Curriculum – Teach Solutions

Finish Strong

This blog gives advice for all the things teachers should and should not be doing in that run up to exam season

A while ago I wrote a blog aimed at giving tips on how to start strong with a new class at the start of a year, it’s here and was called “Starting Strong”. As the countdown to exams have started it felt right to close the loop with this one.

Here are some dos and don’ts for working with pupils as their exams beckon. I am going to focus this around Y11 Maths in England but I suspect it wouldn’t take too much work for someone to decide what parts would apply to them with a different subject/country/age-group.

Let’s start with 7 “don’ts”. These are things I see often enough that they warrant a warning sticker.

Don’t make them sit paper after paper

It’s important to remember that students aren’t going to start learning any differently just because exams are nearer. Don’t put one lesson a week aside for them to complete an exam paper if you haven’t had time to address all the major gaps in their learning from the last one. This is a form of “means end conflation” but getting them to sit lots of papers is not necessarily going to make them any better at completing them.

Don’t review papers by going through them one question at a time

If students have completed a paper, it isn’t a good use of their time to simply see the teacher go through it on a visualiser whilst they self-assess. If the pupil has got a question correct, they learn nothing. If they got it wrong, they need some teaching and purposeful practice on whatever the concept is. If students learnt an idea by simply seeing a teacher complete one very specific example one time and then moving on straight away, teaching would be a very easy profession.

Don’t intervene by grade

Don’t make intervention groups purely based on grade. Identify key areas of curriculum weakness and group them by these where possible.

Don’t assume students know how to revise

Don’t set homework of just “revise” unless you have explicitly taught them how to do this. Even then, be as specific as you can.

Don’t overload them with resources

It isn’t helpful to give them 2 revision guides, 6 exam papers, 10 knowledge organisers, and 3 websites to use. Yes, you will give students all the tools they may need but this is overwhelming and lacks accountability. Keep things tight and achievable. Find one or two great resources and invest in these. Less is more.

Don’t try and cover everything

It isn’t ideal to cover every aspect of the curriculum if it means a large part of it won’t be learnt well. Making the hard decision to cut content, but learn fewer things well, can lead to students performing better in their final exam.

Don’t think you’ve ever “completed” the curriculum

This one is just a little bugbear but I often hear the phrase that a certain class has “completed/finished the curriculum”. I then look at data and they aren’t all achieving 100%. It makes me wonder in what sense the curriculum has been completed. It would be equivalent to painting a patchy first coat of paint on a wall and saying, well, I’ve covered the whole wall so I’m lost for what to do next. The curriculum is not a thing to be completed, it’s a thing to be taught, studied and learnt.

Let’s move on to some “dos” then. Some of these are a cheat because they are the opposite of some above but, it still counts. Most link to bigger ideas in blogs I’ve written previously. Check any out that you may be unfamiliar with.

Focus on exam technique

Knowing the course content is one thing, but there will be advice you can give which is specific to the way the exam is assessed or written. I think, in maths, the difference between two students with equal maths knowledge but with opposite exam techniques can easily be a grade. See here for how to get more marks on a maths paper without knowing any more maths.

Use QLAs effectively

Instead of going through an exam paper from front to back, use QLAs wisely. Advise on that here.

Share your plans with the students

When you’ve created your plan for your final run of lessons, share this with pupils. That knowledge, combined with them having ownership of their own most up to date QLAs will let them know the small subset of topics that they will need to revise independently because it won’t be covered with everybody in class.

Feedback effectively to assessments

I wrote in the “don’ts” the ways you shouldn’t feedback to an exam, here’s how to do it well.

Teach them how to revise

Revision is hard and effective revision can sometimes be counter intuitive. Teach them how to revise. For more on that, see this blog.

The Main Point

It is so tempting to feel the need to drastically change things up as exam seasons gets closer and closer. It is your job, ultimately, to still teach students how to do things they cannot do. This has been your job all through the year with every year group you teach. Hold fast and carry on doing the same thing. Keep the balance of modelling and practice. Keep the balance of checks for understanding and responsive teaching. The only thing I can see a good argument for changing is the ratio of time spent retrieving content, simply because by this point there is so much more to retrieve. It can be hard to resist the urge to change things up but if you believe you’ve been doing a good job for students the rest of the year, there is nothing special that needs to happen. Hold fast. Stay the course. You got this!

Rethinking Results Day: A Guide for School Improvement

We’re used to thinking about winners are losers, and this summer of sport has been no different. But how can this lens be a used productively when thinking about results day?

As the Euros blurred into Wimbledon which in turn blurred into the Olympics, a summer of sport is soon going to take a hiatus for the most important competition of the year; results days. Whilst the rest have very clear definitions of what winning looks like, results day does not.

This is an incredibly fitting reference for this blog but is also very niche (2 points if you got it)

It’s likely your school will have numerical targets that have been set which may or may not end up being met… but there are no winners, not officially. Some schools will top league tables for various metrics but there are over 3,400 schools in England so does this mean there will be a handful of winners and a hell of a lot of losers. That doesn’t seem right though, not when so many schools are working hard, doing the right thing, and making good progress. It’s time to rethink how schools interpret results day. Let’s do that through answering a series of questions.

Here are the questions:

Is competition OK?
How should results be analysed through the lens of school improvement?
How much improvement is enough?

Is competition OK?

100% it is. Teachers are some of the most consistently competitive people I’ve ever met. Competition is no bad thing and, when gone about the right way, can be a powerful and useful leverage. Just be very careful who you get into competition with. There are some amazing schools out there and some of those will likely have a similar demographic to you. There are state schools delivering transformational educations in inner city, rural locations, coastal settings… using these, especially those in a similar situation to yourself, for inspiration makes perfect sense, but for competition does not.

The only school I think is worthwhile any school being in competition with is itself. Schools leaders inherit schools in various states and the only requirement on them should be to try and work towards improving the school at the quickest rate they can whilst remaining sustainable in the long run. Competing with an established school that has been doing this longer than you, is like trying to win a race against an Olympic athlete who already has a head start.

In some years this might mean an increase in exam results is expected, in others, if there have been massive staff shortages, local troubles, finance issues, strikes… then even maintaining results could be considered a win. Context is king here.

How should results be analysed through the lens of school improvement?

The short answer to this is: CAREFULLY!

Let’s say you’ve visited a school that you love. It’s results are amazing, it’s staff and students are happy. It’s everything you ever wanted to create. Let’s then say that you spent last year building that in your school and it was a success. If all that has happened then your results that year still aren’t even going to be close to emulating the results of the other. Results are the slowest thing to be affected by school improvement initiatives. Why is this? Simply it’s because results aren’t the result of the current state of the school but the culmination of a learner’s entire journey through it. No matter how good a student’s Year 11 experience is, no matter how much intervention you threw at them, how much you spent on residentials, nothing even comes close to the power of 5 years of consistently high-quality teaching.

This means new initiatives should not be abandoned just because they appear ineffective in the short term. A sensible follow-up question this does raise is how do you know if something IS working?

Well, the safest thing to do here is not to innovate but to personalise. We know enough about what works to know that if you are leading in a school or department sitting outside the top 5% performing then it shouldn’t be your job or responsibility to invent something. It should instead be to implement something which has been proven to work elsewhere in a similar setting. This still will require levels of personalisation as, no matter how closely aligned to your setting it is that you can find a great school, yours will be unique and strategies will need adapting. You need to focus on the active ingredients of what made it work for the other school. (For an example of this when it comes to the effective teaching and learning, check out the T&L Framework here: https://teachsolutions.uk/files-and-documents/).

There is too often a need in education for people to reinvent the wheel, to discover some new silver bullet, to innovate. In education, you don’t need a USP, you don’t need to compete with the market in the same way that Samsung and Apple do, you can shamelessly copy what works without fear of being sued, so do it! Take the 90% of the active ingredients that make great schools great and use them. Just be careful not to visit a school and then only take the easy superficial stuff (for more on that idea, read this https://teachsolutions.uk/2023/07/18/buying-coconut-oil-didnt-give-me-a-six-pack/).

Too often also, school initiatives belong to individuals, rather than to the school. School’s policies, visions, systems… should reign supreme here. Anything major that a leader starts, should be approved from their line manager with careful thought about how this work can, if successful, be continued when the leader leaves the building. What documentation exists? What writing exists? Senior leaders tend to stay in schools from between 4-7 years. That is just over 1 full cohort of Y7-11 going through. To ensure that the school doesn’t have to start again from scratch but that systems can be tweaked, rather than created anew, structures (and not just temporary scaffolding) need to exist which ensure the school can continue to move from strength to strength.

How much improvement is enough?

If we change what winning looks like to thinking about improvement, year-on-year, a very reasonable question is “how much progress is enough?”. This is a tricky one. At this point I can only comment on what I have seen and lead on myself. As a head of department in a school with supportive systems, a fully staffed department (though with our fair share of ECTs), we managed a consistent 0.45 progress increase year on year from 0 when I took over to 1.8 the year after I left. That is a target I informally set heads of department to make (whilst appreciating there are lots of mitigating circumstances that might make it not possible). Whatever other metrics you might have in place, at the end of day, there should be a real impact on the children being served and, although it might not be how we would always want them to be judged, the outside world treat exam results as a keys where the higher the results are, the more doors you can open. Until that changes, exam results are crucial when judging our impact as educators.

The big day

When the day comes then, take time to celebrate successes, to congratulate colleagues, to spend time celebrating with proud students and their families and consoling/coaching those who are less happy. Then, when it comes to doing the analysis, be sure to not look around the country and your local area so much but look at your past self. When drawing up or editing school improvement plans, don’t throw everything away if you’re not happy, remember that change, real change, takes time.

Independent Feedback Loops

The content discusses the impact of immediate feedback on learning. It highlights the importance of independent feedback loops in subjects and suggests strategies for creating effective feedback in different learning scenarios.

Imagine you are at a carnival. There is a target you need to hit with a bow and arrow. There is also a blindfold which you have to wear. The person running the stand shows you where to aim and models themselves doing it perfectly and hits the bullseye. Now it’s your turn. You have 10 attempts. You also have the choice between two different scenarios you can choose between.

Scenario A – You can remove your blindfold after each attempt to see how close the last shot was.

Scenario B – You have to wait until all 10 of your attempts are up before removing the blindfold.

Which scenario is going to yield the better result? Undeniably, it’s going to be A. This is despite both involving the exact same modelling and equal opportunities to practise. It’s because A has the advantage over B in allowing you to adjust your practice based on the near-instant and ongoing feedback.

Let’s call scenario A an “independent feedback loop”. This is where the user receives feedback which they can act upon instantly with no direct input from another expert needed, and now let’s move this into the classroom. How do independent feedback loops play out at school.

Some subjects lend themselves naturally to these loops. When teaching a serve in tennis, certain techniques in art, music, DT…. The practical subjects where there is a clear model of excellence and the user can see instantly the difference between what they are producing and what they should be producing. Compare this to completing a set of maths questions, analysing an historical source or writing a piece of fiction and suddenly the benefits of an independent feedback loop disappear. The question of this piece is, for situations like those just mentioned, can an independent feedback loop be created and, if not, what’s the closest we can get to simulating one?

Let’s start off with a maths example. Scenario B would translate as students working away at 10 questions and then, once they are all done, the teacher shows the answer to the class and they find out how they have performed. Some might find out they have got everything wrong, some only parts and others might be relieved to get 10/10. For those who got some or most wrong, their time spent practising at best was a waste and at worst has helped embed some misconceptions which might move learning backwards for them. Now, if a lesson does get to this point, the teacher would have a variety of options open to them, but this article is exploring if anything could have been done during the practise phase of the lesson.

Subjects where there is a pre-determined correct response.

1. Don’t wait until the end to share the answers: When questions involve multiple steps and there is no way that students could just pluck the answer out of thin air, there is no harm in sharing answers alongside the questions straight away. The usual safeguard of protecting against copying is not needed since the working out is what will hold them accountable. If questions can be solved with no need to show working out, then having an “answer bank” which has all the answers but in a random order displayed, can achieve a similar effect whilst maintaining high levels of accountability. What this won’t do is tell the students where they went wrong. It might encourage them to check their work and they may be able to self-correct. At the very least though, they will know they need some help before continuing.

2. Combine the above with backwards faded examples: If the problems require multiple steps to complete then, by using backwards faded examples which add an extra step as the questions develop, combined with answers being shared, leaners will be able to pinpoint the exact step at which they have a gap in their learning. That knowledge combined with clear notes or examples, should help them self-correct. The worst-case scenario here is that the student knows specifically what they can’t do but is unsure on how to correct it.

3. Build self-checking mechanisms explicitly into the task: If it’s possible to equip learners with the skills to check their own work, that would be ideal. In certain questions where answers can be self-checked with substitution or some other process, teachers should make it an explicit part of the task that is being completed. Instead of the question only saying “solve this…”, including a part which says “using substitution, check your answer”. Estimating answers beforehand can also be a useful tip.

Again, do not rely on learners doing this themselves, adding in an initial part as “estimate your answer to the question” before asking them to solve it, will help encourage these behaviours. Estimating and checking are both things learners are often asked to do implicitly but without making it an explicit part of the question it will not happen and never become a habit. Too often students will do the minimum required of them so if the wording in the question (the ultimate source of authority here) doesn’t ask for something, it is less likely to happen.

Subjects where there is no one right answer and also no in-built independent feedback loop

1. Clear and sequenced success criteria: Giving learners explicit success criteria to hit at specific points can help them self-assess their work. Giving a physical checklist containing targets like “in paragraph 1 make sure you include…” or “in your final paragraph make sure you refer back to…” can help learners assess and improve their work as they move through it. Where the success criteria is less pinned to a specific part of their work, a checklist can do the same thing. Asking learners, after an allotted amount of time, to highlight in their work where they have hit the criteria that they are aiming for can help them reflect and improve.

2. Share examples and non-examples before the end: Pausing learners and sharing some great exemplars and some misconceptions can also help learners reflect on their own work. Again, it’s important this is done before the end of their allotted practice time. When doing this it is important that the teacher ensures everyone understands the underlying properties that make the work being shared good or bad. Everyone’s work will be different and it’s important that the essence of what makes it great or not is discussed, beyond just the superficial content of the work.

Summary

Teachers can do a lot before independent work starts to check learners are as ready as possible and they can do a lot after independent work finishes to rectify any mistakes that have emerged. Let us not forget that there is also plenty that can be done, through careful thought and task design, to ensure that time spent practising is always time well spent.

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.

Teaching Mixed Attainment Maths at KS3

Advice on how mixed attainment maths at KS3 can work

I am both a big advocate for and against mixed attainment maths teaching at Key Stage 3. When done right I believe it is better both academically and ethically for the children. I know it can work, I’ve seen it work, I’ve been the Head of Department of a school that taught mixed attainment maths in KS3 and got some of the highest progress scores in the country. I have no doubt it can lead to incredible outcomes. The difficulty comes in “doing it right”. It takes A LOT to do this. And the risk of not getting it right I believe is greater than when teaching more homogenous groups. It’s a high risk high reward strategy.

What worries me is that people may make the ideological choice to move to mixed attainment teaching, or they may do so for some other logistical reason (staffing, timetabling…), and although it may be worthwhile in the long run, if it isn’t implemented right in the short-term it can be detrimental to all involved. Staff can be overworked when suddenly shifting to a whole new pedagogical approach and students end up receiving a worse education than they were originally. In the worst cases this is not only done without consulting the maths team, it is done against their own desires. Whilst it might be OK in a few years, there is an initial cohort of both teachers and learners who suffer needlessly in the immediacy.

Maths is innately more hierarchical than most other subjects and the decision to teach it in mixed attainment groups must be deeply considered by school leaders.

Below I want to go through some of the key principles that I have seen and used that have made it work in practice. These often are not things which can be implemented overnight.

The key points I’m going to speak on are:

The curriculum
Early intervention
Atomisation
The well-worn path
Effort over attainment
Means of mass participation
Explicit instruction

Curriculum – A rising tide lifts all ships

One of the biggest issue in mixed attainment maths teaching is students not having the pre-requisite knowledge to engage meaningfully in things their peers can. The department should still endeavour to teach the entirety of the KS3 curriculum but this needs to be done over 3 years. They should ensure that none of the topics that sometimes “leak” into Y7-9 from KS4 appear (factorising quadratics, solving simultaneous equations algebraically, index laws…). The scheme of work needs to go back to basics and build up slowly. It should start with numeracy and the basics need securing and mastering.

There are plenty of rich activities which can be used to both challenge students whilst helping others practice. If some students need “stretching” then exercises should go deeper rather than broader with the key concepts being taught. It is impossible to perfectly cater for all students all the time.

Teachers should be secure in the knowledge that, over 5 years, students will encounter all the content they need to get 100% in their GCSEs. They shouldn’t worry about holding a few students back in the short term for the betterment of all in the long run. Holding some students back to ensure all can access the content is better than the converse of letting some fly whilst others never master the basics. My second in department used to routinely remind me that “a rising tide lifts all ships”.

Early intervention – Build on solid foundations

Linked to the above, if there are students who join you in Y7 who cannot access the beginning of your course due to weak numeracy then you need to intervene. This should be a relatively small number of pupils. The culture around intervention needs to shift from happening at the end of Y11 to the start of Y7. Intervene early. Either employ or upskill staff on the teaching of Ks1-2 maths and put all the effort you would put into Y11 in the run up to their GCSEs into identifying and addressing serious gaps at the start of Y7.

This is the strategy that all schools should be using anyway, since if you sort the basics out then students will spend the rest of their time on the course building on solid foundations.

Atomisation – Break it down and build it up

Before teaching any new concepts teachers should go through a rigorous process of “atomisation”. Of breaking the concept down into the component parts that make it up. They should go through the list and decide what they can safely assume students know, what is essential to master this new concept, and what might be a “nice to have”. All of the essentials should be checked or reintroduced in the lesson prior to teaching the new content.

When it comes to teachers deciding what students may already know it is always better to underestimate than overestimate. If you underestimate then you only risk wasting a minute or two whilst you check for understanding and realise students can do it. If you overestimate, you risk tying yourself in knots later in the lesson and having students leave without grasping a thing. Whatever new concept you are teaching, break it down and build it up.

Well-worn path – Visit everyone but do not give them all your time equally

Do a well-worn path; this is a technique to be used whilst students are working independently. It involves mapping out a route around the classroom in which you can have eyes on every student’s work. As well as using it to check all necessary accessibility arrangements are in place (glasses, readers, dictionaries…) you can use it to check everyone’s work. It is worth starting a lap visiting your highest attainers first. These are a good proxy for any serious misunderstandings since if they are stuck it is likely everybody is and you can bring everyone back together. It is worth ending your lap with those who often require the most help. This is so that you can help them AFTER you’ve briefly touched base with everyone else.

It is OK to spend more time with some students than others. It is also OK, if there is a TA, for them to not always work with those who need the most help as the teacher may be better placed to intervene effectively. We are not aiming for equality but for equity. That involves visiting everyone but not giving your time equally.

Classroom culture – Praise effort over attainment

Maths undeniably has a PR problem. Some (most?) students will, by the time they start in Y7, already have a pre-conceived idea of how much they can achieve in maths. It’s important to build a culture where all students believe in themselves, perhaps more so in a mixed attainment setting where some will be doing maths alongside peers who are much more confident than themselves.

Take the time to praise the right behaviours that students exhibit. The peak-end rule suggests that what happens at the end of the lesson will really stick with students. To leverage this, end on something attainable, you shouldn’t be finishing your lessons with the hardest content. Treat your lesson like an exercise class and end with a warm down, not a sweat-fest. Make sure they leave feeling successful. Catch those most vulnerable doing good early on the lesson and make them feel great. In every interaction ensure that you are praising effort over attainment.

The final two are kind of cheats because they don’t apply specifically to mixed attainment maths teaching, I think they just apply to all teaching, but it can often be the case that people don’t think they do apply in this setting so I just wanted to make the point that they most certainly have a place.

Means of mass participation – who cares if less is in their books if more is in their heads

You need to have a system set up in the lesson to ensure that, as much as possible, everyone is ACTIVELY participating for as much of the lesson as they can. Mini whiteboards are the obvious (and best I’ve seen so far) solution to this. When checking pre-requisite knowledge, why ask one student when you can ask everyone? This is especially important in a less homogenous group where gaps and misconceptions can be harder to predict.

When it comes to students working in books it is nearly impossible to see everything that is happening. If more questions than usual are completed together (but still independently) on mini whiteboards then the teacher can be sure that if the need arises for students to work in books or on a sheet or something that they will be able to do so without embedding any misconceptions or being stuck. Remember that practice doesn’t make perfect, it makes permanent. Also remember that it shouldn’t matter if there is less in their books at the end of a lesson if there is more in their heads.

Explicit instruction – all the principles of effective teaching still apply

A common misconception that I see is the idea that mixed attainment teaching is not compatible with explicit instruction. This is far from the truth. It can be tempting to think that with so many different starting points in the room tasks need to be really open or many tasks need to be available. This simply isn’t the case.

When mixed attainment teaching either hasn’t been very effective for a few years or starts at once in Y8 or Y9 it’s easy to see how this conclusion is reached. With all of the above in place though, you can start from the ground and build up remembering that all the principles of effective teaching still apply.

Things to definitely avoid

As well as doing all of the above, here are some brief “do nots”:

Do not start mixed attainment teaching at KS3 all at once, begin at Y7 and build it up
Do not start it and THEN put the CPD in place, get the CPD sorted first then make the switch
Do not do this TO the maths department, do it WITH them

The end and the future?

I sincerely hope that mixed attainment maths becomes the norm in the future but this is not a change that can happen quickly and I fear that we are putting more and more staff off it at the moment due to poor implementation. If the above ends up being of any use, I’ll be a happy man.

The most boring (but important) reasons that centralised planning fails

This post is about the common pitfalls in departments who use centralised planning. It discusses the issues and offers solutions.

A while ago I was invited onto Craig Barton’s Tips for Teachers podcast. I had to think of my top 5 tips I wanted to share with folks. The second one I went for was “leave a legacy”. This was about ensuring that when you leave a school or a position in a school that you have put systems in place that exist outside of the individual. That when you leave, your successor has something to build upon, rather than something which was only in place because it existed on your shoulders which will crumble when you leave.

A key aspect of this is for heads of department are the implementation of centralised resources. I firmly believe that any department head who does not advocate for this approach is doing a disservice to both their students and staff.

I encounter lots of schools trying to implement this (which is great!) but I sometimes see some barriers which prevent it from being as effective as it could. This post is about exploring those reasons and giving some antidotes.

This post comes with a health warning though because the reasons are incredibly dull. Vitally important. But dull as dishwater.

Centralised Planning

Quickly, before diving in, I just want to clarify what I mean by centralised planning, just in case it means something different to you. A department that uses centralised planning would have “base lessons” that are produced by members of the team and quality assured by leaders. These capture the key curriculum aims, contain pre-agreed models of working, and fit whatever lesson structure the school or department has. These then need to be personalised by every teacher before delivery to ensure it is bespoke for the unique group of individuals in that class.

Staff should still feel that they have the autonomy to personalise these resources but only to an extent. It must not jeopardise a consistent and high quality curriculum being delivered for the students over the time they study the course.

The benefits of centralised planning to the students far outweigh any negatives and, with the considerations below, most of the main criticisms laid against it (leading to lazy teaching, stripping all autonomy from teachers…) are mitigated against.

It does undeniably take some autonomy away from teachers but if what one individual wants to do is better then it should become the new normal for the department. If what that individual wants to do is worse, then it shouldn’t happen.

If this, or some version of it, is not in place then you do not end up with a department, you just have a group of individuals who happen to teach the same subject in the same building.

Reason #1

Online folder structures.

There it is. I told you it was dull. But, you’ve made it this far so let’s keep going.

The way that leaders choose to organise their subject area on whatever cloud-based systems their school uses can make or break centralised planning. Leaders need to ensure that all the base lessons are available, sure, that’s the easy bit.

They, more importantly, also need to ensure that they can access all of the adapted versions that their staff produce. Staff should not be operating in silos and saving things in some private area. The work they produce should be readily available to all. This is because:

Improvements compound – The base lessons won’t be the best and changes/additions that staff make will in some cases improve the quality of the resource. These need saving centrally so that over time the resources go from strength to strength.
Adaptations exist – Certain classes will contain students with additional needs (lower reading ages, colour blindness, weak numeracy…). When staff make these adaptations once and save them centrally, they will not have to be adapted from scratch if classes with similar needs need teaching in the future.
Quality assurance – Leaders need to ensure that engagement with the resources is happening and getting into every lesson is not feasible. Having access to all resources is though. This helps with quality assurance, the sharing of good ideas and with accountability for all staff.
Cover/Absences – If students are absent or if classes need emergency cover leaders having access to upcoming or previously taught lessons saves time.

The folder structure should not be designed around staff having their own spaces within a shared area but should be designed around the learning experiences of the pupils. I.e. folders should be grouped by year group and unit, so that it is easy to navigate a child’s learning experience rather than an individual teacher’s experience.

Example structure:

Reason #2

Live modelling

When producing centralised resources it can be useful to pre-populate or pre-animate models and processes which need teaching. There is nothing wrong with this in and of itself. It can help ensure that there is a consistency in the delivery of key concepts in the department which will help students over time.

The danger comes in teachers not getting rid of these by the time it comes to them delivering the lesson. When modelling it MUST be done live. Whether that’s on a visualiser or a relatively blank board it doesn’t really matter. What is important is that the teacher knows, by the time they deliver the lesson, that they cannot “outsource” the teaching.

Reason #3

Medium-term plans

When teaching with centralised resources it can be easy to go from one lesson to the next without having a sense of any overall aim or important threads throughout the unit. Staff should engage with the unit as a whole in advance of teaching the first lesson and produce their own sequence of what their lessons will cover. This may involve merging or splitting existing resources to cater for the specific needs of their class. It should also involve a brief conversation before the teaching each unit (I’m saying a unit will last roughly a half term), with them explaining to a peer any adpatations they’ve made and why and demonstrating an understanding of what the unit’s purpose and aims.

Overview

Centralised planning saves time, increase the quality of resources in a department and ensure that students get a consistent curriculum experience with the same models/metaphors/scaffolds… used throughout. It is a worthy aim but takes time and effort to implement well.

Folder structures, ensisting on live modelling and engaging in personalised medium-term planning all help ensure it ends up being more effective than it otherwise could be.

If you’re interested in the other 4 tips I shared check out the full episode here Craig Barton’s Tips for Teachers.

Beware the Ends of Branches

This post looks at certain topics which are often neglected when it comes to retrieval, why that happens, and what can be done about it.

Let’s start with a quick question. What seemingly accessible topics in your subject do students never seem to be able to remember?

In my subject, this is an easy one. Ask any maths teacher and their list will most likely include:

Loci
Constructions
Congruency
Simultaneous Equations
Cumulative Frequency Graphs
Averages from a table

Retrieval

Retrieval, retrieval, retrieval. It is a necessary part of learning (remembering?). Learning, not just performing, does not happen when something is seen once and then never again. You need introducing to something, you need to almost forget it, then you need to rescue it from your mind before it fades away just in time to keep it in your head for that little while longer.

In mathematics, some topics are naturally retrieved. With no effort from the teacher they will recur again and again. If we take solving two-step equations as an example, once taught as a discrete topic, it will rear it’s cheeky head when students move onto:

Forming and solving equations
More complex linear equations e.g. three step or with unknowns on both sides
Simultaneous equations
Quadratic equations
…

If we take basic angle facts, these will reappear when moving onto:

Angles in parallel lines
Forming and solving equations
Certain ratio problems
Angles in polygons
Circle theorems
Bearings
…

Why does this matter?

Retrieval, retrieval, retrieval. It’s just so important in embedding content, it means that the ideas above that recur are more likely to be learnt (remembered?).

A Curriculum Tree

If we imagine a tree of maths knowledge representing a curriculum. In this tree, the core ideas which appear everywhere form part of the sturdy trunk. Let’s imagine branches grow from pre-requisite materials, these more fundamental ideas mentioned above would form some of the more solid parts which would have many offshoots. As we track any branch to its end, you would find a topic that is not needed for any other topic for that curriculum.

The closer a topic is to the trunk the more naturally it will be retrieved. The topics at the end of the branches, however, are not going to naturally be retrieved whilst going through a curriculum. This is a problem. Why? Because retrieval, retrieval, retrieval, is so important to remembering (learning?).

Ends of the Branch

Because of how important retrieval, retrieval, retrieval is to learning (remembering?) we need to pay special attention to the ends of the branches. These will not recur naturally so we must find ways to force them into the curriculum. Most schools in the UK these days achieve this at the start of the lesson with some sort of retrieval activity. I think this is a great idea. Without revisiting content regularly there is a risk of it not being remembered and the start of the lessons seems a better place than most in which to do this.

It follows (if you believe all of the above) that the topics at the ends of the branch need special care and attention when designing these retrieval tasks. Beware the end of branches!

This all seems simple enough. Problem solved, right? Well, hold up a second.

There are some topics that, for various reasons, just complicate things.

I see hundreds of lessons a year and am yet to see a retrieval starter in which students need to recall loci or constructions, and very few where they retrieve cumulative frequency graphs, averages from a table or simultaneous equations etc. Does that list look familiar? (Don’t worry if you’ve forgotten it, we haven’t retrieved it yet), but it’s the list that we started this post with.

There is an uncanny crossover between what I do not see retrieved and the seemingly accessible topics that teachers will proport students struggle to remember. Could it be that it’s because students are not asked to retrieve this content as often? I would say so.

It’s perfectly understandable that this happens though. Nobody wants to spend the beginning of their lesson retrieving loci or constructions because it will inevitably lead to chaos as students do not have the necessary equipment.

Cumulative frequency graphs and averages from a table questions will require printing which is logistical barrier.

Simultaneous equations and congruency questions often require so much writing they may not fit into a snappy 5-minute starter routine your school so heavily insists on.

Solutions

If you or your department uses starts of lessons in this way then please beware the ends of branches. Not all of them, but those which require that little extra consideration. These can be easy wins but without putting in that extra effort every now and then to ensure students retrieve these topics, they are doomed to be forgotten (not learnt?).

Remember:

Take time to mark out explicitly when teachers should be reviewing these
Have some pre-prepared printable sheets ready
Have a class-set of equipment on standby for certain weeks
Be ready to (justifiably) take that little bit longer on the starter

Without taking special care, some branches will never be able to blossom.

QLAs – How to Use Them Well

Question level analysis (big old spreadsheets which look very colourful and contain data about how every student did on every question) are time consuming to produce and, by themselves, are not useful. Data managers and trust-leads might insist on them but they are nothing but a superficial exercise until they are used purposefully. This post will explore some common pitfalls and what should be done instead to make the most out of these documents.

Don’t forget what the question was. It’s typical to give a brief name to the columns that refer to the broad topic being assessed. When you see a big column of red under a question title, do not just assume everything about that topic needs to be retaught. Go back and look at the exact question that was in the paper, then look at a select group of student responses. Was there a common misconception that needs addressing? Was this question quite a complex reasoning question and the subject knowledge on the actual topic is fine? Was this combined with one or two other topics which is where the weaknesses actually lay?
Focus on the highest leverage areas. When choosing which columns to focus on, the ones with the most “red” are not necessarily the best. Near the end of the paper it would be typical for questions to be harder. Where possible, compare the performance with a nationally representative data set. From here you should focus in on where the biggest differences from the norm are. That way you know you are focusing on marks which are more accessible.
Teach a few things well, not everything poorly. It can be tempting when presented with data like this to what to go over every single gap. Produce 30 individualised worksheets that all focus on different weak areas for students. The issue here is that without being able to give them all 1-1 tuition (giving them model answers does not count) they won’t be able to learn from this experience. It is your job when reviewing whole class assessments to do the greatest good for the greatest number, teaching those things well is better than teaching everything poorly.
Praise the good. As teachers we are always looking for the gains, our eyes will immediately be drawn to the red. Take time out to praise the class on their areas of strengths. Highlight the positives and, where possible, show them the progress they’ve been making over time. Tests can be stressful and saying “well done” is not just something they’ve earned, it’s the right thing to do.
Be proactive as well as reactive. This data is going to be produced as a result of the teaching this class had. As well as being reactive in the moment to this class don’t forget to be proactive as well. Making any alterations to the curriculum so that future classes don’t fall into the same trap as your current class is going to ensure future students benefit from this knowledge.
Quick-wins vs Reteach. There will be some minor errors that some students made and some quick-wins which can be easily addressed but may need to be revisited frequently. This will also show up some huge gaps in their learning which may need multiple lessons to address. Split these up accordingly. Have a group of things which will require substantial re-teach time and a group of smaller things which can be addressed at the starts to lessons.
Don’t focus on the specifics of the question. When a question has bene identified as one that has been underperformed on then make sure you do not address the specifics of the question but rather the root cause of the mistakes. It is pointless going through that specific question in detail and then giving students time to practice almost identical questions just with different numbers. You need to diagnose the gap in their understanding and teach more holistically. That exact question won’t come up again, make sure you fix the cause, and not just the symptom.

I think QLAs can be an incredibly powerful tool but it’s important to remember that is all they are, a tool. A tool can be used well and it can be used poorly. If you have any other tips to add please share them in the comments.

Also, if you’re reading this because mock-season is coming then you may also be interested in this post about marking papers to ensure the data is reliable in the first place.

Marking Maths: It’s Either Right or Wrong. Right? Wrong!

Looking at how maths marking is harder than people think, why it’s important and what can be done about it.

“It’s either right or wrong” isn’t it? Well, is it? No, I don’t think so. It isn’t? No, it isn’t. It’s more than that? It is. How do you know? Here’s how.

On Twitter, when it was still called Twitter, I put 6 mock student responses to questions up alongside the mark scheme. Underneath each was a poll that captured the marks people would award the student. Here are the questions and results. I’ll put the questions first so if you want to play along and mark them yourself without being swayed, feel free. The results are after. Note that the answer highlighted in blue is just the most common response, not necessarily the correct response. The correct responses will be looked at near the end of this post. Each was answered by about 2,000 people.

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Poll results (answer in blue is not necessarily correct, just most popular):

I have done this exercise, or similar, with teachers and every time the results are about as varied as this. It shows, fairly conclusively, that marking a maths paper is not as simple as some might think. Let’s go through why this is important and what can be done about it.

Why is this important?

No matter what your philosophy of mathematics teaching is and regardless of what you think about exams etc, it is hard to argue that we are doing students a disservice if we don’t prepare them for their exams. A small but crucial part of this is exam technique. If teachers don’t know what does and doesn’t give you marks and, maybe more importantly, what you can and cannot be penalised for, then two students who know the same amount of content, can get different grades due to how well their teacher has prepared them in the technicalities of how the paper will be marked.

What can be done about it?

First of all we should acknowledge that there is an issue here. Yes, maths papers may be quicker to mark than others, but it doesn’t mean they are easier to mark. There is a page in every GCSE mark scheme that often gets ignored. It is maybe the most important page in the whole document. It outlines the underlying principles that should guide the examiners marking as they go through the paper. It decodes what all the letters mean and gives overarching advice applicable to every paper.

CPD Resources

If you want to test yourself, I made some resources. They consistent of an exam paper with mock responses and an MS Form where you can input the marks you have awarded the student. The Form will give you your score, not the score the student got, but a score of how accurately you marked the paper. This paper has been completed many times already and there is an Excel doc which has collated all the misconceptions that teachers have had when marking the paper. There is advice in there which can not only be taken forward when marking in the future but which can be shared with students as a way of increasing the marks they may achieve.

Here are the correct responses for the 6 questions used above along with the reasons why:

Here are links to the resources mentioned above or you can find them in the documents part of this site.

As a HoD or Curriculum Lead in a school this could be a good activity to check the quality of marking in the department. As an individual, you could just use this to test yourself. As a non-maths teacher, you can just use this to appreciate some of the finer complexities we have to deal with.

Structuring a Maths Curriculum

A look at different curricula models alongside their strengths and necessary considerations.

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.

Emotion in the Curriculum

This short piece explores the big idea of including subject-specific emotions in our curricula, alongside the content and skills we may want students to learn.

Intro

Einstein said “Education is that which remains when one has forgotten everything one learned in school.” He alludes to forgetting content but not to forgetting how one was made to feel at school; I suspect, perhaps more than anything else, that is actually what remains.

What first hooked you onto your subject? What gave you that passion? How a subject makes us feel is crucial to our relationship to it. I worry that we too often leave our students emotional connections to our subjects to chance instead of finding explicit ways to create positive experiences.

The Good with the Bad

How often do we discuss how we want our students to feel? If it is our aim for students to become enthralled by our subject and develop a passion for it then emotions must be part of the discussion; the good and the bad. The joy of solving a maths problem is only enhanced by the struggle and turmoil that precedes it. The thrill of a win in sport is compounded by knowing the feeling of loss.

We need to ensure that we do not mollycoddle our students throughout their entire schooling giving them a sterlised and safe one-note experience. For without experiencing struggle, success is numbed. Without knowing sadness, one cannot appreciate joy. I worry in the past I have been guilty of this.

Every curriculum I’ve ever seen orders topics and skills. Not a single one talks about how they want their students to feel. Does yours? (If it does I’d love to see it). I’m sure most teachers would say they want students to feel certain ways but without making this explicit and mapping it out as a team I wonder how often this is achieved. Do you? Have you?

How does it make you feel?

How does doing your subject make you feel? Not when you teach it, but when you actually do it. What are the strongest emotions it can elicit?

I think the answers here vary subject-to-subject:

Maths – frustrated, surprised, proud, confused…

History – empathetic, optimistic, pessimistic, connected…

PE – exhausted, satisfied, proud, part of a team…

Art – creative, free, mindful, shook, pensive…

What would it be for your subject? If one of the above, what would you add? What would you change? Please add in the comments on to this very empty thread.

Entitlement

This should not require students to reach a certain level. If I want students to feel resilient in maths I can find a task designed for that purpose for any current attainment level. The same goes for making them feel surprised, happy, proud, stuck….

It might not be a tangible or measurable aim. It might not be something you can assess in a topic-test but it doesn’t make it not worthwhile.

Einstein said “Education is that which remains when one has forgotten everything one learned in school.” – he never mentioned forgetting how one felt; I suspect, more than anything else, that is actually what remains.