I’m lucky enough to either have worked with or visited more schools than most people would ever get to see in a “typical” career. Of all the top-performing schools there are many things that are universal that won’t come as a surprise: high expectations produce a disruption-free learning environment, responsive teaching through mass participation (normally always using mini-whiteboards), explicit instruction as the main driver of information transfer, teachers know their students and make adaptations as necessary so they can access the curriculum on a par with their peers.
What can vary is the design of the curriculum as a whole. Despite how similar the how of the teaching can look, the what and the when can look very different.
I’m going to go through various models that I’ve seen and discuss the strengths and vulnerabilities of each approach as I see it.
- The “Mastery” Model
The Idea: Topics are explored in depth for long periods of time before moving on.
Rationale: With lessons fresh in students’ minds, ideas can be explored in real detail and “mastery” of each topic can be reached. The time is given to fully embed concepts meaning that students need not revisit them formally.
Vulnerabilities: With large gaps between revisiting content forgetting ideas is almost inevitable. Careful consideration of how ideas are retrieved over time is needed (typically this will happen at the start of lessons). Also, with ideas revisited less often there is a danger that students who do not understand the content first time around will be lost later. Ensuring content is pitched appropriately and that the key ideas from each unit are understood before moving on is essential.
- The Super Spiral
The Idea: The same ideas are seen frequently over time with each revisit becoming increasingly complex
Rationale: By seeing topics frequently content is unlikely to be forgotten. By going back a step each time to ensure content is secure before being built upon, you ensure understanding is solid.
Vulnerabilities: By spending little time on a topic there is a danger content is not explored in enough depth before moving on. Also, without good knowledge of a class’s current levels of understanding, topics risk being needlessly revisited each cycle. Accurate data capture is important in making sure time is not wasted in this model.
- The Big Question
The Idea: The curriculum is mapped to various themes or questions that engage and inspire students. For example, a question like “How can one zombie cause an apocalypse?” can bring in ideas from the world of statistics, proportion, graphs, exponential growth, and compound interest.
Rationale: Students are galvanised by an interesting question. Maths is made contextual and therefore engaging. Due to multiple ideas being explored in one theme, the links between seemingly disparate parts of the curriculum can be explored.
Vulnerabilities: Careful planning is needed to ensure complete curriculum coverage. The underlying structure of the mathematics must still shine through so students know what to apply and when in other contexts. Some ideas will be hard to not just be shoe-horned in due to their abstract nature – this risks devaluing the question being explored. Hard to differentiate for low-attainers if concepts are pinned to specific content and therefore harder to adapt.
- The Retriever
The Idea: Two or more topics are delivered simultaneously in an ABAB or ABCABC… lesson cycle.
Rationale: The benefits of mastery and retrieval are captured, with students given longer between ideas before they are revisited but with one topic still be explored over a relatively long time-frame.
Vulnerabilities: Lessons become the space of time with which learning needs to happen and this rigid structure can make the flexibility that is inevitably needed when teaching a unit hard to come by. Students missing a lesson can have more of an impact due to the disconnected nature of what is delivered. Complex concepts can become trickier to teach due to the larger than usual gaps between connected lessons.
Which is best?
Who knows? I believe I’ve seen most of them work well in different settings. In my experience the first one, the “mastery” model (inverted commas because of how contentious this phrase can be) is the easiest to implement effectively. They all have pitfalls though and need careful consideration
What do they ALL need to work?
No matter what approach is taken there are some universal considerations which must be made.
Flexibility – teachers need to have the autonomy to teach the content their class needs in relation to whatever topic should be covered at that point.
Accountability – systems need to be in place to ensure staff are progressing at a suitable pace for each class (time is not your friend when it comes to delivering the maths curriculum).
AO2/Ao3 – content cannot be the sole focus. Problem solving and reasoning needs to be weaved throughout the course.
Retrieval – however it is mapped out, once is never enough. Concepts need to be revisited over time.
Sequencing – parts of maths are more hierarchical than others.The ordering of some concepts are largely superfluous but others need careful consideration.
Tiering – at some point there needs to be a decision on the best diet to expose students to based on the tier of paper they will sit at the end of Y11.
Methodologies – no matter how the concepts are sequenced, where a model can be used across multiple concepts (bar models, grid method, proportion tables…) these should be agreed and universal across the department.
Summary
There is no perfect model and no “one size fits all” solution. Whichever model you choose ensure both the specific and universal considerations are made in order to maximise the strengths but minimise the inevitable weaknesses of your choice.
I’m always interested in what people make of this so please feel free to comment with thoughts, questions or incomplete musings. Follow this or my Twitter account Teach_Solutions for similar content in the future. Also, check out the rest of this site, there’s some good stuff knocking about the place.
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