Does any school subject divide public opinion as much as maths?
Earlier this year, prime minister Rishi Sunak reignited the debate on the purpose of maths when he said he wanted every student in England to study it until they were 18.
While some were delighted by the idea, others saw it as a waste of time, believing that the maths we learn in school, particularly at GCSE and beyond, has little bearing on most people’s day-to-day lives.
But that belief stems, I think, from a misunderstanding about what maths is, and what it is not – or, at least, what it shouldn’t be: a collection of facts and procedures. Presenting maths in this way is what leads to the belief that studying maths is ultimately a recall exercise, with pupils expected to memorise disparate facts and processes that have little real-world relevance.
The reality, though, is that these facts and processes arise from the concepts that underpin the subject. So, if we really want to engage children in maths and equip them with skills that last, conceptual maths is what we should focus on.
More teaching and learning:
What does this look like in practice?
Consider percentages: many pupils are successfully taught to calculate simple percentages of a given value. However, percentages are just one example of what is called a “multiplicative relationship”. Exactly the same relationship exists within (most) unit conversions, within pie charts, within speed calculations, right the way up to algebraic proportion relationships.
What pupils aren’t often taught is the deep multiplicative structure that ties all of these different “topics” together. One way to do this is using a consistent representation, such as a ratio table, another is dual number line.
The use of a consistent representation allows pupils to see how the same structure is being applied to all of these “different” questions. In this case, the existence and use of the functional multiplier (the value is always 0.4 times the percentage) or the scalar multiplier (the second row of the table is always one one-hundredth the size of the first row) are the crucial aspects of the multiplicative relationship we would want pupils to learn about, and they are clearly identifiable by pupils and teachers in both representations.
The idea is that if students are able to see how the facts and processes arise and function, they will be better able to assimilate new maths knowledge and link that knowledge to what they have previously learnt. You will know they are beginning to consistently recognise the structure of an underlying concept when they start to say things like “Oh, that’s just like when we did…” when you introduce them to a new procedure.
Being able to teach the underlying concepts of maths relies on teachers developing students’ knowledge in three ways.
The first is to make sure the teachers themselves have a secure understanding of how concepts develop and link together. They need to be able to make explicit, for example, the links between percentages and unit conversions, and appreciate how to represent concepts and make sense of them, such as through the ratio tables and dual number lines above.
They also need to change how they think about questioning; questions should be used to draw attention to and reinforce the concepts that underpin tasks.
For example, if we want pupils to see percentage as a proportional idea, we might devise questions like:
It’s also worth including questions that would be better solved using the functional multiplier between the percentage and the value, such as: “30 per cent of a quantity is 120, work out 73 per cent of the quantity”.
Last, teachers need to know how the procedures that we teach pupils to carry out arise from the concepts that they are associated with. In the case below, the standard procedure is multiplication by the equivalent decimal. However, these can be explained as scalar multipliers which turn 100 per cent into each of the other percentages, for example:
The idea here is to help pupils recognise that no matter what the value associated with 100 per cent, if we want to find 40 per cent, we will always multiply by 0.4; to find 44 per cent we will always multiply by 0.44 and so on.
Every concept in school-level maths has these links, representations and the like that can be explored with and taught to pupils so that their journey through school level maths is coherent and makes sense.
Of course, to take full advantage of this approach to maths teaching we would need a curriculum properly resourced and structured over a pupil’s entire time at school. However, schools and teachers can take steps on their own to ensure that they are teaching pupils to make sense of mathematics and mathematical ideas rather than just carry out calculations and follow processes.
If we do that, students will understand what it means to learn about mathematics rather than just do mathematics – and it’s this that will lead to more of them wanting to study the subject until the age of 18.
Peter Mattock is an assistant principal at Brockington College in Leicestershire and author of Conceptual Maths and Visible Maths
When it comes to measuring levels of understanding in the moment, multiple-choice or short-answer questions are popular solutions.
Both have their limitations: multiple-choice questions give a one-in-four chance to guess the correct answer, and, if short-answer questions are answered on mini whiteboards (as is often the case), it’s all too easy for students to glance at their neighbours’ boards if they become stuck. As teaching strategies, however, both are cost- and time-effective.
But which has the greater impact on student attainment? I decided to undertake some action research to find out.
Over two months, I compared the use of short-answer questions (SAQs), and the use of multiple-choice questions (MCQs) in two mixed-ability Year 7 maths classes.
After carrying out a literature review to ensure the interventions I carried out were grounded in good practice, I taught each class two topics: equations of lines and fractions.
For class A, I measured progress using MCQs for fractions and SAQs for equations of lines. For class B, I used SAQs for fractions and MCQs for equations of lines. Both strategies were used within each lesson as a learning check before independent practice.
MCQs were delivered via Google Forms in each class’s Google Classroom, which pupils accessed through our class set of iPads. The Google Form entailed five questions, each with four possible answers. Each incorrect answer was based on a potential misconception.
For SAQs, I used the whiteboard feature on the online mathematical website DrFrostMaths. This is software that transforms individual hand-held devices, such as iPads, into whiteboards. The students write their answers on their digital whiteboard, and these answers are all sent to the teacher’s device. The teacher can write and model answers live on their digital whiteboard and it will be replicated on all students’ whiteboards.
Both classes completed a pre-topic assessment for each topic, but no feedback was given. At the end of each topic, students repeated the assessment. This allowed me to compare the best strategy for each class, but also the best strategy for each topic.
Students who completed both the pre-topic assessment and the post-topic assessment also completed a questionnaire, with a range of open and closed questions, asking them about their experiences of using both approaches.
So what did I find? Well, across both classes and topics, there was a larger improvement in assessment scores when using SAQs compared to MCQs.
For equations of lines, Class A improved 20 per cent more than Class B, whereas for fractions, Class B improved 22.8 per cent more than Class A. This suggests that using SAQs can improve progress by an extra 20 per cent than using multiple choice questions.
Results from the questionnaire also demonstrated that students preferred SAQs; this approach scored higher than MCQs in both an enjoyment rating and an effectiveness of learning rating. It’s also the strategy that more students said they would like to see used in future lessons.
Overall, my results showed SAQs to be the more effective learning check. However, this was only a small-scale piece of action research, and I can’t say whether the results would be the same in another context – when working with a different age group, in a different subject or in a different type of school.
It’s also worth noting that the use of iPads may also have improved the effectiveness of both methods, giving independent routines for the students, while providing teachers with feedback that could be used to guide future lessons.
What, then, will I take away from this project?
I have now tailored my approach in almost all lessons to include some style of SAQs as a learning check, which has been made considerably easier through the use of hand-held devices within the classroom. It is, however, important to use this alongside other methods, such as using MCQs or Think Pair Share, to keep learners engaged.
Matthew Jones is a maths teacher at Windsor High School and Sixth Form in Halesowen, which is part of the Windsor Academy Trust
These days, exit tickets are a fairly common feedback tool.
If you’re unsure as to how they work, at the end of each lesson, teachers ask the pupils a question or two that will demonstrate understanding, the pupils will write down their answers on a piece of paper and then hand them to the teacher on their way out. You can then clearly see who has understood the concept you’ve been teaching, and who hasn’t.
Personally, I’m not a fan. I don’t think exit tickets should be part of your classroom routine and I think there are much better alternatives out there.
Why don’t I like them? There are three reasons.
The first – and main – reason is the workload it takes to create, administer and evaluate them. They can be thrown together quite quickly, but for any meaningful insight, questions need to be very carefully crafted. Producing these exit tickets for each lesson you teach in a week, as well as taking the time to review student answers, really adds up.
I’d also argue that they can quickly become redundant, especially when pre-prepared. If students make quicker progress in a lesson than anticipated, or, conversely, less progress than anticipated, the questions included can be out of kilter with what you actually want to know.
And finally, I simply don’t think exit tickets are the most effective teaching and learning strategy. In any lesson, questioning has a dual aim: for the teacher to know what students have understood and for students to know if they understand the newly taught content.
An exit ticket provides the former, but knowing this when students are leaving the lesson is too late. There needs to be time for re-teaching, alternative modelling, additional questioning and student feedback within the lesson itself.
This approach also doesn’t provide the students with any insight into their own understanding. Sometimes, students will self- or peer-mark their exit ticket questions, but often there isn’t time for teacher feedback. Therefore, if a student leaves a lesson with a low score, they’ll leave knowing they haven’t mastered the content, but without knowing why.
So, what are the alternatives?
Mini whiteboards
Mini whiteboards provide live feedback to teachers about student understanding; and to students about their own understanding. A teacher can instantly respond to misconceptions and mistakes, giving students the feedback they need to know on why they’ve gone wrong and what they need to do to improve. Follow-up questions can easily be added, depending on what the answers to the first questions were.
Mini whiteboards can also be used at any point in the lesson and there’s plenty of flexibility to them. Teachers can provide written or verbal questions, which either require short answers written down, or multi-choice options where students note down the correct option. Using mini whiteboards also ensures 100 per cent class participation, rather than the 20 per cent or so that cold calling or hands-up questions allow.
Hinge questions
Much like the exit ticket allows you to evaluate student knowledge of content taught in a lesson, a hinge question (or questions) must be answered correctly before students can move on to the next section of learning.
For example, if students are learning how to solve linear equations, they may have to complete hinge questions on solving one-step equations (such as 4x=12), before moving on to two-step equations (such as 4x-2=10).
If, for example, 90 per cent of students get the question correct, then the class can move on. If not, then re-teaching is needed.
Rather than waiting until the end of the lesson, hinge questions can be used wherever you are about to take a step up in learning, and so never become redundant bits of planning.
Live marking
If we consider the information that exit tickets provide us with – an overview of student understanding of just taught content – there is a very easy way to assess this early in the lesson, through live marking.
Live marking involves circulating the class and marking work as you go. This allows you to provide reactive feedback to students and ensures that the students know they are on the right track. It also allows you to quickly identify common mistakes being made and address them, potentially through a whole class re-model, very quickly. There’s no need to wait until the next lesson (which could be a week away) as you might have to with exit tickets.
These are just three alternatives; there are bound to be many more. They all require minimal workload, are highly adaptive, and support students to understand their own learning, and therefore are much more effective than the exit ticket. Yes, in my opinion, it’s definitely time to show exit tickets the door.
Nathan Burns is the head of maths at a school in Derbyshire
In early February, Ofsted published an extensive review of science education in the UK, highlighting effective teaching and learning practices observed by inspectors in both primary and secondary schools, as well as gaps in provision.
However, according to Haira Gandolfi, a lecturer in education at the University of Cambridge, something is missing: the need to diversify and decolonise the secondary curriculum.
Conversations around decolonising the curriculum have become increasingly common in staffrooms across the UK. When those conversations take place, though, the focus is likely on subjects like English, history and the arts.
That needs to change, stresses Gandolfi, who specialises in decoloniality, curriculum and pedagogy in science education. She believes that science, too, needs to be put under the microscope.
Whether science teachers agree with that or not is another matter. But Gandolfi says there is a legacy of issues related to colonisation, racism and a lack of diversity in all three of the science subjects.
In biology, she highlights the history of eugenics research.
“Several intelligence tests, such as the IQ test, were developed based on ideas from scientists who had an underlying hypothesis that there was a distribution of intelligence levels across different races, ethnic groups and socioeconomic backgrounds,” she explains. “Later research tells us this is not true, but that assumption is still present in society.”
In chemistry, there is a long-standing connection between mineral extraction and metallurgy with the exploitation of natural resources in indigenous lands, she continues. Peru, Bolivia and Brazil, for example, were colonised with the intent of getting access to resources like silver, gold and iron.
“We can still see the legacies of these colonial histories in several of these countries; the Democratic Republic of Congo, for example, is one of the most important sources of tin, tantalum, tungsten and gold, which end up in electronic devices, like our mobile phones,” Gandolfi explains.
Similar links can be made in physics, especially around energy generation and consumption.
“Many global environmental issues we face nowadays, including our overreliance on fossil fuels, can be traced back to the history of thermodynamics and the industrial revolution. The use of coal across the world was heavily expanded by the British Empire, for instance,” she says.
It’s important that young people are aware of these connections, she continues – it’s part of what helps to debunk myths brought about by “bad” science – and school may be the only opportunity many get to explore this.
“Are we using school science as an avenue to bring those conversations and challenge some of those misconceptions that were created by racist perspectives within science? I’m not convinced,” Gandolfi says.
But what do science teachers think? George Duoblys is a school improvement lead for science at Greenshaw Learning Trust, and he agrees with a “good deal” of what Gandolfi is advocating for.
“Too often, science teaching ignores the means by which scientific knowledge was produced, leaving students with a bewildering array of seemingly disconnected information,” he says.
“Whatever one’s position on wider debates around decolonising the curriculum, it is surely a good thing to teach students more about the sociohistorical trajectories of science, so that they may develop a more meaningful relationship to the knowledge the scientific disciplines have produced.”
However, he is cautious about a few things: he stresses that the science curriculum should not be replaced with a sociology of science curriculum, and says that schools need to be clear about the distinction between scientific knowledge and the scientists who generated it.
“The scientists themselves are a different matter, but we should not ignore the truths they handed down to us,” he says. “Sir Isaac Newton, for example, apparently had links to the slave trade. However reprehensible you think this is, it would be a grave mistake if it became the basis on which we downgraded his insights into the forces on moving bodies.”
Gandolfi agrees that there are barriers to this work – some of which have been put there by the national curriculum.
“The way science is framed in England’s curriculum, the teaching specifications, the assessments and the questions asked of students, all pushes for a drier perspective of what science really is, and a perception of science that is devoid of context and nuance,” she says.
“Decolonising science is about understanding this more nuanced science in relation to the rest of society, making that history, and current examples, visible. It’s not necessarily about changing the science curriculum itself, but how we talk about science in a lesson.”
She’s not looking to pile more work onto teachers’ plates, but hopes to see a change in the distribution of time spent on different areas – with traditional content knowledge and practicals being mixed with nuanced conversations about the links between science and society.
Embedding those changes needs to happen at a national level, over time, she suggests – but there are things that science departments can do now if they are interested in beginning this work sooner.
It all starts, she says, with teachers developing a broader awareness of their subjects (with a particular focus on the sociohistorical trajectories of science, and how this relates to other subjects, like history, politics and economics) through engaging with wider reading, documentaries and podcasts. Forming partnerships with colleagues in other departments can also help here, she adds.
Once staff feel confident in their extended awareness, Gandolfi recommends that subject teams work together to conduct a curriculum audit. This is about identifying opportunities to incorporate conversations about cultural and historical context into the existing schemes of work.
For example, she encourages teachers to think about positive contributions from people from diverse backgrounds to illuminate key concepts – both historical and contemporary. She also suggests exploring power imbalances and ethical complexities behind the links between science, development and society, as in the examples discussed earlier in this article.
It’s best to start small, she recommends: choose a topic or area you feel more comfortable with and think about how you would go about decolonising it.
“The best way to do this is through collaboration,” Gandolfi says. “We know from years of research on school-based curricular innovations that they have better results (and are more sustainable) when done by a group of teachers and not in isolation.”
Only once all this groundwork has been laid should teachers start to bring these ideas into their classroom practice, she adds. This should be done in a measured way.
“Be pragmatic: you don’t have to do that in every single lesson, in the same way we don’t do experiments in every science lesson,” Gandolfi says.
“In addition, consider including students’ voices as part of this, making use of dialogic teaching to create a safe space for students to contribute ideas, or their own experiences and conceptions about some of the complex ideas involved in exploring issues of oppression, race and so on, within lessons.”
It’s a lot of work for science teachers, and some may argue that they simply don’t have the time within the existing demands of the curriculum.
However, Duoblys says he does believe there is room for this work, if “careful thought” goes into how it’s related to more traditional content.
In his view, time isn’t the issue: expertise is.
“Where English and history teachers, say, have tended to do this very well, science teachers often have very little knowledge of the history and philosophy of science. I think this is a big problem, not least in debates around race and ethnicity,” he says.
“The worst thing we could do as a profession would be to wade clumsily into complex debates, making sweeping, unsubstantiated statements that trivialise the work carried out by those who have devoted their lives to generating knowledge.
“If any of us are serious about introducing social and historical aspects of science into the curriculum on a large scale, then we have to look at the training required to become a science teacher and what options we can offer to those already in the profession.”
Gandolfi appreciates that all of this might not be an easy shift for science teachers – but points out that they will soon have more support, as groups such as the Institute for Physics and the Royal Society of Chemistry are stepping into the conversation about decolonisation, along with some exam boards.
“There are people at particular exam boards who are listening and starting to engage with decolonisation and diversity in science. They are thinking about what that means for assessment, and the textbooks and resources they produce,” she says.
Going forward, then, it looks as though conversations around decolonisation won’t be restricted to the humanities – and Gandolfi is hoping her advice might help science teachers to get ahead of the curve.
Knowledge organisers divide opinion: they take time to produce and critics argue that they lead to “inflexible knowledge”.
This is where students can only recognise the knowledge they need to use when they are questioned on it in one specific way. While Daniel Willingham argues that this type of knowledge provides an “essential foundation for expertise”, others say that, in isolation, it can lead to shallow learning and simplistic mental models.
However, when used effectively, knowledge organisers are invaluable.
We began to introduce knowledge organisers at my school three years ago, as part of a radical curriculum overhaul. We wanted students to have a clear view of everything they needed to learn and a tool to help them to know more and remember more. We were also developing our approach to retrieval practice, so knowledge organisers were a logical choice for our curriculum development.
More teaching and learning:
The way we use knowledge organisers has evolved over time. After creating an evidence-informed template design, and training students to self-quiz in their own time using a very basic “look, cover, write, check” method, we realised that we were only scratching the surface. The approach wasn’t helping them to understand what it was they were now able to recall more fluently, and we began to see some of the signs of inflexible knowledge.
A lot of reading, researching and conversations with colleagues from other schools helped us to crystallise a strategy to mitigate those issues.
So, how do we use knowledge organisers today?
We call the strategy “Quiz it, link it, map it, shrink it” (QILIMISI). Students are given independent learning booklets (ILBs) each half-term: these are produced collaboratively, in school, and contain every knowledge organiser students need for that half-term.
We explicitly teach students how to complete the QILIMISI activities through our metacognition tutor programme, supported by explanations in the ILBs, and video walkthroughs, which can be accessed on our website.
We encourage students to independently do 20 minutes of QILIMISI a day, as part of our home learning expectation. Students have some discretion in choosing the topic and activity they want to work on, but because the options are finite, over a half-term there is a natural variation.
The pages are in a repeating pattern of activities as follows:
Quiz it: Students fill in pre-identified parts of their blank knowledge organisers, from memory, and use the completed version to check and correct. We use “look, cover, write, check” for rehearsal (if students are encountering the knowledge for the first time) or just “cover, write, check” for retrieval practice (to ensure students are definitely recalling from memory). This is an adaptation from our original self-quizzing approach, which did not sufficiently discriminate between rehearsal and retrieval.
Link it: Students choose two to six items from their knowledge organisers and write three sentences to show how they link together. This could be any combination of a compare/contrast statement, a cause/effect statement or a support/refute statement. Students are also encouraged to explain these statements using “because…”. This helps them to develop their understanding and make more sophisticated connections in their schema.
Map it: Students choose an appropriate way to represent the knowledge from a section or topic with a graphic organiser. They choose from an initial selection of four but can then diversify as they progress/become more skilled. Examples include a mind-map to categorise information or a fishbone diagram to show cause and effect.
Shrink it: Students are taught to summarise effectively as part of the work we do around the whole-school literacy strategy. They employ this technique to write a summary of the topic, illustrating their understanding.
We launched this approach in June last year and so far we have seen a real improvement in both the amount and the quality of students’ independent learning. Feedback tells us that knowledge organisers are highly valued by staff, students, and their families.
Of course, this strategy, in itself, does not entirely negate the problems of inflexible knowledge, but as part of a wider curriculum, which incorporates a broad range of different encounters with that knowledge, we’re getting closer.
As with any strategy, success comes down to how you adapt and refine it to suit your own context. But if you would like to do something like this in your own school, I’d recommend designing a knowledge organiser template and sticking to it to reduce cognitive load for students and staff. Before the roll-out, decide how you want students to use their knowledge organisers, and then teach this explicitly and repeatedly so it becomes routine.
You should also carefully consider how you will support students’ understanding, and plan a variety of other encounters with the knowledge that require students to think hard. And lastly, I’d urge you to make knowledge organisers high-profile, and regularly refer to them in lessons.
At the end of the day, there is no point having them unless they are an integral part of your curriculum.
Kelly Tatlock is an assistant headteacher, teaching and learning, in West Yorkshire
Marking has long been seen as the bane of teachers’ lives, involving hours spent reading through piles of books and composing individualised feedback for every child.
But according to data from Teacher Tapp, published in April 2022, marking is not as time-consuming as it used to be. The survey app found that, compared with 2020, almost twice as many teachers now spend less than an hour marking books each week.
This shift is largely down to the fact that many schools have caught on that there are more efficient feedback approaches than writing extensive comments in every book – and those schools are increasingly supporting staff to go their own way when it comes to marking.
Rachael Chong, a maths teacher at Greenford High School, in Middlesex, has done exactly this, developing her own feedback solution.
Seven years ago, after becoming increasingly fed up with how long her marking was taking, she turned to her brother, a computer programmer, for help. Together they developed Feed Forward, an online platform that provides automatic, personalised feedback, drawn from raw mark scores.
So, how exactly does it work?
The process starts with a specifically designed assessment, with questions that are linked to different topics: for example, the first question might be on calculating time, while the second is about probability scales.
After pupils complete the assessment, teachers record the marks for each question on a spreadsheet. The programme considers these marks, and then generates an individualised feedback sheet for each pupil.
There are two options for the format of this feedback: the simplified version (in which students receive comments about what went well, target areas for improvement and specific questions to review) or a more detailed version, which provides a complete overview of the assessment, filtering the questions into coloured categories (green, amber and red), based on how successfully the student answered them.
Teachers can choose which option is most appropriate, depending on students’ prior attainment and any additional needs. There is also an option for teachers to add a “hint” or link to a resource for each question, so that when students receive feedback, they are directed towards advice or materials that will help them to improve.
The teacher is still an important part of the process, says Chong.
“The reports give the students an understanding of what they need to work on going forward, but they are still very much reliant on the teachers giving in-depth feedback lessons as a whole class, and providing that expertise. It just replaces that written feedback step,” she explains.
More teaching and learning:
How much time does the programme really save, then? While there are other tools out there that promise to automate the entire marking process, Feed Forward still requires teachers to mark each paper and enter individual scores.
“The amount of time it takes depends on your focus. If you’re really on it, it could take a second per student to put it in, but it depends on who is inputting the data,” says Chong.
Although the reports are generated instantly, teachers generally spend around 40 minutes entering mark data into the spreadsheet, on top of marking the questions themselves, she adds.
With this in mind, Chong says it’s not something her department uses daily, or even weekly.
“We primarily use it for big assessments. Every half-term we will give each class across all the key stages a test to see how they are progressing, and use Feed Forward to offer them that personalised feedback,” she says.
There’s still a time commitment, then. But, after using Feed Forward with her department for the past seven years, Chong is positive about the impact it can have: the response from teachers has been really encouraging, she says, with colleagues acknowledging that the time spent inputting the marks is “a small amount of time to give up in comparison to how long it would have taken them to write assessment feedback similar to the quality produced by Feed Forward”.
And there’s an additional benefit: the reports help to plan future homework. Chong explains that the traffic light system or improvement section makes it clear which areas students need to work on, and they are expected to go away and evidence the steps they have taken towards this, as homework.
Before Feed Forward was introduced, some teachers weren’t providing any individualised written feedback at all, and instead using verbal whole-class feedback, says Chong.
Now, in maths, every child receives written feedback every half-term, and for students this has made a big difference.
“Students are really happy that as well as getting their paper back, they get told individually what they need to be working on going forward. Having it all printed out on a list that they can refer to really helps them to recognise their targets for improvement,” Chong says.
“The system really promotes and encourages independent learning, and the parents like to look at the reports, too.”
Although the programme is working well within her department, Chong has bigger plans for it. This year she was awarded funding by Shine, an education charity that encourages teachers to develop teaching and learning innovations.
Currently Feed Forward can only be used with the computer software at Greenford, but Chong is developing a website that will offer all schools access to the programme. She also plans to extend the advice that accompanies the reports students receive.
“I think the programme could identify three key topics that they could work on, and then provide a booklet of some hints and some key questions for them to practise,” she says. “I think that could be a really good way for students to move forward independently, and bridge that gap of understanding.”
And while Feed Forward is only used by the maths department for now, Chong sees the potential for it to be adapted to work in other subjects – although she admits this is currently a long way off.
“I know that maths is much more binary than other subjects, but I could really see it working in subjects like the humanities, too. It would just look a little different. It might be using a success criteria, instead of actual questions,” she says.
In the immediate future it will just be maths teachers, and students, who can benefit from Feed Forward. But, as artificial intelligence increasingly becomes part of the teaching and learning landscape, we’re bound to see more and more grassroots marking solutions, like this one, which can work for all subjects.
The premise of whole-class feedback is simple: read the students’ work, make a note of common misconceptions, and reteach the group based on these misconceptions.
Yet, as is so often the case in education, things that seem straightforward are often far more complex.
Over many years, I’ve tweaked and changed my approach to whole-class feedback, and, after several iterations, I finally have a model that I really believe in. Here’s how it works.
My strategy begins with a template. It’s divided into two areas: defining excellence and a list of possible next steps. Each student has a copy of this template in their books.
When I mark work, I set aside an hour to read through a class set, with a highlighter in hand.
Every time I read something I like, I highlight it.
I might make very light marginal annotations, but this stage is more about the highlighter than the pen. The main goal is to draw attention to the positives and indicate to students that their work is valued, while also correcting the odd spelling or grammar error.
At the same time, I am actively looking out for moments of excellence.
More teaching and learning:
I do this by choosing an area of focus – in English, this could be depth of analysis, precision and fluidity of embedded quotation, coherence of argument, use of context to illuminate, and so on. I then select two examples, taken from students’ work, of what excellence in that area looks like
I jot these examples down on my personal copy of the template, which I will later take into the whole-class feedback lesson. In students’ books, the excellence section stays blank for now.
The next steps list is a pre-filled list of skills, attributes or features that lead to success. What goes on to this list will vary from subject to subject, but the process of thinking about success in this way is hugely beneficial for teachers and students of all subjects.
Once I’ve finished marking an essay, I’ll highlight one or two relevant targets from the list for each student. I’ll also make a note, on my own template, of any recurring issues that will need to be addressed.
As this list is pre-filled, this creates very little additional workload.
After the initial marking process, it’s time for the feedback lesson. The first thing I do is hand back the books, and ask students to read their work, paying particular attention to the parts I have highlighted. This is a great way to show students that I’ve read and enjoyed their work, but it also scaffolds a metacognitive process of self-reflection.
Next, we move on to defining excellence. I begin by reiterating that there are certain things that some of us are doing really well already, but I want every single person in the room to aspire to do these things just as well.
After defining the first aspect of excellence, I then live model an example of what it looks like, usually taken from student work but anonymised. The template is left blank so that students can write along with me.
As I live model, I explain exactly what makes it excellent, disclosing the moves the student has taken to arrive here. There’s also a motivational boost for students to see their work being publicly, but anonymously, celebrated and commended.
As we read student work, we highlight one or two of the targets in the next steps list.
I then ask students to look at their specific targets. I usually try to select examples of excellence that help to address common next steps within the class, and so many of these personal targets have already been explained. However, I might also pick out a couple of other common ones, reteaching or offering further examples as appropriate.
For whatever time we have left in this lesson, students complete a task that will benefit everyone. The task can take many different forms, whether reapplying feedback from the lesson in another similar but different context or extending their thinking around the topic in some way. Ideally, it should be connected to the already outlined definitions of excellence or next steps, helping to bring together the different strands of the lesson.
Although this is the end of the lesson, the work done is simply a snapshot of a much longer journey and will feed into future cycles as we continue to monitor common misconceptions, looking to see whether students act on their next steps and seeking out other moments of excellence.
Andrew Atherton is an English teacher in Oxfordshire
When it comes to revision, we know that most students procrastinate. In fact, researchers estimated that, in academic settings in the US, over 70 per cent of students exhibited this behaviour.
Often, students procrastinate because they do not know how to revise or where to start with their revision. Sometimes, procrastination can even look like revision: rereading and highlighting notes, creating beautiful flashcards that never get used, as well as other activities that make students feel like they are revising even though nothing is being remembered. This is especially true for disadvantaged students who may be the first members of their families working towards attending university.
As teachers, we need to set the conditions for revision: we need to provide them with techniques that are proven to work and model how to use them. We know that if all staff consistently model one technique to support students with their revision it can have the biggest impact.
Below, we have listed six revision techniques that we believe are the most effective in the classroom. The central component is the effortful retrieval of knowledge from long-term memory.
Without this, students have not truly revised so much as revisited their knowledge, which will make it harder for them to use it when they really need it – in an exam.
The key benefit of the “look, cover, write, check” technique (LCWC) is that when our brains have to work hard to retrieve information, we remember it better in the long term, as well as provide a more accurate picture of what we know and what we need to revisit it.
How to teach LCWC
Students should read information, cover it up, attempt to write it from memory and then check they have written it correctly.
Teachers should model LCWC to students using a visualiser, narrating to them how to approach revision and explaining the purpose and technique of each step as they go. It’s important to explain to students that they should be chunking the information they revise and that this should become sequentially more challenging in terms of complexity and quantity.
Be sure to provide students with opportunities to practise in lessons, so you can monitor and support them where necessary to address any issues.
Where do teachers go wrong?
Teachers accept superficial performance of LCWC without checking that it is really having an impact on students’ recall of knowledge, or believe that if students are working in silence then they must be revising, when in reality, students are just copying their notes rather than covering the notes first.
Often, students struggle to structure notes in a way that will also make them useful revision tools. Cornell note-taking addresses this by giving students a simple but effective structure that helps to make their notes productive and valuable for later revision.
How to teach Cornell Notes
Cornell Notes use a three-part page setup: notes, questions or cues, and summary. The first time you use them with students, you should live model the technique, and take notes in response to the information you are going to teach them. Split your page into three, making a wide margin on the left of the page for questions and cues, and a two-inch section at the bottom for a summary, leaving the remaining space for the notes.
Set aside dedicated time in lessons for students to practise using Cornell Notes, paraphrasing what they heard or read into their own concise notes, using every other line so they can make changes if necessary.
Model using Cornell Notes as a revision tool by covering up the notes section and recalling the information based on the questions and cues, or use LCWC to revise the key points in the summary.
Where do teachers go wrong?
Teachers do not explicitly model or give time for supporting sections of Cornell Notes (questions, cues and summary), so they become another form of unstructured notes for students.
Mnemonics are sequences or lists of information that you want students to remember, using the first letters to create a memorable word or phrase.
How to teach mnemonics
First, think about the information you want students to learn and whether a mnemonic could help them: it could be a single word (such as BEEF to describe the steps of a basketball shot – balance, eyes, elbow, follow-through), or a sentence using each first letter (such as My Very Educated Mother Just Served Us Nachos for the planets of the solar system).
Introduce the mnemonic when teaching the topic for the first time, and remember that they are much more effective when they have stories and images attached to them. For example, Mrs Nerg for the seven life processes (movement, respiration, sensitivity, nutrition, excretion, reproduction and growth) is more effective if students can link this to a picture of an actual person called Mrs Nerg.
Mention the mnemonic every single time you come back to the information, and model the use of it for recall for students.
Where do teachers go wrong?
Mnemonics are introduced at the start of a topic but never returned to, so their memorable qualities are lost and they do not aid students’ recall.
We know that students learn more effectively when they test themselves because they have to think hard to recall the information from their memory.
How to teach self-quizzing
Whenever students receive or create revision materials, discuss and explicitly instruct them how they should use these to revise. Take the time to model the process of self-quizzing, and show students how you would create, revise for, and respond to a self-generated quiz on revision materials.
Provide students with the opportunity to practise self-quizzing within a lesson, and share excellent examples from students who have created quizzes that deliberately target gaps in their understanding. This should encourage students to create quizzes on topics they find difficult, rather than aiming for superficial success by focusing on topics they already know.
Once students are comfortable with self-quizzing, encourage them to practise interleaving topics so they mix recently taught material with things they previously learned.
Where do teachers go wrong?
Students do not include challenging questions, because they prefer to feel the success of answering questions they already know. This is not picked up on or challenged by teachers, meaning self-quizzing becomes less effective. To mitigate this, create a checklist of key knowledge with students that they can refer to.
This is where students simply write everything they remember about a topic, either as notes or a mind map. This allows students to move their current knowledge about a topic onto paper so that they can then begin to empirically visualise what they know and can remember about the topics they are studying and the links between different topics and concepts.
How to teach brain dump
Model the process to students, stressing that they should not be concerned about structure or connections at the first, but simply write down whatever comes into their memory. Next, encourage students to make connections between different chunks of knowledge and expand their notes using “how” and “why” questions.
Make sure they have time to check what they’ve written against another revision source, and tell them to add anything they’ve missed in green pen, emphasising that this is what they should focus on in revision.
Where do teachers go wrong?
Brain dump exacerbates rather than addresses gaps in learning because students do not know what they don’t know, and therefore, their original misconceptions and/or gaps in knowledge remain. It causes anxiety in students as a blank page can be intimidating. This can cause panic and a false belief that they do not know anything about the topic. This can then be reinforced because they cannot remember anything to write, creating a negative self-fulfilling prophecy.
This technique should therefore only be used once students are relatively secure in their knowledge.
Here, students begin with their core knowledge about a topic and then interrogate it with “how” and “why” questions to build upon it. This trains students to generate questions that lead to a deeper understanding of the topics they are revising and to connect knowledge from different parts of the curriculum.
How to teach elaborative interrogation
Model the process to students by generating a chunk of knowledge, for example: “People moved from the countryside to cities during the Industrial Revolution”. Then create questions to build on it. Students should use “how” questions like: “How did moving to cities change daily life for people?”, and “why” questions such as: “Why did people move from the countryside to cities?”.
Students could recall the answers to these questions, or use revision resources to find them. Make sure students know that this process can be continued almost indefinitely. For example, once you’ve established that people moved to cities to work in factories, you could ask: “Why were factories being built?” and once you know it was due to the development of mass-production technologies, you could ask: “How did this affect small producers?”.
Where do teachers go wrong?
Teachers do not establish at each stage that students have a solid foundation in the core knowledge they need, so their elaboration is taking place using incorrect and incomplete knowledge. Students could be trained to check this themselves using a checklist strategy.
Michael Feely is principal of Dixons City Academy in Bradford. Ben Karlin is associate dean at the Ambition Institute. This is an edited extract from their book, The Teaching and Learning Playbook, which is available at a 20 per cent discount with code TES (expires March 31 2023)
