to serve what ever purpose its study ultimately requires; a depth that allows for fluency and confidence in the use and manipulation of concepts to develop; opportunities to review and reinforce prior learning; flexibility to respond to the needs of individual groups and students; a balance of detail between prescription and autonomy. In addition to all of this, you’ve got to allow for opportunities to assess progress at varying degrees of detail, checking and responding to the effectiveness of your curriculum overall.
Before we go each of the points outlined above, and start to think about how one can start addressing some of these issues, there’s an elephant in the room that needs addressing.
What should your curriculum serve as its purpose?
I’ve mentioned before that there are ultimately two poles of thought when it comes to determining purpose when teaching Mathematics in Secondary education: are we here to turn students into mathematicians, or are we here to get them the best qualification possible? It’s a morally challenging one, but I’ve also mentioned before that the two sides are not mutually exclusive. However in the context of how the GCSE programme of study is structured, and the obligations on schools to deliver in terms of student progress pegged to levels and grades, then the best qualifications possible take priority. I do feel, however, that we have a moral obligation to give students as rounded an understanding of our subject as possible, even within the very tight constraints our vocation is placed within.
With that in mind, let’s go through the various facets of curriculum design.
As an absolute minimum, any curriculum one designs should be built around whatever the GCSE programme of study your students are expected to cover. This may seem like you are teaching to the test, but remember my point above – it is the nature of our vocation presently that this must take precendence over anything else. It is great to have the aims of creating a whole school of students skilled in the art of problem solving and thinking truly mathematically, but if you’ve only got three hours a week with a class, you simply don’t have the time. If you’re lucky enough to have significantly more than that, you can then start to develop that more rounded approach I alluded to earlier.
Time really is a factor. When the occasion comes to discussing timetabling the whole school curriculum, you should fight for as much lesson time as much as possible. I am a great believer in the need for a balanced curriculum that encompasses the arts, sciences, humanties and physical education as much as it does English and Mathematics – but you’re the head of department, the servant leader – lesson time is one of the best gifts you can give your staff!
Depth, part 1
Breadth and depth, of course, are inversely proportional to each other, with reference to the time capacity you have in hand. It is at this stage, that I am going to first address the ‘m’ word.
Mastery seems to have undergone an Orwellian, Newspeak-ish variety of interpretations over recent months. The notion of a mastery curriculum is nothing new, and the variety of interpretations causes meaning to be lost and the value of the concept to disappear/be undermined. The central tenet of mastery seems to be ‘do less, better’; narrow the curriculum, and cover concepts as deep as possible for as long as possible.
You’ll see some departments really narrow their curriculum down in Y7 and Y8 so that the core ideas are embedded with the view of accelerating students through the broader skills in Y9-Y11, as a result of their fluency. Other departments will keep a broad range of curriculum strands through Y7-Y11, perhaps not going into as much depth in Y7 and Y8 but exposing students to the wider curriculum earlier with the notion of ‘knitting’ curriculum strands as students move through the syllabus. The latter differs from a spiral curriculum in the sense that longer blocks of time are spent on concept study, usually around four to six weeks.
I have my personal preferences, but whatever way you choose one has to understand that a mastery approach is not just about the curriculum but also wider aspects: an embedded whole-school numeracy policy; an assessment system that allows forgetting, retrieval and review of prior learning (see below); a configuration of units so that concepts that are interconnected are taught together – e.g. for multiplication including area, even though traditionally these would be taught seperately…
Whichever way you look, you’ll see a mastery curriculum, or something that advertises itself as being so. Outcomes are the acid test of a mastery curriculum.
Depth, part 2
Whether or not you plump for a particular flavour of mastery, you’ve then got to decide how you’ll sequence the steps you’ll take in teaching. It’s pretty old school, but my approach has always been:
- teach the basic principals, methods, processes, etc
- cover how these can be applied in a range of contexts
- build connections between what you’re presently covering and what you have, or will be covering.
Well, duh, yeah? This attitude is about as revolutionary as the idea of the Earth revolving round the Sun, but it’s damn effective. That said, this approach often gets questioned, particularly from the constructivist, discovery learning advocates. It’s up to you what you decide, but your experience will guide your hand, and if your experience is minimal, then it’s simple – look at what the best schoos are doing.
The model I outlined above applies at not just the macro level within a unit of a scheme of work, but also at the micro level within the coverage of a topic. But that’s a story for another day.
In terms of what this looks like at the macro level, let’s say you have a unit on ratio. The basic principles might be along the lines of comparing amounts as a ratio and dividing an amount in a given ratio. Applications can include things like finding the whole given the part and ratio, finding other parts given the part and ratio, and contextual problems. Building connections can be done through coverage of drawing pie charts and even stratified sampling, which let’s face are both ratio division problems in different guises. That’s very quick and dirty approach to starting the design of a unit of teaching, but I hope you can get the general idea.
It’s imperative that students get chance as much as possible to build connections. It is the grand challenge of a curriculum that students do not see Mathematics as set of fragmented ideas loosely grouped together, but as a continuum of concepts that are interdependent; conceptual strength and fluency in one area feeds into improvement in other field of the curriculum.
Determining what the purpose of your curriculum is down to what the environment you are working in expects and allows. In most cases, this will start from the GCSE programme of study. Your curriculum should be designed so that students have the time to go into a level of depth that develops fluency and confidence whilst allowing chance for application and building connections across the spectrum of strands within the subject. This is not easy, it is our greatest challenge as departmental leaders, but it is a massive lever in terms of successful teaching and learning.
In the second part of this section, we’ll explore review, flexibility, the balance of prescription and autonomy, and how assessment fits in. Looking forward to it!