This post summarises some of my thoughts, plans and actions undertaken with regards to the implementation of the Maths AOLE for Curriculum for Wales (CfW). Writing this helps crystallise my own thoughts and I’ve shared it as it may possibly be useful to other maths leads in Wales. Neither me nor my Maths department are curriculum experts, but realise the responsibility we have to make CfW a success for the many students in our care.
Whilst other AOLEs debate what they’re going to teach, we in Maths have it fairly straight forward. The body of mathematical knowledge passed from generation to generation has changed little in the past century or more. This means we can spend more time now thinking about sequencing topics, progression within topics, and coherence across topics. Many schemes of learning are ‘bought in’ or follow the order of whatever textbook has been invested in. Our department re-designed our schemes of work about 4 years ago and took influences from White Rose Maths, Mastery approaches, and visits to other schools. Still, we have work to do in order to adapt our curriculum to meet the demands of CfW.
Luckily, curriculum is all the rage at the moment and there are many blogs and books dedicated to it. I found Jo Morgan’s writing useful here about sequencing of Maths topics at KS3. Also, the NCETM and the DfE have recently published a report concerning Mathematics Guidance for KS3. It’s worth a read here. They suggest that a good mathematics curriculum should:
- “Offers a clear and coherent sequencing of mathematical ideas, concepts, knowledge, and techniques both within each year and across years so that new ideas are built on the firm foundations of existing ones.
- Gives a coherent view of mathematics that highlights important unifying ideas and links between them so that students experience mathematics not as a collection of disparate topics but as a connected whole.”
Of course, none of this matters unless it is matched with high quality teaching. CfW has tried to influence teachers’ mode of delivery in a few different ways, most notable by promoting mathematical proficiencies.
Lesson Planning with the 5 Proficiencies
The 5 mathematical proficiencies are a key element within the CfW Framework. They are Conceptual Understanding, Communication Using Symbols, Fluency, Logical Reasoning and Strategic Competence. The documentation states that they “are central to progression at each stage of mathematics learning” and that “all five need to be developed during a particular mathematical concept”. Although it’s clear that this expectation is for each concept rather than each lesson, I would expect that most of these proficiencies are promoted every maths lesson. What is a maths lesson without logical reasoning?
In a recent lesson observation, I trialled swapping our normal lesson planning proforma for one based around the 5 proficiencies. It was a lesson on dividing by decimals and I mapped different elements of the lesson to each proficiency. For example, under ‘conceptual understanding’ I wanted students to understand that division did not always make a number smaller, and why division by zero was not possible. I enjoyed the planning process and it certainly made the proficiencies take centre stage. I was more aware of giving time to students to develop their fluency, and more aware to emphasise the importance of accurate use of the symbols that students often misuse.
Qualification Wales Announcement
One common complaint I often hear is “How are we meant to plan a curriculum when we don’t know how the assessments will look like?”. I have quickly grown tired of this question because the assessments are not the end goal. Being good at maths is the end goal. If your maths curriculum provides depth, breadth and powerful mathematical knowledge and your teachers are able to implement it successfully, then students’ exam results will look after themselves. Recently, Qualification Wales have released their report “Qualified for the Future” documenting the future of assessments in Wales. The main proposal in the Maths AOLE is that a new Mathematics & Numeracy GCSE will be created which will replace the current Maths GCSE and the Numeracy GCSE. This new GCSE will be worth about 1 ½ GCSEs. This proposal makes sense to me and was welcomed by the majority. Other, more controversial decisions were made in other AOLEs. More here.
The CfW documentation contains a list of ‘Considerations for Curriculum Development’ to take into account when designing the maths curriculum. Some of these are good thought provoking suggestions which our department arguably do not do enough of currently. The suggestions also give a glimpse into the pedagogical approaches that are being promoted within the Maths AOLE. One I particularly like it that we are asked to “introduce a reasoning and problem-solving approach to all mathematics and numeracy experiences”. I imagine this would be a significant change of direction in the ways that Maths is viewed, taught and learned in Wales. And a particular challenge too for teachers who many not be maths specialists or teachers who have not experienced maths taught in such a way to develop students’ mathematical reasoning and understanding. Other points made include giving learners “opportunities to explore mathematically rich environments both indoors and outdoors” as well as “making connections between the concrete, the pictorial and the abstract”. We also, of course, have the opportunity to make explicit more of Welsh culture and history that has touched mathematics. Examples include Robert Recorde’s equals symbol, the Welsh vigesimal counting system (81 is ‘pedwar ugain ac un’ ie ‘four twenties and one’) and William Jones’ pi symbol.
Our next step as a department is to consider progression within maths by looking at how students’ understanding of key concepts develops over time. Some questions we will attempt to answer include; What are the absolute key skills and knowledge required to make progress in maths? When are students first introduced to key topics? How do we know what they’ve retained from Year 6 and what can we do to ensure that Year 7 is not a recap year? How is their progression throughout the topic managed through their time with us? What balance of re-visiting to introducing new topics do we want? How can we make mathematical connections and transfer learning to new contexts/problems?
As always, comments or ideas welcomed.