Curriculum: A longer read.

The word curriculum is apparently a near-constant part of my life lately.

I tweeted on November 10, 2023, this:

Curriculum... a thread 🧵

Since 2017 I've thought a lot about curriculum. In my sixteen years in the classroom, I've followed schemes of learning based on textbooks, from exam boards and 'for our kids'.

— Dave Taylor (@taylorda01) November 10, 2023

It led to a bit of attention, and ultimately to a guest appearance with Matt Findlay and Femi Adineran on the Beyond Good podcast. Since recording, Jonathan Hall started an event called a Maths Fuddle through Mathsbot, and his first talking point referenced curriculum too.

Tonight we're talking all things curriculum and schemes. Let's kick of with a binary poll...

What’s more important, a good teacher or a good curriculum?#MathsFuddle1

— Jonathan Hall (@StudyMaths) January 12, 2024

This is one the things, and there aren't many of them, where Jonny and I disagree. He's team 'Teacher', and I'm team 'curriculum'.

I want to put my thoughts down in full, so here goes...

Google's define: function returns this for 'define: curriculum'... the subjects comprising a course of study in a school or college. Straight off the bat, I want to clarify what I mean by curriculum, by saying that I mean the content that is intended to be taught to students. I use the term curriculum within the maths department interchangeably with scheme of learning or scheme of work.

In my 16 years in the classroom, I have followed various schemes with various cohorts of children. I've followed textbooks with KS3, and exam-board provided route maps with KS4. I've followed textbooks with KS4 too, as well as bespoke curriculum at KS3 (spoiler alert: it wasn't bespoke, it was self-made). I've followed off-the-shelf curriculums, and I've looked in to others that I haven't followed, and one thing was true every time... It wasn't the curriculum that was the problem, it was the implementation.

The implementation came down to many factors, but all led back to the thought that 'This is costing us money/has been shared by an exam board/is used by many, so it must be what we should be doing'. My main thought here is 'Well, just because everyone else is doing it wrong, doesn't mean we should'.

Take the exam-board-provided example (and I'll consider things outside of my lived experience, but close to). AQA provide route maps for their qualifications, and they're pretty good. They provide a decent journey through the specification (as pretty much all curricula do), but they don't provide the journey that my cohort needs. 

Their one-year resit route map begins with equivalent fractions, decimals and percentages, and this is often question 1/2/3 on a Foundation paper, but if I gave that to a group of students who achieved a grade 3, this is likely to be unnecessary for them to be taught. For those who achieved a grade U or 1,  this is likely to be the right thing. But, what will happen (and this is probably well-meaning, and it makes sense) is that leaders will see this journey, see that it has an AQA badge on it, and say 'The exam board are saying this is what we should do, so we'll do that'. I don't think that they're saying that you should, but they are saying that you could.

The same goes for CIMT/Complete Maths/Lumen/Sparx/White Rose Education, those Collins textbooks sitting on the shelf in the workroom, and those 1990s Maths Frameworking textbooks that have seen more dust than classroom time in the last 15 years. The main issue is that when an age is attached (as a guide, more than anything), children of that age must be expected to work with that content.

But what about the Year 7 child who hasn't grasped the column method for subtraction, the Year 8 child who hasn't mastered the idea of division, the Year 9 who hasn't learnt how to measure an angle, or the Year 10 child who hasn't learnt his times tables?! (These are all children I've worked with in the last week).

Should they be asked to look at Graphical Forms of Sequences, or Sharing Amounts in a Given Ratio, or Trigonometry, or Simultaneous Equations? (Spoiler: absolutely not). Experienced teachers know that they shouldn't, and effective teachers alter their instruction to the needs of their students. But here's what I believe... 

Simultaneous Equations as a topic is likely to be appropriate for about a fifth of the students in Year 10 (based on my experience), so the other four-fifths need something different. The experienced teachers know this, but those without that experience don't. The experienced teachers then teach something else - something that they're expected to decide, and the inexperienced teachers teach simultaneous equations with disastrous outcomes, because that's what the curriculum tells them to do. 

The curriculum should tell teachers what the students in their class need to cover next, not what the top 20% need to cover, and the rest of you should do something else. The journey through maths is well-defined, and differentiating down means that this isn't the journey that students see. They see something that's a bit like it, but easier. Because they're journey isn't well-defined, they find it harder to make progress, because their journey isn't coherent.

The gold standard of a curriculum is one that adapts to the needs of the students. I have experience here, and spent around 400 hours in a past role collating a curriculum that took students on a journey from the Year 3 National Curriculum, to AQA's Level 2 Further Maths qualification. We found that student behaviour improved, enjoyment levels increased, and attainment improved, taking us from 61% 4+ in 2018 to 75.7% 4+ in 2022. 7+ increased from 8.0% to 18.1%. Teaching became a joy and privilege.

So, how did I go about putting this in motion?

I think my first experience of realising that we needed something better was with a Year 10 bottom set, scoring less than 10% on tests, and then laughing about it. This had become so natural to them, that they expected to fail, and then it became a race to the bottom. My solution was to have them do the Entry Level Certificate in lessons, score 80% on each assessment, and development a culture of success, and wanting to do better.

A few months later I was approached by a colleague who'd taught Pythagoras to students. This was the second topic in the textbook. He commented that they were fine with the procedure, but hadn't a clue how to find square roots of square numbers. This was topic 5 in the textbook.

All students were doing the same tests, from bottom sets to top sets, with the top sets scoring 70% plus, and the bottom scoring 20% and below. This was accepted as the norm, and those students would just score that and be happy with it. This is where I targeted my first action - by having multiple assessments that staff could choose from to give their classes, that were comparable between groups, but gave students more success.

I worked, and continue to work, in challenging circumstances. High levels of disadvantage, high proportions of EAL, low levels of aspiration, and prior attainment below the national average. I'd experienced motivation in KS3 fall away since KS3 SATs were abolished, and the same at KS4 when modular qualifications were culled. Whether this is the outcome of external tests that means that students are taught the right maths when 'revising', or the students' motivation to perform on external assessments, I'm not sure, but either way, I wanted to harness this, and took inspiration from both.

I decided that I'd split the year in to 5 modules. The content of each module wasn't overly important, but the expectation that students would improve on their modular assessment from the year before was. Each of the 5 modules was split in to 9 units, where the content was hierarchical, and content is expected to be mastered before moving on.

The five modules were called Module A, B, C, D and E, with units going from 1 to 9. Module A consisted of Place Value, Symmetry and Transformations and Averages. B was Calculations, Angles and Sequences. Module C was Algebraic Manipulation, Charts, Fractions and Shapes. D consisted of Decimals, Equations, Properties of Numbers and Units. Module E consisted of Graphs, Perimeter, Area & Volume, Percentages, Probability and Ratio. I felt this gave time for skills to be taught before using them in later modules, but it's also important to state that content didn't necessarily begin in Unit 1 (Averages began in Unit 4, and Algebraic Manipulation was introduced in Unit 5). The whole journey is here (be warned of large file size).

A recent paragraph stated that 'content is expected to be mastered before moving on'. How do you achieve that? Well, this came down to assessment. Assessments were designed so that each Modular assessment had 9 sections (one for each unit). Each section consisted of 20 marks, so the Module A assessment was 180 marks long, but students only sat 60 marks from this assessment, decided by their teacher. If students had succeeded with content up to Unit 4, they sat the assessment consisting of sections 2, 3 and 4. If students achieved 15 marks in a section, they were able to achieve in the next unit, and have their assessment recorded as this.

A quick recap: A student would work on content from, say, Module C. They had been taught content from Units 3, 4 and 5, for example, so sat a 60-mark assessment on content from sections 3, 4 and 5. They might score 18 marks on the content from Unit 3, 12 marks on the content from Unit 4 and 9 marks on the content from Unit 5. This would mean that they had mastered the content from Unit 3, but not quite from Unit 4, and this is where their instruction would begin the following Year. In terms of recording this assessment grade, this would be recorded as 4.5 on the departmental tracker, indicating that they've had some success with Unit 4, and should work from this point in the next academic year when they return to Module C. Comparatively, a score of 18/16/9 would be recorded as '5.2' where .2 represents scoring 5 marks, .5 is 10 marks, and .8 is 15, which means they 'graduate' up to the next section of their assessment.

From a departmental leadership perspective, the tracker then provided an up-to-date record where students are on the journey in each Module (on each of the sections of 'the dartboard' as we referred to the image shared earlier), as well as a ranking based on the average of their 5 modules (updated with their most recent assessment. This means that sets can be assigned using the average level of proficiency across the 5 units, and tinkered with at the top and the bottom of each set to ensure that the spread of attainment in each group is as small as possible. Assessment data, as well as their set from each year remains visible so that trends can be spotted, but progress is calculated between each module from the current academic year and the previous academic year to celebrate progress made by students (rewarding the lowest attainers too, as they make good progress, rather than always those who go on to score the highest grades). The list of students making the most progress between modules was printed off and displayed proudly, so that those students who might not normally find their name on these lists were there, could tell their parents they were on the wall at school, and their peers can celebrate them too.

From a class teacher perspective, when you moved to another Module on the scheme, you looked at the tracker and saw where their attainment was last year. Acknowledging forgetting, this is where your instruction started, to activate prior knowledge, and then bridge to new content over time, confident that students were going to grasp the content that you were teaching. By the end of the Module, you 'ordered' assessments based on the levels of success that students were experiencing in lessons, and departmental leadership were able to check that staff were being aspirational when ordering their assessments, based on the spread of prior attainment visible from the tracker, and the numbers of each assessment ordered on the order form. 

From a student perspective, they were never out of their depth because they were building on success from the last time with content from that module, so they were motivated to succeed, their behaviour improved and so did their participation in lessons. They were accountable for making progress between modules, and celebrated when they did.

Heading back to the class teacher perspective, as in inexperienced teacher you were able to develop your pedagogy with motivated students, participating in lessons, knowing that if students weren't grasping the idea, that it was down to you, rather than the content. Teachers were also accountable for ensuring progress occurred.

I'll acknowledge some of the challenges associated with this operation, and there were many, but I won't remember all of them. But, where do you start with Year 7 students? Taking into account their prior attainment, start them on unit 1, 2, 3 or 4. It wasn't ideal, because their prior attainment wasn't recorded by us, and was sometimes quite different to what we experienced. But there was an acceptance that even if the level of complexity was a little off in Year 7, by the time we got back around to Module A we had assessment data from Year 7, and getting the level of maths right was much easier.
What about tiering at GCSE? They still did Year 10 mocks, Year 11 mocks, and from that we had grades and expected progress between each assessment point and the end of Year 11. We left tiering decisions until as late as possible, but in my eyes, if you're not going to achieve a grade 6, then you should be doing Foundation.
What about students who made no progress repeatedly? Well, we have their progress from previous years, and they're identified as needing more attention. They are the first students you check in with in periods of independent work, the first mini whiteboards that you check, seated close to the teacher for additional attention.
What if a class hasn't covered the content for the assessment? The class teacher chooses their assessment. A lack of progress is picked up at departmental leadership level if class-wide, and medium term planning can be looked at with the teacher in question.

Whilst I've been writing this, this has been in my notifications:

I think a strong curriculum can have a wider positive impact than a strong teacher but I think the impact of a strong teacher is greater on those that they teach.

A strong teacher will find a way of making the most bonkers curricula work

— Jshm (@jshmtn) January 13, 2024

This is why I think having a good curriculum model in place is more important than having the best teachers. The curriculum's impact is felt beyond the four walls of an individual teacher's classroom, and from a departmental leadership perspective, this is what we should be aiming for.

This blog may be incomplete in places - sorry if that's the case. Feel free to pull at loose ends and ask for clarification. I'm sure that you'll be able to pick holes in my beliefs, and that's fine by me, because I'm happy to be told that I'm wrong. I just happen to believe that I got most of 'how a maths curriculum can work' right, backed up by a significant improvement in outcomes, and would love to see more places adopt a similar strategy.

Assessment Feedback Lessons

With a little time having passed between the end of term and now, and with my mind turning its attention back to work mode, I've had a little time to collect my thoughts about leaving and come back to assessment feedback lessons.

Not every assessment feedback lesson can be ideal, due to time constraints, school events, school holidays, lack of technology, and other issues, but this is where my thinking is at in terms of how I'd like to do assessment feedback moving forward.

1. Assessment is completed.

2. Assessment is marked and scores are entered into a QLA document.

3. 'WAGOLL' provided to pupils.

4. Key points are fed back.

5. Identified areas are revisited.

Each of these steps is briefly outlined below.

1. Pupils sit the assessment. There's an argument that sitting assessments is a poor use of curriculum time, and whilst I see that all classroom time would be best spent teaching pupils content, I also want my assessment data to be as reliable as possible. For me, this is that it's sat in (as close as possible to) exam conditions, in front of me, so I know that I can trust it.

2. Marking is time-consuming, but when it comes to assessments, I think this is an appropriate use of time. I want to see the misconceptions that pupils still hold, I want to be able to feedback on common incorrect answers and the remedies for these, and I want to see the effort that pupils are putting in terms of resilience (answering every question) and presentation (taking pride in their work).

QLAs also seem to split the profession, but I like them. I get a feeling for how well pupils have done on a specific question when I mark, but after QLA'ing, I get cold, hard data that I can use to direct my intentions, and I love cold, hard data.

I don't see much value in the QLA document only providing information to the teacher, so I like my QLA to provide a printout for each pupil to give them a visual representation of their scores (in terms of Red, Amber and Green). This printout will also include three questions that are directed at the pupil, identified as being the three most important questions that I'd like them to be getting correct. Some pupils may have more that I want them to be getting correct, but these are the priorities.

I've been working on a new QLA spreadsheet recently, to 'supercharge' the information that I get. I might blog about that at another time.

3. If you're unaware, 'WAGOLL' stands for 'What a Good One Looks Like'. This could be in the form of a handwritten completed assessment, or it could be in the form of me completing the assessment on video. It could even be pictures of their own work, collated, to make a 'Best Of...' compilation. This allows pupils to re-engage with the questions and see what their answers should have been. The improvement in tech over recent years would probably see this uploaded to Google Classroom for pupils to access.

4. Whilst completing the QLA and preparing individualised printouts, I identified three key questions for pupils to complete, but in doing so, I've identified all of the key areas of deficiency within the understanding of my class. 

In my assessment feedback lesson, I would be sharing common wrong answers, why they're wrong, and what pupils should have done, and what's important here is that I'll follow this up with an opportunity for them to correct their mistakes in the form of example-problem pairs or backward faded activities. 'Going through the paper' with pupils annotating with the correct answers isn't enough - copying doesn't engage pupils in thinking, so it's important that we follow this up with pupils having something to 'do' with the feedback.

Following the example-problem pairs and backward faded activities pupils will be given their scores and printouts (these have been held back to increase curiosity and engagement), and the time to complete their targeted questions mimicking the exam conditions, allowing pupils to be successful with something that they previously weren't. I'll then mark these questions to check whether pupils have responded to the feedback they have been given.

5. The most important part of these lessons is that they should be focused on learning, rather than performance. We should all be well aware that simply because pupils are getting questions correct, doesn't mean that they've learnt it. Learning happens over time, rather than in the moment. With this in mind, it's important to provide opportunities for pupils to revisit this understanding at spaced intervals, to maximise the chance of pupils learning this stuff rather than just performing with it in the moment. I'd be adding these to my medium-term plans, to incorporate spaced retrieval opportunities a day later, a week later, a month later and three months later.

My aim is to provide pupils with many opportunities with which to learn from their mistakes. The 'WAGOLL' gives pupils who are keen and enthusiastic the opportunity to engage with the whole assessment. The individualised printout forces those who are less keen and less enthusiastic to engage with key material. The spacing of the ideas in terms of retrieval is the key aspect here, as learning occurs over time and performance is a poor proxy for learning. I want pupils to perform with the ideas many times, in multiple representations, which will imply that they've learnt the idea that they were previously struggling with.

This blog felt a little quick and short. If you have any queries, or if you have any suggestions to enhance this procedure in any way, please let me know how!

The Plan

So, my thoughts have settled, my plans are somewhat in place, and I'm hamstrung by events beyond my control.

Following their mock exams, I've seen my Year 10s once (immediately after their last exam, which was a maths paper) and they had a 'mock results day' on Friday (July 7). I had a timetabled lesson on that day and could not strike due to my union choices, but I was staffing a rewards trip for Year 7 and Year 8. My next lesson with them is on Tuesday (July 11) which is cut short by staff training, but I am also on an induction day at the school I am joining in September. I then have a lesson with them on Friday (July 14) and Tuesday (July 18) before we break up for the summer holidays.

The lack of time and a proper opportunity to follow up going into Year 11 has impacted what I intended to do, but here's the plan of action...

They sat two OCR papers for their mocks - a calculator and a non-calculator. They were given a revision list to aid their revision, a revision course on TUTOR, a practice paper geared towards their mock papers, and the opportunity to join us in the dining hall on the morning of their exams to settle their nerves. Paper 1 was the better-answered of the two papers, but both highlighted the need to revisit some key topics over the next year.

Due to the rewards trip and my induction day, I have had 150 minutes of cover to set, and I've been leaning on Backward Faded Maths, and the associated techniques, to resource these lessons.

The questions that I've chosen from paper 1 are questions on 'Reverse Compound Interest' (11% of the marks achieved), 'Angles in Polygons' (42%), 'Proportional Reasoning' (54%), 'Calculating With Bounds' (40%), 'Algebraic Proof' (36%) and 'Equation of a Circle' (39%).
The rest of the paper was better answered, but there are a few areas that I'll be reminded pupils about in a lesson (probably on Friday July 14), as well as a note that pupils need to revisit 'Circle Theorems' (26%) in more depth.

From paper 2, I'll be leaving backward faded activities on 'Writing Ratios in the form 1:n' (36%), 'Using Relative Frequency' (51%), 'Probability' (52%), 'Simplifying Surds' (18%), 'Multiplying Recurring Decimals' (51%).
These aren't the only needs, but they're the ones which are most suited to backward fading, and in my lesson on Tuesday, July 18 we're likely to spend some time looking at 'Calculating Percentage Increase' (51%), Indices and Powers (60%) and Rearranging Formulae (56%). I've also got more notes, with pupils needing to revisit 'Using Kinematics Formulae' (32%), 'Constructions and Loci' (37%), 'Enlargements from a Point' and 'Describing Transformations' (54% and 23%), 'Plotting and Using Quadratic Graphs' (28%) and 'Forming and Solving Equations' (14% and 10%).

The 100-minute cover lesson, with a non-specialist cover supervisor, that I set for Friday started with a 'Do Now' with solutions left, followed by six activities from Backward Faded Maths with 'follow-up' extension questions. The 50-minute lesson has been assigned with the same structure.

When I get back to seeing the pupils, I'll give them a 'Do Now' to be completed in exam conditions and then we'll mark them (comparing the mark schemes from their mocks to the 'shadow' questions), seeing the improvements made and adding these to their scores. We can then compare these to grade boundaries, to see if anyone tips over to the next grade. I've also, whilst marking, made scribbles of 'W' and 'M' within papers, where writing (more of) their Working would have had an impact, or where they've made a silly Mistake that they shouldn't be making. We'll add these to the scores we've just calculated and compare them to the grade boundaries again. The aim of this is to give them a confidence boost to increase motivation over the summer, as I hope that their first experience of sitting a 'formal' exam has been a learning process.

I'll finish up the lesson with a Q&A about their papers, where I'll answer any queries they might have about what they did in their exam and what they should have done, before sharing what this might look like as GCSE grades if they follow 'average models of progression from their Year 10 mock to GCSEs from our recent outcome data.

The lesson for their second paper will follow the same structure. This isn't what I'd liked to have done, but with time limited and a lack of an ability to continue this into next year, I hope that I've given it the best I can!

I might follow this up with an ideal structure for an assessment feedback routine, because I know that this is far from ideal!

What Am I Trying To Achieve?

The last five blogs have led to this one, and I think the main question that anyone should be asking when they do anything is 'What am I trying to achieve?'. A task without a goal, a purpose, feels a little pointless.

What am I trying to achieve when I'm feeding back assessments to my classes? Well, that's a big one.

Ultimately, I want them to be proud of what they've achieved and to be spurred on to greater things, or I want them to take away an impetus to improve in some way. Dylan Wiliam says that 'feedback should improve the learner', so I don't simply want an exam script that looks more like a rainbow and has a larger number on it than it did when I gave it back to them. I want pupils to have a moment of realisation. It could be as small as a mistake that they made is corrected (not just once, but for the rest of time) or it could be the understanding that if they begin to apply themselves more, and give more time to practicing maths, they can be better at it.

My Year 10s - the class that I'm going to trial this with - sat the first paper of their mock exams, and as it stands I have marked the papers, but haven't yet analysed them for individual areas for improvement, or whole-group areas for improvement. My plan is to sort this tomorrow, identifying areas of need for individuals/small groups, and identifying areas that the whole class need corrective instruction with.

In terms of what to do with the individuals, this tweet gave me some inspiration:

Get them to identify if it is a minor mistake or something they have to work on. Watch a video on DrFrost Maths or the model answer for the older ones which we make ourselves. Then they need to practice the skills on DrFrost Maths as our scheme of work/courses are linked on it

— Mrs Hudson (@MrsHuds43995523) January 8, 2023

We have included Mathswatch clip numbers on pupils' printouts from the QLA spreadsheet but it's always been self-directed. It's felt like a tick-box exercise, and it hasn't done much to improve the learner, their responsibility, or them as a mathematician. I'm tempted to record some example-problem pairs for key topics and share these with pupils, or provide backward-faded worked examples with further problems to be completed independently.
If I record videos I can post these on Google Classroom and use a computer room, whereas the backward-faded activities can be used in the classroom. I also have a couple of days that need cover setting coming up, and these two could be completed with cover teachers.

Pick 4 or 5 questions where the majority made silly mistakes. Go through them and then do shadow questions. They then compare the marks to see how many extra they would have got. It's superficial but it boosts their confidence for how they are going to move forward..

— Laura Jacobs (@Miss_L_Jacobs) January 9, 2023

I think I can set the videos/BFM tasks where pupils have made daft errors or have taken a wrong turn somewhere, and set the problem (in the example-problem pairs) as the shadow question. Or maybe I can write the problem part and they'll complete the shadow questions at a later date. This should allow me to discern performance from learning and they can re-do them in conditions akin to an exam hall for 20 minutes or so.

I have a couple of weeks until we can share the results with the pupils, and I'll formulate a plan between now and then. The next blog is likely to be the one which outlines my plans.

Take Responsibility

In a previous blog post, I wrote about three key learning points. In this blog, we'll look at the third of those...

Key learning point 3: Don't leave revision to pupils, and plan in activities to revisit key information.

I've worked in schools in challenging circumstances in Inner City Leeds for 15 years, and I love it. I love the relationships, I love the challenge and I love teaching. I am, however, a realist, and I wouldn't expect many of my pupils to be able to direct their own ongoing revision so that they were improving. They could definitely revisit ideas, but they'll go for the ones that make them feel good about themselves, or they'll go for the ones that everyone found hard, and this approach to learning and revision isn't one that will maximise the impact.

I'd be willing to bet that less than 10% of pupils I've taught over the last 15 years have had an area set aside for keeping their school work organised, never mind planning out their 'ongoing revision and study'.

With that in mind, I space out their learning for them and provided opportunities for retrieval so that ideas stick and learning occurs. Rome wasn't built in a day, and in a similar way, learning happens over time rather than in time. This means repeated exposure to ideas that pupils have succeeded with is important, so that learning occurs. So important that, following an assessment, we can't just expect pupils to be self-directed to revisit the things that they don't understand and we need to recognise that these areas of need should be revisited regularly.

We should take responsibility and present them with spaced repetition opportunities to improve the likelihood that learning DOES take place following the identification of this idea as an area of need from the assessment and following their first re-exposure in lessons.

To help with this, I use this spreadsheet. Adding topics into the 'Completed Learning' column will map the ideas forward in time by a day, a week, a month and three months (ish...) and provide a reminder to revisit these ideas with your classes.

In the next blog, I'll outline my plan for feeding back Year 10 mocks, taking into account others' responses to the original tweet.

Feedback in Moderation

In a prior blog, I wrote about three key learning points. In this blog, we'll focus on the second of those... 

Key learning point 2: Don't go through the whole paper. Focus on key questions.

This learning was in response to going through all of a paper, and whilst there's probably some merit to going through the whole thing I think you'll get more out of giving feedback in moderation.
Exercise is good for the body, until you push the body too far and cause injury (as I type this, I can feel my knees creaking), and the same can be said for feedback. Too much feedback can overwhelm our learners, but can also dilute the important messages that we're sending. We can be more impactful by focusing our feedback on the things that we need pupils to take away.

In response to key learning point 1, I stated that I find three areas of need for each pupil and try to maximise my gains by getting as much as possible out of each question I choose. In an ideal world, I'll be able to only revisit three questions, but it's more likely that we'll look at ten or so due to gaps in pupils' learning.

Only looking at three key skills would be great, but looking at ten or so questions rather than the 20 from the test still prevents pupils from becoming overwhelmed during our 'assessment feedback lesson', and we know that our feedback will garner more attention from pupils as we narrow our focus.

In the lesson, pupils will see the correct solution to the question from the assessment and be presented with a question with both a similar surface structure and a similar deep structure to complete, to develop near transfer. Follow-up questions could go on to alter either of these structures, but the likelihood is that we want pupils to develop confidence with these ideas without alteration as they've recently struggled with this idea in the assessment. We'll repeat this for the ideas that we're asking pupils to re-do.

They'll then work on three of these ideas identified from their assessment, independently, in order to give further attention to ideas that they've recently shown a lack of understanding over (in the 'test') and had success with (in our example-problem pairs).

This is how this is done:

I always mark tests and then enter the scores in a QLA spreadsheet. A template is here, and I recommend downloading it as .xlsx rather than using it within Google Sheets.

On the first tab, enter pupil names, and enter their scores. You can see the percentage score for the class across the bottom, and this is great for identifying needs. It has to be said that this data must be used in context, and specific issues should have been picked up during marking.

The second tab has a list of scores, and only scores, and for graded exams normally looks up grades and assigns these rather than having to type them individually.

The third tab is labelled 'Next Steps', and this requires further use of the first sheet. These are the needs identified for each pupil. I do this by highlighting cells, highlighting the question number at the top and then typing the question number in the 'NS' boxes at the end. This assigns individual questions for pupils to work on, and highlighting keeps track of the questions I need to go through in full as well as reminding me to write a new question in this third tab. Writing questions on this tab will mean that individualised questions are automatically assigned to pupils on their printouts when I go on to the fourth tab.

The fourth tab brings this all together. The mark for each question for each pupil is RAG'd when their surname is entered, and the identified questions for them to work on are on the same sheet, ready to be printed and given to them for completion independently of each other, to check that we've fed back has landed for each learner.

It's then incredibly important that pupils are given further retrieval opportunities, so they'll be written into my medium-term plans for starters/settlers/Do-Nows/homework as retrieval practice. They couldn't do it to begin with - revisiting the idea once in a feedback lesson when emotions are running high isn't going to solve the problem. This brings me back to Josh's tweet from the last instalment:

Yeah absolutely. I think when identifying the questions to go through we should ask ourselves ‘do they fundamentally not understand this? Or are they close to getting there?’

The latter are for review lessons, the former are for your medium term plans.

— Jshm (@jshmtn) January 8, 2023

The way that I've done this over the years has varied, but I've settled on this spreadsheet.
I write my medium-term plans in the 'Intended Learning' column and update this based on how well the lesson has gone.
In 'Completed Learning' I type a few words to describe the content covered. This is then mapped forward by one day, seven days, 31 days and 90 days.
This then forms my list of topics that need to be dropped in for retrieval opportunities. The dates don't always line up, so I keep track by shading 'covered' topics and adding them to the 'Completed Learning' column where there isn't a lesson in the event that I want it to come up in the rotation again.

Focus on Feedback, not on Performance

In the last blog, I wrote about three key learning points.

In this blog, we'll look at the first of these...

Key learning point 1: Try to give feedback without returning pupils' scores/grades/papers. This removes the emotional response to a score/grade, and maintains pupils' curiosity in the questions that the teacher has identified to go through.

When this was suggested to me, it sounded weird.
When I first tried it, it felt weird.
But I tried it and I've observed a trainee do the same. 

I'm sold. Pupils are more open to corrections, they're more curious about the answers, and they're more engaged in the feedback.

Logistically, this is how I've gone about feeding back.

1. Pupils complete a 'test', and I mark it before the next lesson. I've always valued a speedy turnaround, and like to plan my 'assessment lessons' so that I have time to mark and prepare an 'assessment feedback lesson' for the next lesson on the timetable.

2. I identify three areas of need for each pupil and set them follow up work on these questions. I try to make sure that each area of need catches as many pupils as I can, to minimise my work load and maximise the impact for the minimum effort, and also that the area of need isn't too far from their current level of understanding.
I do this by completing a QLA document (template here) and identifying the greatest areas of need by looking for the topics I expect 100% on, and seeing where gaps exist. I'll highlight the question in yellow, type the question number in at the end as their 'Next Step' and create similar questions in another sheet which are then sent to each pupils' individual printout. 

3. I write example-problem pairs for the areas of need. The example that I use is always the test question, as that develops motivation - pupils recognise it, and they want to know the answer. The problems have a similar surface structure and similar deep structure, as my aim is to develop near transfer. Additional problems can vary in terms of the surface structure or their deep structure, but my main aim is to develop near transfer with this idea for those that didn't get this right in the 'test'.

4. We run through the example-problem pairs as a class with whole-class response systems. Pupils answer questions on mini-whiteboards and hold them up on my say-so, or we use multiple-choice questions to draw out misconceptions. At this stage pupils don't know what they scored on each question, so engagement is maximised. Pupils are responding on mini-whiteboards or with their fingers, so participation is maximised.

5. The pupils complete independent work on their three areas of need on their individual printouts. This way, their independent work is focused on their areas of need, not on the simple stuff that others got wrong, or on the stuff they found way too hard.

6. It's important to keep this stuff 'live' in the classroom, with opportunities for retrieval prepared in future lessons. With this in mind, the topics are added to my medium term plans as settlers/starters/Do Nows/homeworks with retrieval in mind.

I've mentioned this in a previous blog, and it's definitely important - emotions run high in 'assessment feedback lessons'.
Either there's a feeling of contentment, of relief, after successes that leave the learner feeling relaxed and like they don't need the feedback because they've 'smashed it'. Not giving them their 'test' back avoids this lack of focus and maintains their motivation.
The other side of the coin is that the pupil has 'failed' the 'test' and is now questioning their self worth, and the point of working hard if they 'keep doing crap in tests'. Not giving them their 'test' back until later delays this emotional response, maintains motivation and increases participation in the example-problem pair part of the lesson.

Karen Hancock had this to say on the issue:

I rarely put marks on the students' work. I mark directly into a spreadsheet and then I'll either do the paper live for them to mark or we create video solutions and they watch those.
We usually have a shadow paper so that they can demonstrate they can do the questions now.

— Karen (@karenshancock) January 8, 2023

This strikes me as being similar to what I've done, in that there's no focus on performance, but supercharged. Completing a QLA is something I do anyway, so I think the only difference is a lack of writing on scripts. I would, however, be wary of marking live, as there can be so many slight differences that can score marks on a five-mark question (for example) that I'd feel as though I'm losing control of the lesson. The video solutions is something I could go with - my current thoughts are to share worked solutions (on something like Google Classroom), but recording me writing these and talking about my thought process would be useful to pupils, I expect.
Using a shadow paper is an excellent idea, too, and something we do, but I think that their use could be more impactful too. Maybe they don't need to complete the entire shadow paper, but I can pick and choose those questions based on pupil need.

Nicky Gale replied with this tweet:

I work in a sixth form college. We do a video solution for all the questions and a shadow paper. In the lesson, students watch videos and correct any they didn’t get full marks for, then try the similar questions. We then have an individual conversation with them and set targets.

— Nicky Gale (@nicnaks79) January 9, 2023

This sounds excellent, and where I'd like to go with Karen's suggestion, but I don't think I could do this for 30 pupils in a lesson. I'd love to handover responsibility to the pupils, to watch the videos, to correctly answer the questions, and then work on the similar questions, but I'm not sure that I'd get what I want out of some of my pupils. 
I feel like I need to direct this, and this is what Helen Scott had to say:

Pick 2-3 "should" have been able to model, DIRT questions after this. Ticks the policy box.
We all know the real learning comes from the retrieval and learning over time when they see the question again over starters and then in a quiz.

— Helen Scott (@HelenScott88) January 9, 2023

I feel as though 2-3 questions wouldn't cover everything from the paper in terms of pupil need, but I'm fully alongside the message of the tweet. I think choosing 2-3 per pupil, which might become 8-10 over the class is achievable and acceptable, with pupils working on the shadow questions for those 2-3 questions in terms of the 'feedback cycle' expected within schools, with (as Helen said) the real learning coming over time as pupils are re-exposed to the idea (using questions with a similar structure in the short term, and altering the surface or deep structure as we go).

In terms of how we go about this, Josh tweeted:

Yeah absolutely. I think when identifying the questions to go through we should ask ourselves ‘do they fundamentally not understand this? Or are they close to getting there?’

The latter are for review lessons, the former are for your medium term plans.

— Jshm (@jshmtn) January 8, 2023

This seems like an important point to end the blog on. Just because a pupil has got a question wrong doesn't mean that they don't understand the idea. On top of this, just because a pupil got a question correct doesn't mean they do understand the idea. Sometimes a pupil guesses, sometimes they fumble through their working, taking leaps and getting to the right answer despite not understanding the journey, and sometimes pupils struggle to apply their understanding in a high-pressure situation. 

Be wary of assessment data.

Assessment Feedback Lessons: A Post-mortem

I once read or heard, that assessment regularly comes across as a post-mortem, identifying issues long after they became issues. What we really should be doing, though, is using assessment as a wellness check, an MOT, to identify issues before they become issues. Rather than looking back on successes or failures, we should be using assessment to shape future successes.

I think it's always useful when thinking about making changes to first consider what we're aiming to move away from. Some things might be worth saving, whereas others can almost certainly get in the bin.
If you're reading this, you might be looking to move away from a 'traditional assessment feedback lesson', and you might find that this follows a pattern similar to:

0. A class has sat a 'test' and the teacher has marked it between lessons.
1. The teacher gives back the test papers and scores to pupils.
2. The teacher goes through the answers to the test while pupils annotate the paper with correct answers.
3. The teacher suggests that pupils use this later in the year as revision.

Here are a few reflections on these lessons:

I feel as though step 1 seems like the most sensible thing to do following an assessment. It feels natural. Pupils sat the assessment, so we should let them know how they did. Allow them to find out by looking at their papers, and re-focus their attention before we move on to addressing identified issues.

From my experience, I've found that handing out papers in that way results in one of two feelings:
Pupils are happy with their score/grade, or pupils are disappointed with their score/grade. I feel as though any middle ground is minimal.

Suppose that you're happy with your score - you'll want to tell everyone, you'll brag about it, and you'll want to know where you sit in terms of rankings within the class. You're probably feeling like you'll be towards the top, so you're looking at the scores/grades of the perceived 'clever' kids in the class and comparing yourself against these, hoping that you're the one who's on top.

If you're unhappy with your score, the disappointment is likely to cause you to switch off, and you're likely to want to know how everyone else did. There's a desire to see if you're an anomaly, or that this was a 'hard test', and that everyone did poorly.

In both cases, the emotional response is huge and leaves pupils in the wrong frame of mind for growth. In the case of the happy pupil, as soon as you start to go through the paper they're wondering 'Why am I doing this? I answered these questions well!' and the unhappy pupil is thinking 'What's the point?! This always happens!'.

Key learning point 1: Try to give feedback without returning pupils' scores/grades/papers. This removes the emotional response to a score/grade and maintains pupils' curiosity in the questions that the teacher has identified to go through.

Step 2 seems as reasonable as Step 1. Pupils didn't have the correct answers, so we should tell them what they were. We've all deemed this 'test' to be important, so we're hoping that giving them the right answers will trigger something, and they'll remember next time.
Pupils are taking a different coloured pen and writing the correct answers on their scripts, but what is this actually achieving?
Copying down requires little cognitive activity, and Willingham suggests that 'memory is the residue of thought'. What other activity is lacking in active thought as much as copying down?

Suppose that the test was out of 80, and the scores range from 30/80 to 57/80. That's 27 marks that the lowest attainer didn't achieve, that the highest attainer did, and while you go through those 27 marks, the highest attainer is giving minimal attention to the lesson. The teacher is going through the questions one by one, focusing their efforts on questions that some pupils got wrong, but the ones who didn't get them wrong know that they didn't get them wrong. The highest attainer didn't make these mistakes, so their attention is elsewhere.
We then get to question 8 - the first question that the highest attainer didn't get right - so they need to give attention to their mistakes and to the correct method, but because the first 7 questions didn't need their focus, they're not in the frame of mind to give attention to their mistake and learn from it. They're still grinning from ear to ear as they're top of the class.
Now scale this across the class, and you've got pupils across the room giving minimal attention to the answers that the teacher is sharing as they don't need them, and being unable to give attention when needed.

Key learning point 2: Don't go through the whole paper. Focus on key questions to maintain pace and attention.

In Step 3 we might see the teacher hand out pupils' folders and put their assessments away for safe-keeping, or they might ask the pupils to put them in their bags to take away and store with their school work at home for revision purposes.
In my experience, the test put away in the folder never comes back out, and pupils don't have a filing system for their school work at home, other than the bin. The test is almost never revisited, despite the best of intentions. The thing is though, without spacing out revisiting the corrections we just made we're unlikely to learn from these mistakes, rendering the whole activity a little bit pointless.

Key learning point 3: Don't leave revision to pupils, and plan activities for pupils to revisit key information within your medium-term plans.

In the next instalments, I'll look at ways that we can amend the 'traditional assessment feedback lesson' based on the three key learning points here, as well as a few other ideas from replies to the original tweet I put out.

Worked Examples

Michael Pershan's book 'Teaching Math With Examples' was one of many books I'd purchased and not got around to reading. My better half hates me for it, but at least I'm not buying golf clubs any more! A long car journey to Legoland gave me an opportunity in the summer, but my 4 year old had other plans. One chapter on, and put on hold for a few months.
Since then she's started swimming lessons and I've managed to read a bit while she swims, and whilst watching a film on Christmas Day I managed to get through the rest!

I found it to be thought-provoking and enjoyable. Michael's writing style is accessible, even to someone who finds it difficult to pick a book up and stick with it, and ultimately, I've been convinced to bring worked examples into my lessons as part of my repertoire.
I think that pupils need a broad and balanced diet in their education, and if it would be appropriate for me to introduce an idea with a worked example, rather than through the standard method of me telling them stuff or an inquiry approach, then great!

My main take away from the book is that pupils won't learn unless they're thinking. This is a common theme through CPD I've taken in lately and arcs back to Willingham's "Memory is the residue of thought" quote.
For me, it means that automaticity needs to be broken to encourage thought, taking pupils out of autopilot and their normal routine by doing something different, or asking a different question where it might not be expected, and making changes to how ideas are shared is a simple way in which to do this. 

I'm thinking mostly about using them to introduce an idea - during the early acquisition phase. Maybe to introduce a new formula, so pupils see a formula and its use simultaneously, or to introduce a simple procedure so that I don't oversimplify things in my own explanations and pupils engage with, and think about, this new idea fully.
Having introduced a formula through worked examples, problem solving tasks can then build upon the new knowledge. This way pupils have had the opportunity to learn something new in a different way to how we'll discuss problem solving - rather than me always verbally telling them something, then them working on it, and repeat.
But what about multiple methods to do the same thing? Well, we can present these as worked examples side-by-side, referred to as 'case comparisons'. This will give pupils the opportunity to idea what's the same and what's different between the methods to develop a deeper understanding. 

An interesting piece in the book was about attributing an example to a person - fictitious or an actual person in the room - and how this can discourage pupils from using this method ("This is what Molly does, not me..."), and so I'm likely to not use names with worked examples, but to present them as either correct or incorrect. Method 1 and method 2 would work just as well as 'Dave's method' and 'Mel's method'. 

A different option I'm exploring is to use a worked example to begin problem solving, in what we call 'Red Zone conditions' - independently of others, and the hardest thing they'll do that lesson. Self-explanations will be key here, to give pupils a real opportunity to engage with the problems deeply and to develop deeper understanding. In the early stages, that's likely to require prompts to allow pupils to develop the behaviour of self explaining, which might be something like:

What was the first step?

Would it have been OK to write _____? Why/why not?

Why was _____ and _____combined?

I'm also looking at their use with incorrect worked examples to elicit understanding and reasoning. A huge part here is that they must be clearly labelled as incorrect, potentially with a giant red cross, so that pupils don't interpret them as a correct worked solution. Now, does this mean that when presenting a correct worked example, this should be labelled as so, maybe using a big green tick? 

Michael's book has also put me on the track of backwards faded examples, where an example is presented in full, with successive examples fading out the latter parts allowing pupils to build up the methods from the end backwards. This follows with the hierarchical nature of mathematics, with preceding steps being an extension of earlier developed ideas.

You can buy Michael's book from John Catt or from a more devious bookseller. 

I hope you enjoy it too. 

How on Earth do students learn?! Meaning making with manipulatives...

A quote from somewhere has been rattling around my head for a while. It gets rolled out every now and then by me when a colleague claims that they told their class something, that 'it was so basic' and that they 'have no idea how they haven't remembered it'.

"Students don't learn from what you say and do. They learn from their interpretation of what you say and do".

I've concluded from this that my job is to not only share the knowledge with students, but to then ascertain whether what I shared was understood in the way that I wanted it to be understood.

I've delivered, sat in and talked about lessons over the last 11 years whereby I and other staff have walked away from a lesson fully confident that they'd done a good job in sharing knowledge, where I and they have done no such thing.

I'm starting to understand why this occurs, and it all boils down to the Curse of Knowledge. An idea is shared by a person with a complex understanding of that idea and everything that connects it, but this complex web of ideas isn't shared. What is shared is the surface structure of the idea - but without the connecting ideas in place (the prerequisites), the idea cannot be understood, no matter how simple it may seem.

'Two negatives make a positive' makes sense to me. I am an expert at working with negative numbers. I've learnt the complex relationships between directed numbers and have developed a way to work more efficiently when subtracting a negative number, or multiplying/dividing using negative numbers. Unfortunately, Billy in Year 8 doesn't have the complex web of understanding that I hold, so when I tell him this, he learns that 'When there are two negatives, it's positive', so he applies it to -7 + -3, and writes down 10 as his answer.

Complete Maths has given me a banquet of food for thought this year and last - incredible CPD opportunities as well as an online platform that continues to go from strength to strength - and much of this is feeding the way that we shape our curriculum.

I am one half of the leadership team in our department and my role is the teaching and learning bit - the fun bit, the bit that's interesting and the bit that makes the biggest difference in the long term.
Our teaching has been very procedural for years (I've been at my current place of work for over 9 years, so I'm confident in saying this) and we need to shift to understanding and depth.

The biggest shift in my thinking has been the shift from 'Well, that task is pointless... It's nothing like what I'm asking them to do in the end...' to 'This task will make them think like this, which I need on the journey to make them think in a different way in the end...'.
This has largely come down to manipulatives.
I've never worked in a department where I've been given CPD on using manipulatives. With that in mind, for 10 years I've always seen them as a distraction, a behaviour management issue and an organisational issue in terms of minimising the disruption when organising them.
At the end of last year, I went on the look out for manipulatives around the department. We have LOADS of pairs of compasses for drywipe boards, but had no double sided counters. We have weights and weighing scales, but no geoboards. I did, however, find two almost complete boxes of Cuisenaire Rods, a whole lot of Numicon and lots of multilink cubes.

My job is to now order more manipulatives, add opportunities for their use to the SOL, direct staff as to when they can use them and how they can use them, and give CPD to our department so that they feel confident in using them and that their use will be worthwhile.

In the first eight weeks we've taught Place Value, Symmetry and Transformations and Averages. I've had some fantastic successes with the multilink cubes (to introduce the mean to students, especially giving meaning to those pesky 'Five numbers have a mean of 8...' type questions) and Dienes blocks (to compare decimals, hammering home what a 'tenth', 'hundredth' and 'thousandth' represents).

Onwards and upwards... Calculations, Angles and Sequences are up next!

How to teach (the 'disadvantaged'...)

I saw an article on The Times via Twitter the other day/week (I've lost track of time!) titled "Disadvantaged pupils fall behind despite funding". My initial response was 'You mean, there's a problem that can't be solved by just throwing money at it, and your response is that the funding is the issue?!'. My more thoughtful response was 'The issues that disadvantaged pupils suffer are not due to their schooling, but down to society. The (approximate) 14% of their time they spend in schools is not the deciding factor on their disadvantage and throwing money at that time in schools won't change that.'

I decided to blog about this due to the size of our 'disadvantaged' cohort, the discussions that I've been a part of around the 'disadvantaged' and my record with classes over the last 3 years, as well as a few conversations I've had throughout this year.



I work in a school where approximately 50% of our students are 'disadvantaged'. We're compared to schools whose 'disadvantaged' cohort isn't almost 500, but is 5 or 15, and we're expected to churn out the same results as them with a drastically different intake (but that's a different issue altogether, isn't it?!).
For what it's worth, our school results are approximately 50% 5 A*-C incl. English and Maths and whilst I'm aware that this isn't good enough, it's a bloody good effort given our circumstances.


In 2013-14 I taught our set 2 of 8, with 91.7% of the students in my class making 3 levels of progress. (45.8% 4LOP)
In 2014-15 I taught our set 5, with 80% of my students making 3LOP. (10% 4LOP)
In 2015-16 I taught our set 1, with 93.1% of my students making 3LOP. (65.5% 4LOP)

In 2015, "36.5% of pupils classified as disadvantaged received five good passes including English and maths, compared with 64% of all other pupils", so we're looking at a 27.5% gap between disadvantaged and non-disadvantaged students.

In 2013-14 I taught our set 2 of 8, with 100% of the 'disadvantaged' students in my class making 3 levels of progress. (80% 4LOP)
In 2014-15 I taught our set 5, with 80% of my 'disadvantaged' students making 3LOP. (20% 4LOP)
In 2015-16 I taught our set 1, with 87.5% of my 'disadvantaged' students making 3LOP. (50% 4LOP)


Whilst out on interview this year, I was told that the figures for the 'disadvantaged' students in my classes are excellent and challenge 'non-disadvantaged' figures in schools up and down the country. I was also asked 'What do you do for your disadvantaged students that makes a difference?'.

I couldn't say - not because these are my methods and secrets, but because I didn't know. I've thought long and hard. I still don't know. I teach them, I guess.

'What do you do for your disadvantaged students that makes a difference?'

It's tough to answer that when your 'disadvantaged' cohort for the school is 50% of your students, and not just 5 kids in a year group who you can identify what you do differently for them. I've sat through training on 'narrowing the gap', where the question is 'what can you do differently for your disadvantaged students?' and I've come to the conclusion that there are no definitive answers. It's a question that has been asked, multiple times, without giving any answers. I've not come across one person, training session, blog or book that can tell me (or anyone else in the same situation) how to narrow the gap when 50% of your cohort/class is 'disadvantaged'.

I came to the conclusion that the only option you have (with 'disadvantaged' and 'non-disadvantaged' students) is to give them everything you've got. Teach them like their lives (and futures) depend on it. If you're doing it for 'disadvantaged' Doris, why aren't you doing it for 'non-disadvantaged' Nicky?

With that in mind, here's what I do with/for my GCSE classes:

• Get them organised from day one. 'These are your exam dates, write them in your journal'. First mocks, second mocks, exams. 'Who needs a revision guide?' Schools can buy revision guides from CGP for about £3 a pop. Pass these savings on to your students - send a letter to parents offering them revision guides and collect the money before ordering. Have their revision night organised from day one. 'On Wednesdays, we have revision. Be there!'.
  
• Challenge them from day one. 'Here's your target: 20 A and A* grades. I don't care who, just make it happen!'. It turned out to be 18, but would've been 23 without an increase in the A/B boundary.
  
• Offer them help from day one. 'This is work. This is my job. If you need help, before, during or after school, come to my classroom. Struggling on an evening, weekend or holiday? Send me an e-mail. My job is to help you get the grade you want, so ask for help.'
  
• Have routines. No - not, Alan gives out the books and Betty gives out the textbooks. Have routines, which give children the opportunity to consolidate learning and maximise progress. I have work on the board at the beginning of EVERY lesson. I give them about 15 minutes of my 100-minute lesson to recap a few of the things we've done a few weeks ago - they did in lesson, they did it for homework and now they're doing it again.
  
• Fill in their gaps. It's tough when you have no data. You just start with the scheme of learning and hope it all goes well. But once you have data, use it. 'You did an assessment last Friday and I can see that as a class we can't do X, Y and Z. We're going off-menu and we're doing that again. I need you to be able to do that. We'll do it 5 times if we need to!'. There is no point trying to work out the surface area of a cone if your class is not comfortable calculating the area of a circle, or using pi.
  
• Help them to fill in their gaps. Use a QLA. I don't care if you don't like completing them, your students can get more from them that you know. After every assessment give them a printout of their scores pointing them to a video (Mathswatch, Hegartymaths, Corbettmaths) that they can watch with some work they can do. 'The things in red and yellow - these are the things you couldn't do. It might be an easy fix, it might take longer. This is yor revision list from now.' In 2013-14, a girl got a C in her November mock. Totally disheartened. Her printout showed her she lost 10 marks on solving equations, having missed out by 8 marks. Fixed that, carried on, and got an A.
  
• Point out their mistakes. Your students make too many of them. Even your best ones. They think 10-1 is 8 on their calculator paper. Highlight 'silly mistake marks' (marks they should definitely have scored) on their mocks, or have them do it themselves when you run through it. Add them all up and add it to their score. Compare it to the grade boundaries. 'This is the grade you would have - should have got - if you cared a little more, checked your work and didn't waste your time in your exam.' One student was 1 mark off an A* in their March mock, and scored 4/5 on an AQA best value question, working out the prices perfectly but writing the wrong bike as his conclusion for the cheapest - that's an A, not an A*.
  
• Point out their improvements. If, between mock 1 and mock 2 hardworking Helen or silly Sean improve by a grade, shout about it. Challenge them to do it again.
  
• Give them choices. I usually give them the option of doing one last mock at the beginning of May, in class, or to continue with normal lessons. They choose the last mock (this is how much they value the individual feedback and direction that completing the QLA offers them).
  
• Count down. Have a countdown to their GCSE exams. Number of days, number of school days, number of maths lessons. Show them that it's crunch time. Remind them that they need to be doing - now more than ever.

Why would you only do some of these things for some of your students?! To use a phrase I heard a few years ago, your work should be 'a relentless pursuit of excellence'. Not for some of your students, but for all of them - 'disadvantaged' or not.

How do you plan yours?

I'm writing this post in response to a conversation I had with a colleague on Thursday evening. It is advice aimed at them, as well as others who are at an early stage of their career, but I hope that others can take something from it too.

We were talking about staffroom politics and gossip and discussed something historical. The details aren't important, but the general topic of the conversation was...

I've been teaching for 8 years. In those 8 years, I've worked in challenging circumstances for 9 of them. I feel as though this is where I'm needed and where I want to be, to have an impact, to change outcomes for our less fortunate. In those 8 years, I've never had a results day where I was personally disappointed. Whether this is through indifference in my earlier teaching days, a lack of remembering those days, or that they haven't happened (as my recollections seem to be...). I've brought our departmental results up in each of those years, and I'm proud to say that.

In my 8 years of teaching, I've worked with some great guys, some wonderful women, some fantastic practitioners and some who were less so. I've worked with teachers who over time don't start a fire and always churn results out, and I've worked with those who, day-to-day, do all the right things and the results just don't happen. I think the latter is an issue in the schools in which I've worked and I think it all comes down to a lack of thought and planning, and that by changing the way you go about your lessons in the short and medium term can have a fantastic effect in the long term.

The advice I'd like to give my colleague, those at an early stage of their career, and others who might think that the results aren't coming despite their hard work is to consider the Ebbinghaus Forgetting Curve.

I'm likely to oversimplify this, as I'm not much of a researcher. I like to skim read and take my own conclusions from things. If I oversimplify this, and this hurts you in any way, please accept my most sincere apologies.

The Forgetting Curve says that the greater the number of times you repeat something, the more likely you are to recall it at a later date. That every time you revisit it, you forget it less. This has been a large part of my planning for a few years now, but not quite so prescriptive as I'm about to lay out.

I sat down over Christmas to plan my lessons until half term. I did a lot of jotting in my electronic planner (I use Microsoft Excel), simply noting a 'Settler' activity for each of my classes. This settler was chosen rather simply - I looked at what I'd taught them at the beginning of the year and assigned the activities in the same order. A week or so later, I added a note to set them a homework on that topic, as well as the topics they'd recently covered.

My classroom is not a place where I sing and I dance. Sometimes I sing, but there are seldom children present. It is a place where my knowledge is laid out and my students are expected to take this in. It is a place where I give students the opportunity to revisit things a number of times before I expect them to have understand.

To paraphrase my ramblings, my advice is: Think more about the diet your students are getting and how they probably need to try things a few times to taste it properly. Teach your students a topic, but make sure they're get a suitable amount of practice on it, and a few weeks later drop it in a homework, and a few weeks later drop it in a settler activity (or 'Do Now', or 'Bell Work', or 'Mr Motivator's Morning Maths Madness' or whatever it's called in your school) and give students 3, 4 or 5 opportunities to revisit a concept. In the long run, this will pay out much greater dividends than your card sort activity or your follow me cards that you spent an hour or two printing on coloured paper, laminating and cutting out.