Zooming into a maths curriculum

Schema

Curriculum is a large focus for lots of leaders at the moment and rightly so, in my opinion. The whats, whens and hows are important pieces of information that need to be spelt out to those following your curriculum. Another important question is, ‘why?’

Why have you chosen to teach that particular concept? Why have you chosen to sequence things in the the way you have? Why have you chosen to not teach something at a particular point in time? Why should the content be introduced in this way? Why have you recommended that particular teaching resource?

The answers to those questions are driven by the values and beliefs of the people in charge of developing your curriculum, be it the trust, the school, a team within it or one maybe one person.

In this blog I am going to explain about the practicalities and format of our curriculum design moving forwards so that I can gain feedback and advice from the people I respect the most. There will be things that we have not though of. You must remember, however, that no body knows our context, pupils and staff better than us so I will try to justify the whys behind the decisions.

I am going to focus on something that I have not been able to find a lot of detail on in blogs and articles: what sits behind the overview and sequence to support staff?

Context

I recently joined the MAT in September as Assistant Principle for a school that is RI. We have a number of primary schools and 7 secondary schools in the trust. Leaders meet once a half term at a secondary level. Our focus more recently has been curriculum design. We have just appointed a new Director of Maths for the trust, that will oversee this group of leaders and who we are excited to work with, adding some more direction and extra capacity for this important issue.

My school is the largest secondary in Blackpool, around 1200 pupils without a sixth form. We have a department with a range of experience from 25 years+ teaching to Teach First trainees to non-specialists in their first year of teaching maths out of subject. Before I arrived, there have been over 60 teachers teach maths here in the last 5-6 years… 60! We now have more stable team so fixing the curriculum arrives at a time when we have capacity to build.

Cycle overview

We have 3 cycles of data collection as a trust, where summative data is collected. This is a reduction on previous data collection frequency.

Next year we will plan 12 week cycles of  that look like this:

Overview

Above you can see a template for our cycle overview. We specify, at a glance:

  • The topic to be taught
  • Our entry task focus (starter/do now)
  • Hegarty maths focus (a range of recommended task numbers to be set for that class that week)

You will also notice to the weeks we have Q and LRL – this stands for Quiz and Learning Review Week. Once per fortnight the students carry out a carefully designed formative assessment on the topic recently taught as well as including some cumulative questions in a revision section. This specifies which we weeks we recommend to do those on. The learning review week will contain a lesson that we close gaps from the quiz and provide whole class feedback. The reason for being prescriptive around this is work load. Staff create/adapt their quizzes in collaboration with each other based on where they have got up to in the topic. No one class will take exactly the same quiz but the underlying principles of that topic will be tested based on teacher discretion. The questions are short and often closed questions that really get to the core of what students do and do not know. Designing questions (like Craig Barton’s Diagnostic Question site) really help to identify where students are going wrong and provide information to plan the gap closing in the learning review lesson week (LRL).

Staggered entry tasks and homework

You will notice that home learning and entry tasks are staggered. This is to aid long term memory and retrieval. We want lessons to have recap opportunities from last half term and longer. These “short term” entry tasks will be 5-10 short questions that are key to the previous topic(s). The “long term” entry tasks we are going to use Mathsbox GCSE 5 question quizzes to review a range of key concepts to take advantage of the spacing effect, not necessarily done recently. Again, there is a degree of autonomy here as teachers can use their knowledge of what students need to recap the most but we will build a bank of these over time too. Why do we have entry tasks? We have a large school so the arrival times of some students differs to lessons. We want students to arrive to a studious environment that acts a lever to retain the key maths that has been taught recently. Our context dictates this and it is working better than other alternatives previously tried.

Unit Overviews

For me, what sits behind this is key for ensuring a greater chance of staff implementing your intended curriculum.

A unit overview will contain:

Prequisite knowledge – what will staff need to assess is secure before teaching this topic?

Hegarty clips relating to the content in this unit – this provides extra support for non-specialists through the video clips, which are all taught using correct mathematical methods (not tricks) as well as being brilliantly atomised.

Key vocabulary and knowledge – a self-quizzable knowledge grid is designed to spell out the key core knowledge and tier 2 and 3 vocab that is required to have a good foundation in that topic. There are rarely processes or concepts – just key vocab and facts. Where procedural knowledge is included, it might be just a key “next step” rather than multi-step processes. All pupils are given a grid and expected to learn 100% of the content. They will be quizzed weekly or even more frequently if necessary. If we want students to be knowledgeable and be able to retrieve key information then we need to spell out this knowledge up front and not leave it to chance that they will just learn it from our lessons. The resources provided should be “retrieval ready.” It also helps novice teachers to ensure that these words and key facts are being taught and explained. Using this grid in isolation will not help students to become expert but inflexible knowledge is the foundation of expertise (Willingham, Why Don’t Students Like School?).

We have also created a student friendly website with the current schemes of learning, linked to Hegarty maths videos. There is a teacher version too, that provides quick links to regularly used resources.

Progression model – what order is this topic best taught in?

Core example types – the typical examples that one might model in order to help students get a grasp of the concept – these are aligned with the Hegarty maths examples to better achieve what Hirsch refers to as a communal knowledge curriculum. A curriculum with a shared language so that what happens in the class room allows them to be successful with tasks set outside, as well as speak to students from other classes using the same language. Too often I have taught a topic then set the home work and realised that Colin (Hegarty) approached it in a different way or included example types that I didn’t. This pre-planning will reduce the number of times that happens.

Non-typical examples – this is to increase the chances of the wider domain of the content being taught. Those weird, more complex example types that staff may forget to include if not made explicit in the overview. This may include ensuring that mean from a table is modelled using a horizontal table, that finding the shorter side of an isosceles right angled triangle is taught or highlighting that examples of finding the median from a cumulative frequency curve should include examples where the max value on the y-axis is the the cumulative frequency and when the max value of the y-axis is more than the cumulative frequency. It’s not left to chance, it’s spelt out.

Representations and modelling – This is to try and create some consistency and better quality in the way topics are explained, or to provide novice teachers with best practice. As the department gain more training in this area, this section will include use of recommended representations, explanations, video links and manipulatives. There are also links to quality interactive material including mathsbot.com and mathspad.co.uk (paid site that I would recommend all departments buy).

Challenge questions – these are questions that may cause students a problem in the topic and questions that we want to spend time modelling to students and letting them have a go at similar problem types.

Misconceptions – as expert, experienced teachers we can pre-empt most (not all) misconceptions and have fix up strategies or teach in a way that mean that the misconception does not form in the first place. I want the overview to contain information on this. There may be some bullet points about potential misconceptions but I have also searched for the topic on diagnosticquestions.com, clicked the quiz in the collections section (curated by Craig Barton) and then clicked “insights”. This then orders the quiz in order of questions that students got wrong the most, along with a summary of which answers they chose. I copy and paste the top 5 or so into the misconceptions section to highlight examples of questions students may get wrong and the possible reasons why. Staff have received department training from Craig recently on use of the site so they can explore this further should they so wish.

Resources and tasks – a list of resources and tasks that are useful for each learning point including worksheets, good question sequences, rich tasks and quizzes.

Problem solving/interleaving – This section provides links and images to:

SSDD problems for that topic

Goal free problems

Synoptic questions that include knowledge of other topics

Reasoning activities such as “more, same, less” (recommended by Chris McGrane) or “fill the gap” from variationtheory.com.

Yes, there is a lot of detail in the unit overviews but what this then allows is for banks of resources to be built and added to this working document.

Advantages of having something centralised like this are:

  1. It allows our Lead Practitioner, who coaches our non-specialists once per week, a central location to talk about upcoming content.

2. The feedback we gain from students can also then inform this document next time this topic is taught. Daisy Christodoulou’s latest blog provides more insight into how feedback can improve the work, the students and, more importantly, the curriculum. Any thing that arises, such as questions or concepts that students found difficult, can directly feed into this document so that we do things better next time around. For example, when we do mock exams and a low percentage of students get a particular ratio question wrong, this can be copied into challenge questions for the unit that topic is first taught and discussions in the department about how we can ensure students have a better chance of overcoming what ever obstacle is standing in the way of success.

3. When staff are creating their formative quizzes each fortnight, there is some consistency in the types of examples we expect students to be able to complete. The central knowledge grid means that meaning of key words are not up for interpretation, they are spelt out for everyone.

4. We also have trust-wide collaborative planning sessions where all maths teachers meet to plan units together. If this is available in advance of those meetings, it makes delegation much simpler in terms of resourcing the unit.

Our curriculum will never be “finished”   – there will always be adaptations and improvements week on week, term on term, year on year. 

In summary, the units are well sequenced by considering the big picture. Attention to detail with out being overly prescriptive means that implementation has a higher chance of success. Staggered learning points, including entry tasks, homework and formative quizzes mean that we are planning for long term retention, not short term performance. Novice teachers are well supported and collaboration is made simpler through a centralised, detailed focal point for the unit.

Here is a link to a concrete example of what this looks like for a unit “Probability II in year 10.”

Example of a unit overview as described above

Examples of a knowledge grid for staff and pupils to be quizzed on

 

 

 

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