Is ‘hard maths’ really putting girls off Physics?

WHS Physics Lesson

Physics teacher Helen Sinclair investigates the claim that ‘hard maths’ puts off girls from studying Physics, and finds that the truth is much more complex than this, and is not limited to gender. She explains how she makes lessons and clubs inclusive.

In April, the Government’s Social Mobility Advisor, Katherine Birbalsingh, told MPs that girls are less likely to choose Physics A-Level because it contains too much “hard maths”. She added, “Research generally, they say that’s just a natural thing… I mean I don’t know. I can’t say – I mean, I’m not an expert at that sort of thing. That’s what they say.”

This provoked unsurprising outrage from those who have spent their working lives trying to understand and solve this problem. Dame Athene Donald, Professor Emerita of Experimental Physics at the University of Cambridge, summed up some of the key points when she spoke to the same committee a few days later.

“[It] starts really young, the message society gives is that they (Physicists) are white males, and I think there is evidence to show that if you are black or if you are a woman, you don’t see yourself fitting in… The internal messages that girls may believe – if teachers aren’t actively trying to counter that, they may not realise that the girls are being driven by things that aren’t their natural choices.”

Whilst Ms Birbalsingh may have subsequently backtracked somewhat from her comments, the question still lingers – why is there such a gender gap in Physics?

A diversity gap

The problem of diversity in Physics is not new. The percentage of female A-Level Physics students has stubbornly remained around 20% for nearly 30 years. In 2011 the Institute of Physics reported that almost half of all mixed schools had no girls studying Physics A-Level and that girls were almost two and a half times more likely to study Physics if they came from a girls’ school rather than a co-ed school. Five years later, the picture had barely changed. Their detailed research over the last decade shows that the causes extend far beyond the Physics classroom: schools with low numbers of girls in Physics often showed gender imbalances in other subjects too, such as English. Furthermore, their research revealed that it wasn’t simply a problem of gender. All kinds of minorities are less likely to study Physics.

Girls often enter the Physics classroom with a narrower range of early, concrete preparations for Physics compared to boys, stemming from the very different toys and pursuits that they are still often exposed to in their early years. This can make it hard for them to easily identify links between core ideas studied in the classroom and their applications to their lives and career ambitions. Research shows that by exploring these applications within lessons, all students (and particularly girls) are better able to see the relevance of Physics as a subject.

Making Physics teaching more inclusive

Girls are also more likely to see value in subjects that link to social and human concerns. Because Physics tends to simplify situations in order to understand key principles, these links can often be lost, making concepts seem irrelevant to students’ lives. By making a conscious effort to link concepts to real-world problems and societal challenges, we can convey the subject’s importance more effectively to girls. For example, this year we have explored Energy Use and Climate Change with Year 9; the Chernobyl disaster, the USSR and the war in Ukraine with Year 10; and the how seatbelts are designed for men and Tonga’s damaged data cable with Year 11.

Research has shown that girls’ self-concept is lower than boys. They also are more interested in achieving mastery of a subject. This is particularly noticeable in our students, who often try to judge their success by comparing their achievements with others’, and who can look at anything other than perfection as a failure. This culture of perfection (which extends well beyond the Physics classroom) can make it harder for students initially to engage with more challenging problems. One of the key ways of supporting students through this is to create a more relaxed atmosphere, allowing them to discuss different approaches, and identify and learn from their mistakes. Embedded use of the Isaac Physics website in lessons has proved a powerful tool to help our students feel successful and identify areas for improvement quickly.

Wimbledon High School Physics

Our Physics lunch club was formed in partnership with some Year 10s who wanted to tackle challenging problems. At first it was run in an ordinary classroom, but it soon became clear that in this formal environment, students were on edge. The following week we relocated to the new private dining room on site. Students ate their lunch and chatted at the same time as completing questions. The informal atmosphere encouraged them to discuss problems, rather than try to solve them individually. It was fascinating to see how the setting and approach of the session had such a significant impact on students’ enjoyment and engagement.

Whilst there are many things an individual teacher can do, it is important to remember that the impacts of these interventions are likely to be limited. Above all, the research consistently shows that girls’ views on Physics are shaped by their interactions in wider society and the bias that is still pervasive there. Surely it is our responsibility as educators to openly address this, not just for the benefit of our students, but also for the benefit of our society.

Could digital learning be the key to a truly inclusive curriculum?

Mrs Rebecca Brown, GDST Maths Trust Consultant Teacher and Teacher of Maths at WHS, looks at how effective use of digital learning could have the potential to give all students personalised learning experiences.

The use of online video tutorials for learning, especially in Maths, can, if used carefully, provide an individualised learning experience where students study concepts at their own pace, allowing them to review, reflect, pause or accelerate. This in turn enables learners to learn in their own way, giving them more confidence to delve deeper into the subject, embed knowledge and solve problems. Suggestions like this evoke a range of strong emotions and opinions among teachers. Is digital learning the future of education? Or does it mean the de-skilling of teachers and students alike?

How do you learn something new?

If I asked you to learn how to make magic milk, how would you begin?  My own first step would be to Google it and watch a top-rated video. Then I would have a go myself. If a student can watch a carefully selected video at their own pace, pause, rewind, replay until they have good understanding of a concept, then surely this is potentially a beneficial personalised learning experience that can be inclusive of the needs of all learners. Moreover, it can help students to overcome anxieties they may face in the classroom.

Video tutorials also give the opportunity for recap, review and consolidation after a lesson or topic has been taught. During the pandemic we saw an increase in online learning and use of video tutorials that supported student and teacher absences and gaps in learning. Now back in the classroom, instead of reverting to what we have always done, what if we considered a different future? How can crisis turn into opportunity, as we use technology in different ways?

Why use digital learning?

Evidence shows that many digital learning resources can be used to develop students’ mathematical capabilities, especially when they are integrated into a rich teaching environment. In a nutshell, the students pre-learn the new content mostly independently, often as homework, and then most of the precious classroom time is spent practicing, asking questions and doing activities with the teacher there to support and guide them.

After watching appropriate, rigorous, considered tutorials, students can engage in richer in-class discussions that help them develop deeper conceptual understanding of Mathematics. This releases lesson time for social interaction, which Vygotsky’s theory of learning as a social process places so much emphasis on.It can also create more time for one-to-one support and direction from teachers. This is a good example of flipped learning, which can be a very powerful pedagogical process.

Fluency gives students the capability to be confident in their calculations and the cognitive capacity to focus on more complex, problem-solving aspects of the curriculum (Foster, 2019).

What could possibly go wrong?

This does all come with an important warning. We need to select the resources that we direct students to use very carefully. I am sure that you know the pitfalls of a YouTube search! This is where selecting and inserting videos into One Note lessons, Google Classroom, Firefly or using resources such as Ed Puzzle can be helpful. Ed Puzzle is an online video editor tool. Your students watch a video, selected by you, at their own pace. You hold every student accountable, observing who is watching and who answers the questions. They are not able to skip ahead or open other tabs. The process is simple – find a video, add questions, and assign it to your class. Watch as they progress, and hold them accountable on their learning journey.

Wimbledon High School Maths Lesson

Another drawback is relying solely on digital resources as a method of instruction for students to learn. While flipped learning does give you the opportunity to dive into applying the content rapidly, the teacher must assess learning quickly and be able to rectify misunderstandings. This method also centralises the role of homework. Students need recreation time for holistic development, so it could also become detrimental when only used outside of lessons, as the commitments of learners beyond the classroom could limit the time available, hindering progress. For it to work properly, parents also need to be fully informed and engaged to support this method.

To conclude

We want to empower our learners to become critical thinkers, curious problem solvers and resilient creatives. Perhaps a flipped learning approach, if rigorously thought out and planned, could help address anxieties, give more opportunities to accommodate different learning styles and needs, and give more time for complex, deeper thinking in the classroom. Developed in this way, it could become the future of a truly inclusive education.

You can learn more about Flipped Learning at the GDST EdTech25 event on 25th May – hosted by Trust Consultant Teachers Fiona Kempton and Rebecca Brown. Sign up here

Trouble with Maths? Maths Anxiety? or Dyscalculia?

Rebecca Brown, GDST Trust Consultant Teacher for Maths and WHS Maths teacher, reviews part of Steve Chinn’s paper on The Trouble with Maths – a practical guide to helping learners with numeracy difficulties.

Each learner needs to be understood as an individual and the teaching style and lessons adapted to suit each individual learner.

Is it Dyscalculia or Mathematical learning difficulties? However it may be described, challenges with Maths create anxiety amongst children and adults alike.

The 2017 National Numeracy booklet, ‘A New Approach to Making the UK Numerate’ stated that ‘Government statistics suggest that 49% of the working-age population of England have the numeracy level that we expect of primary school children’. This indicates that having a difficulty with maths should not automatically earn you the label ‘dyscalculic’. So what does it mean to be successful at Maths and why does it make so many people anxious?

Two key factors which aid learning are ability and attitude. Some learners just feel that they can’t do Maths. They feel helpless around Maths. Maths can create anxiety and anxiety does not facilitate learning. Ashcraft et al (1998) have shown that anxiety in Maths can impact on working memory and thus depress performance even more.

More recent research using brain scanning has found that regions in the brain associated with threat and pain are activated in some people on the anticipation of having to do mathematics.

The key question, when faced with a learner who is struggling with learning maths is, ‘Where do I begin? How far back in Maths do I go to start the intervention?’ This may be a difference between the dyscalculic and the dyslexic learner or any learner who is also bad at maths. It may be that the fundamental concepts such as place value were never truly understood, merely articulated.

None of the underlying contributing factors are truly independent. Anxiety, for example, is a consequence of many influences.

Chinn favours the definition of dyscalculia to be ‘a perseverant condition that affects the ability to acquire mathematical skills despite appropriate instruction.’

A learner’s difficulties with Maths may be exacerbated by anxiety, poor working memory, inability to use and understand symbols, and an inflexible learning style. Chinn suggests adjustments to lessons to assist difficulties in maths based on four principles:

  1. Empathetic classroom management
  2. Responsive flexibility
  3. Developmental methods
  4. Effective communication.

In short, the issue is that not every child or adulty who is failing in Mathematics is dyscalculic. Even for those who do gain this label, it does not predict an outcome or even the level of intervention but as Chinn suggests whatever teaching experiences this pupil has had, they may have not been appropriate.

What do German and Maths have in common?

Alice (Year 12) explores the similarities between languages (specifically German) and Maths. She explores its parity with grammar and syntax, as well the process of learning both subjects. 

Mathematics and language are not as different as we might imagine them to be. Even maths is its own peculiar language (or notation if you prefer) which includes symbols unique to mathematics, such as the ‘=’ or ‘+’ symbol. Galileo Galilei called maths “the language in which God has written the universe” implying that by learning this language, you are opening yourself up to the core mechanisms by which the cosmos operates. Much like travelling to a new land and picking up the native language so you may begin to learn from them and about their culture. 

Generally, there are multiple accepted definitions of ‘language’. A language may be a system of words or codes used within discipline or refer to a system of communication using symbols or sounds. Linguist Noam Chomsky defined language as a set of sentences constructed using a finite set of elements. Some linguists believe language should be able to represent events and abstract concepts. Whichever definition is used, a language contains the following components: 

  • A vocabulary of words or symbols and meaning attached to these. 
  • Grammar, or a set of rules that outline how vocabulary is used. 
  • Syntax, the organisation of these words or symbols into linear structures. 
  • And there must be (or have been) a group of people who use and or understand these words or symbols. 

Mathematics meets all of these requirements. The symbols, their meanings, syntax, and grammar are the same throughout the world and mathematicians, scientists, and other professions use maths to communicate concepts. 

So, by this definition, maths meets the definition of a language. And linguists who don’t consider maths a language, cite its use as a written rather than spoken form of communication. However, sign language would also be disqualified based on this criterion, and most linguists accept sign language as a true language. So, in essence, maths is a universal language. 

But the likening of Maths and German goes even further. More broadly, German is a logical and very mathematical language, the syntax is fairly rigid, and the sentences are consistently structured. Its logicality can clearly be seen through many aspects of the language, one example being compound nouns: joining a number of nouns together to create a new word. Some of my favourite shorter ones include: 

der Handschuh Hand + Schuh Hand + shoe Glove 
eine Glühbirne Glüh[en] + Birne Glow + pear Lightbulb 
ein Wolkenkratzer Wolke[n] + Kratzer Cloud + scratcher Skyscraper 
Die Schlagzeuge Schlag + Zeug[e] Hit + things Drums  
Der Staubsauger Staub + Sauger Dust + sucker Vacuum 
Die Nacktschnecke Nackt + Schnecke Naked + snail Slug 

Compound words are often made up of more than one noun and become excessively long. Mark Twain said in an essay ‘The Awful German Language’ (1880) from ‘A Tramp Abroad’, they are not words, but “alphabetic processions… marching majestically across the page”. They capture precise and complex meanings and are a cause of irritation for novices and an excitement for those who manage to master the language. At least for me, feelings of irritation were very much present whilst I was (attempting) to learn maths. 

German sentence structure is also very logical. There is a strict rule that the words must appear in the order of: Time, Manner, Place.  

To say, “we went to Germany with us last year” in German, it would be “Sie sind letztes Jahr mit uns nach Deutschland gefahren”, which would translate literally to “we went last year with each other to Germany”.  

Time: letztes Jahr – last year 

Manner: mit uns – with each other (with us)

Place: nach Deutschland – to Germany 

In a sentence with only one verb, the verb must be in the second position. So, when an extra phrase or word is added to the front of the sentence, the verb still has to go second. ‘Ich nehme den Bus‘ turns into ‘Meistens nehme ich den Bus‘ (respectively ‘I take the bus’ and ‘mostly I take the bus’) and if another verb is added, the second verb gets sent to the end : “Meistens mag ich den Bus nehmen.” (which means: mostly I like to take the bus) 

In this way, speaking German, and piecing together the sentences is like solving mini equations on the spot. It involves pattern recognition and an attention to detail that one would also find in mathematicians. 

Maths is precise, black and white, logical and direct. And Germans are almost stereotypically seen that way. In fact, one unit of the German A Level is called ‘Deutscher Fleiß’ (German diligence or hardwork). According to an exchange student working in Germany “Der Stereotyp lautet, dass Deutsche Arbeiter keine Freude an ihre Arbeit nehmen, anstatt erledigen sie ihre Aufgaben mit klinischer Effizienz. Der Befragter bestätigt, dass es an dieser Idee etwas Wahrheit gibt. Arbeiter haben klare Zielen und ein genauer Tagesplan und Struktur. Also gibt es die Möglichkeit, ihre Arbeit an Feiertagen hinter sich lassen zu können.” Meaning…  

“The stereotype is that German workers do not enjoy their work, and instead do their jobs with a clinical efficiency. This interviewee confirms that there is some truth to this idea. Workers have clear goals and a precise daily plan and structure. So, there is the possibility to leave your work behind on holidays.” And though these are not direct comparisons, these connotations of accuracy and precision are certainly significant. To further this, in English, when I talk to people, I often find myself using fillers such as: “I feel like… you know… if it’s not too much trouble… possibly… we could do that”. But whilst in there it makes me sound waffly and unsure of myself, in German it rapidly affects the sentence structure and means it is difficult to know where to put the verbs. So almost by force of circumstance, when I speak German, I am more accurate in my language, something that mathematicians must be, in order to obtain the correct answer. 

More generically speaking, Maths and German can be equally frustrating. In Mark Twain’s essay “die schreckliche Deutsche Sprache” (The Awful German Language), he recounts speaking to the keeper of Heidelberg Castle who comments on the “uniqueness” of his German tongue and is interested in adding it to his “museum”. To which Mark Twain responds, “If he had known what it had cost me to acquire my art, he would also have known that it would break any collector to buy it”, implying his language skill and proficiency had been accomplished under great difficulty and annoyance. His exasperation about learning the language is further evident where he proclaims, “a person who has not studied German can form no idea of what a perplexing language it is”. He maintains that there is no other language that is “so slipshod and systemless, and so slippery and elusive to the grasp”. In this way, maths can cause similar problems. Both subjects require you to apply prior knowledge and skills to situations you have not seen before in order to solve problems, and although these problems may be different in topic, the skills and situation are not dissimilar. And in learning either of these languages, you are indeed opening yourself up to new lands (both figuratively and literally), and thus to a universe of new knowledge. 

Do puzzles and games have a net positive impact on student learning?

Mr Patrick Vieira, Teacher of Maths at WHS, looks at how completing puzzles and games can impact student learning.

One day, while travelling to school as a 12-year-old, I saw somebody solving a Rubik’s cube. This person would scramble the cube and solve it very quickly. He would do this repeatedly, and maybe it was just in my head, but he seemed to get quicker with every solve. Seeing a demonstration of that kind was nothing short of captivating to me at the time. It stayed with me throughout the day and when I got home, I told my mother about it and asked her to buy one for me. Neither of us knew what it was called but we took the trip to Hamleys with the hope that they would know. We were in luck! My mother paid for the Original Rubik’s Cube and I took it home excited to begin trying to solve it.

As does everything after a while, excitement quickly faded. The puzzle was difficult and did not come with any instructions. I had managed to solve one face by what seemed like sheer luck (blue, my favourite colour), but when I tried solving another face, my hard work became undone. It was so frustrating that I left it on the mantelpiece where it collected dust for years. Reflecting now, that must be how some of my students feel now when they are given a problem that seems too hard to solve at first.

A Rubik’s Cube (Wikipedia)

Fast forward to 2019 when I first joined Wimbledon High School, where I had the opportunity to join the Rubik’s Cube club as a staff member. Of course, if I needed to help students solve the Rubik’s Cube, I needed to have a good understanding of it myself. This time, I was provided with a set of instructions and I got to work. Solve the white cross, then complete the white face. Finish off the second layer and then begin the top… I repeated the algorithms for each of these over and over again, and eventually I solved my first Rubik’s Cube.

But for me, that was not the part that excited me. As I repeated the moves for each step in isolation, I began to see why these algorithms worked. Every move had a purpose, setting the cube up so that on that final turn, everything comes together. It was as if I were almost tapping into The Matrix of the puzzle and I could feel my perception of 3D space improving with every turn. It was then that it hit me. This could be an amazing educational tool… but has it been researched?

Research related to the Rubik’s Cube is very limited but there are many pieces of anecdotal evidence to suggest that there are huge benefits to learning how to solve the cube. The two which stood out to me were grit and creativity.


Grit is one of the most mysterious personal traits discussed in education. It is widely regarded as the trait most indicative of whether someone will succeed at a task, no matter if it is in business, in the army, or in school.[1] However, it is difficult to nurture. When we complete a task which requires perseverance, the hormone dopamine gets released in our brain. This is the automatic response of the body which reinforces positive behaviours. The more tasks we complete using grit as our fuel, the more we are comfortable and happy being “grittier” – we create a habit of perseverance.[2]

Solving the Rubik’s cube is one way of helping us reinforce that positive trait of using grit. One Maths teacher writes in her blog that after giving her students an assignment to solve the Rubik’s Cube, they showed increased levels of grit.[3] However, just as Carol Dweck writes in her book Mindset: The New Psychology of Success, as educators, we need to still be encouraging our students to persevere and reward their effort rather than their achievement.[4] These will bring about the best results in development of grit.


“Creativity?!” I hear you wonder. “How can you be creative when all you are doing is repeating algorithms?”

I had an interesting experience as I was improving my knowledge on the Rubik’s Cube. After learning the algorithms for the beginner’s method of solving and was able to do it well, I turned to an intermediate stage called the ‘CFOP’ method. There were slightly more algorithms to memorise, but I found my creativity bloom in the process of learning them.

From a fully solved cube, I picked one algorithm and applied it to the cube. Of course, this would mess it up completely. However, just for the fun of it, I kept applying the same algorithm and eventually I got back to a fully solved cube. I wondered why and I tried to see if I could do the same with the other algorithms. It turns out that they do. It takes a different number of repetitions for each algorithm but eventually I end up at a fully solved cube. Just for the fun of it, I also tried to combine algorithms or even reverse them. These made me see different patterns and other ways of solving it. I wasn’t really doing much with the cube but still, I thought to myself, “this is pretty fun.”

Where next?

So pick up your cube. Don’t just leave it on the mantelpiece like I did for years. There is a great opportunity to be had whether you are a teacher or a student. Returning to my opening point, do puzzles really have a positive effect on learning? Nobody really knows yet. But if it helps you develop perseverance and foster your creativity, I think it’s worth a shot to find out for yourself.


[1] See Angela Duckworth – Grit: The Power of Passion and Perseverance

[2] See

[3] See

[4] See Dweck – Mindset: The New Psychology of Success


Why is it socially acceptable to say: “I’m bad at Maths”?

Alys Lloyd, a Maths Teacher at Wimbledon High School, looks at society’s attitude towards Maths, what makes a good mathematician, and how you can compare the retaining of mathematics knowledge to that of languages.

Teachers do have social lives, although to our students this might be a shocking idea. A teacher being spotted outside of school, in the supermarket for example, can send some students into a flat spin. So the idea of a teacher being at a party might be difficult to imagine, but I can assure you, it does happen!

At parties and in social situations with people who don’t know me, I have found that my job can, unfortunately, put a bit of dampener on things. A typical conversation opener is to ask what someone does for a living. The most common response to my saying that I’m a Maths teacher is “oh, wow” then something along the lines of “I was never any good at Maths in school.” Then the person I was talking to politely excuses themselves. I now tend to dodge that kind of question and stick to safer topics.

Why is it socially acceptable to say you are bad at Maths? I doubt that so many people would be so upfront saying that they can’t read… So why does Maths get such bad press?

My Theory

Mathematics is a very black and white subject, with normally only one right answer, although there may be lots of different ways to get there. Many people have been put off Maths because in the past they have got stuck, had a negative experience and not known how to get to the correct solution.

This may have been because the teaching was poor, or the methods they were taught to use didn’t make sense to them, or they didn’t speak up in class so didn’t get help. I believe that by far the most common reason is that they take getting stuck personally. They believe that they didn’t get the right answer because they themselves are bad at Maths. Unfortunately, I don’t think this is something that just happened in the past; it still happens, and I see it happening with the highly achieving girls at WHS. They are not used to getting things wrong, finding something difficult, having to struggle, and they take it personally – they internalise this as a failure: they are bad at Maths.

Which leads us to the question: what makes someone ‘good’ or ‘bad’ at Maths? Who is someone who is ‘good’ at Maths? A Lecturer or Professor of Mathematics? A Maths teacher? Or someone who simply enjoys doing Maths? Is it about who you are comparing yourself to? As a Maths teacher, my level of mathematics is low compared to a Mathematics Professor. Being good at mental arithmetic is not the same as being good at Maths; possibly conversely in fact – professional Mathematicians are notoriously bad at mental arithmetic, as are some Maths teachers!

So, for people who say: “I’m bad at Maths”, they may think that those people who are ‘good’ at Maths never get stuck; never struggle to get to the answer. But I can assure you, that is not the case. I am a Maths teacher and I get stuck on Maths problems. I definitely don’t always immediately know how to get to the answer.

I believe the difference in how you feel about Maths is about what you do when you get stuck, because we ALL get stuck. Being stuck isn’t bad – it’s part of the process. It is a way of forming new connections in the brain; it’s a part of learning.

When I get stuck on a problem I don’t take it personally; I don’t take it as a reflection of my mathematical ability; I think of it as a challenge, a conundrum to be figured out, a puzzle to be solved. If I can’t find a solution quickly, I stop and try to think about it differently. Could it be thought about in another way? Can I visualise it by drawing a sketch or diagram? Is there an alternative approach or method I haven’t tried? Have I used all the information I have available? These are very important problem-solving skills and have lots of relevance to everyday life.

Above: Thinking, via Pexels


Use it or lose it

Mathematics in many ways can be considered its own language. When learning languages, you start with basics: hello, please, thank you, and a few important sentences (dos cervezas, por favor); and build up to be able to communicate fluidly. If you have ever tried to learn a language seriously, you will know that it is not a smooth process. You go through phases of thinking you’re doing great, then you feel like you plateau – you realise that there is a whole verb tense you had no idea existed, that you now need to learn.

Maths is similar. You need to know the basics: numbers, patterns, arithmetic, and a few important ideas like algebra; and you build up to some quite complicated Maths like calculus, proof, complex numbers. With Maths numbers and algebra are the words, and rules like BIDMAS are the grammar. They are a means to the same end as languages – to communicate effectively.

One aspect of learning a language (or learning a musical instrument) is that if you don’t practise it regularly, you start to lose the gains you had made; it becomes more difficult, and eventually you forget. I firmly believe – that like a language – if you don’t use Maths, if you don’t practise it regularly, you start to lose it.

For me, this explains why parents can struggle to remember how to do school-level Maths with their children, even if they found it easy when they were young – they haven’t practised it in years. It can seem like an alien language – it’s hard to pick something up again when you have had such a long gap.

Yet even if you, yourself, haven’t used Maths in years, you are constantly using things that have been programmed by someone using Mathematics. Maths underpins everything ‘modern’ around us: the computer at which I am typing this article, the smartphone in your pocket; it keeps planes in the air and stops them crashing into each other; it’s in our buildings, in our clothes; Maths is fundamental to our modern style of living.

We want to encourage our children to feel it is socially unacceptable to be bad at Maths. We want them to be the ones solving the problems of the future, and part of this will certainly require mathematics.

So, what’s the take-home message? I’d like to think it’s this: in Maths, as in life, we all get stuck, but the people who succeed are the ones who don’t give up. And if you are lucky enough to meet a Maths teacher at a party, please be nice!

Above: Photo by Kaboompics .com from Pexels

Mrs Rebecca Brown reviews Craig Barton’s book: How I wish I’d taught Maths

Mrs Rebecca Brown, teacher of Maths at WHS, reviews Craig Barton’s book How I wish I’d taught Maths, focusing on Chapter 11 about formative assessment and diagnostic questions.

“without an effective formative assessment strategy we are in danger of teaching blindly, being completely unresponsive to the needs of our students.”

Craig begins this chapter by referencing the 2013 Dylan Wiliam tweet:

Example of a really big mistake: calling formative assessments ‘formative assessment’, rather than something like responsive teaching.

It’s only a too familiar scenario – you mention an assessment and a classroom (or staffroom!) erupts into a panic of more pressure and visions of tests, marking and grades. But how do we understand what our pupils know and where we need to begin or continue teaching them from? Even more crucial now, following a period of prolonged guided home learning. My key quotation from the chapter is when Craig explains that ‘without an effective formative assessment strategy we are in danger of teaching blindly, being completely unresponsive to the needs of our students’.

Formative assessment should be about ‘gathering as much accurate information about students’ understanding as possible in the most efficient way possible and making decisions based on that’. In short, it is about adapting our teaching to meet the needs of our students.

He describes elements of great teaching and cites one of Rosenshine’s (2012) ‘Principles of Instruction’ -to check for student understanding: ‘The more effective teachers frequently checked to see if students were learning the new material. These checks provided some of the processing needed to move new learning into long-term memory. These checks also let teachers know if students were developing misconceptions’.

Teaching is only successful if students have understood and learned something. Successful formative assessment can help us to identify problems and begin to fix things in the here and now much more effectively and efficiently. Asking ourselves, do I need to go over this point one more time or can I move on to the next thing?

Craig suggests the use of diagnostic questions to give quick accurate and useful information about students’ understanding. A good diagnostic question is a multiple choice, four-part question, with three incorrect answers that can help you to identify both mistakes and misconceptions. Each incorrect answer must reveal a specific mistake or misconception. If the question is designed well enough, then you should be able to gain reliable evidence about students’ understanding without having to have further discussions.

Diagnostic questions are designed to help identify, and crucially understand students’ mistakes and misconceptions in an efficient and accurate manner. They can be used at any time in a learning episode and are most effective when used throughout, using follow up questions to test the exact same skill as the first question.

Craig has developed a website of diagnostic questions that can be used in a variety of subjects. This year I will be trying to incorporate these into all of my lessons to ensure I have accurate, timely information on student understanding to enable me to effectively teach the girls that I have before me.

The proof behind one of the most famous theorems in mathematics

Vishaali, Year 10, looks behind the proof of one of the most famous mathematical theorems – that of Pythagoras’ theorem.


What is the difference between a theorem and a theory?

A theorem is a mathematical statement that has been proven on the basis of previously established statements. For example, Pythagoras’ theorem uses previously established statements such as all the sides of a square are equal, or that all angles in a square are 90°. The proof of a theorem is often interpreted as justification of the statement that the theorem makes.

On the other hand, a theory is more of an abstract, generalised way of thinking and is not based on absolute facts. Examples of theories include the theory of relativity, theory of evolution and the quantum theory. Take the theory of evolution; this is about the process by which organisms change over time as a result of heritable behavioural or physical traits. This is based on undeniable true facts, but more from experience and from an abstract way of thinking.

It is also important not to confuse mathematical theorems with scientific laws as they are scientific statements based on repeated experiments or observations.

The proof behind Pythagoras’ theorem

You have probably all heard of Pythagoras’ theorem, one of the simplest theorems there is in mathematics, that is relatively easy to remember. Given that it’s so easy to remember and to learn, wouldn’t it be an added bonus to know exactly how this theorem came to be?

The theorem, a²+b²=c², relates the sides of any right-angled triangle enabling you to find the lengths of any side, given you have the lengths of the other two.

This whole theorem is based on a triangle like this:

These four right-angled triangles are exactly the same just rotated slightly differently to create this shape:

Two shapes have been made by putting these triangles in this order. A big square on the outside, and another slightly smaller square in the middle. As all these triangles are the exact same you can label them A, B and C.

You can tell from the labels the triangles have been given, that the bigger square would have the sides (a+b), and the smaller triangle in the middle will have sides of c. Therefore we know the area of the smaller square is c² :

Using the exact same four triangles, we can rotate and translate them to create a slightly different shape:

Now two more squares have been added to this shape. We can call them  a² and b².

Thinking back to the shape we made before, we can also see that the length of this shape is also (a+b). As we know we used the same four right-angled triangles for the shape before and now, we can infer that the two squares  a² and b² are exactly the same as the square from the first shape, c². Hence we get Pythagoras’ theorem, a²+b²=c²:


What is the single most important thing for teachers to know?

Pile of books

Cognitive Load Theory – delivering learning experiences that reduce the overload of working memory

Rebecca Brown – GDST Trust Consultant Teacher, Maths and teacher at Wimbledon High School – explores how overload of the working memory can impact pupils’ ability to learn effectively.

Above: Image via

Over the summer whilst (attempting to) paint and decorate my house, I was truly inspired listening to Craig Barton’s podcasts[1] and the opinions and theories of the fabulous guests that he has interviewed. In particular, his episode with Greg Ashman[2] where they discuss Cognitive Load Theory. I feel slightly embarrassed that I have managed to get through the last twelve years of my teaching practice and not come across this pivotal theory of how students learn before now!

Delving into this deeper, I have since found out that in 2017, Dylan Wiliam (another of my educational idols) tweeted that he had ‘come to the conclusion Sweller’s Cognitive Load Theory[3] is the single most important thing for teachers to know.’ As a self-confessed pedagogical junkie I immediately wanted to know more – so what is Cognitive Load Theory and what impact could it have on the learning of my students?

What is Cognitive Load Theory and where did it come from?

“If nothing has been changed in long term memory then nothing has been learned” – Sweller

In 1998, in his paper Cognitive architecture and instructional design[4], prominent Educational Psychologist Dr John Sweller helped demonstrate that working memory has a limited capacity. He put forward the idea that our working memory – the part of our mind that processes what we are currently doing – can only deal with a limited amount of information at one time.

In essence, it suggests that human memory can be divided into working memory and long term memory. Long term memory is organised into schemas. If nothing is transferred to long term memory then nothing is learned. Processing new information puts cognitive load on working memory, which has a limited capacity and can, therefore, affect learning outcomes.

If we can design learning experiences that reduce working memory load then this can promote schema acquisition. Sweller’s Cognitive Load Theory suggested that our working memory is only able to hold a limited amount of information (around 4 chunks) at any one time and that our teaching methods should avoid overloading our working memory to maximise learning.

De Jong[5] states that ‘cognitive load theory asserts that learning is hampered when working memory capacity is exceeded in a learning task’.

Put simply, in early knowledge acquisition, if we can simplify how we deliver material to students, to focus on what really needs to be learnt so that they are not using up too much working memory, then we have a much higher chance of being able to help the learning stick in their long term memory.

Types of Cognitive Load

The theory identifies three different types of cognitive load:

Intrinsic: the inherent difficulty of material being learnt. This can be influenced by prior knowledge that is already stored in the long term memory. For example, if students know that 5×10=50 this can be retrieved without imposing any strain on working memory but if the calculation required as part of a problem was 398 x 34, students would have to begin to retrieve information on how to do long multiplication which would take up working memory required for new material.

Extraneous: the way in which the subject is taught or the manner in which material presented. Extraneous load is a cognitive load that does not aid learning and should be reduced wherever possible.

Germanic: the load imposed on the working memory by the process of learning itself. That is, moving learning from the working memory into the schemas in long term memory.

So, if we can manage intrinsic load, reduce extraneous load, allow more room in the working memory for Germanic load then we have better chance of learning being transferred into long term memory.

Moving forward

In his enlightening and motivational book How I Wish I’d Taught Maths, Craig Barton[6] summarises that the essence of Cognitive Load Theory is getting students to think hard about the right things in order to facilitate the change in the long-term memory necessary for learning to occur.

Whilst I am so far from being an expert in Cognitive Load Theory, from the research that I have already read, I am positive that my teaching practices will be enhanced by continually considering ways of reducing Cognitive Load and ensuring that students working memories are not overloaded with information that is not conducive to learning.

My next steps are to look further into the research from Mayer[7] on Cognitive Theory of Multimedia Learning to develop how I can best present learning opportunities to students.




[3] Sweller, J., Van Merriednboer, J. J. G. and Paas F.G. W. C. (1998) ‘Cognitive architecture and instructional design’, Educational Pscycholgy Review 10 (3) pp. 251-296

[4] Sweller, J., Van Merriendboer, J.J.G and Paas, F.G. W. C. (1998( ‘ Cognitive architecture and instructional design’, Educational Psychology Review 10 (3) pp. 251-296

[5] De Jong T (2010) Cognitive Load Theory, educational research, and instructional design: Some food for thought. Instructional Science 38 (2): 105-134.

[6] Barton, Craig 2018 How I wish I’d taught Maths

[7] Mayer, R.E (2008) ‘Applying the science of learning: evidence-based principles for the design of multimedia instruction’, American Psychologist 63 (8) pp. 760-769


What happens when maths goes wrong?

Grace, Year 8, looks at why maths is important in everyday life, and what happens when it goes wrong.

Maths is integrated into our lives. Whether it’s telling the time or looking at our budget for the latest gadget that we want to buy, we all use maths. But sometimes we use it incorrectly.

The Leonard v Pepsi court case

One example of maths going wrong is when in 1995 Pepsi ran an advert where people could collect Pepsi points and trade them in for Pepsi-branded items. Points could be collected through purchasing Pepsi products, or through paying 10 cents per point. For example, a T-shirt was worth a mere 75 points whilst a leather jacket was worth 1,450 points.

To end their campaign, Pepsi stated that the Harrier Jet, which was promoted in their advert, could be bought for 7 million Pepsi points. At the time, each Harrier Jet cost the U.S. Marine Corps around $20 million. Knowing its worth, a man called John Leonard tried to cash it in. This was an extensive task with particular rules, all of which John followed. His amount totalled $700,008.50 which he put into an envelope with his attorneys to back the cheque! Pepsi initially refused his claim, but Leonard already had lawyers prepared to take his side and fight. The case involved a lot of discussion, but eventually, the judges sided with Pepsi, even though Leonard v PepsiCo, Inc. is now a part of legal history.

Errors in the news

Does the maths add up?

Sometimes maths goes wrong on a big scale. For example, the Russian shooting team in the 1908 Olympics left with no medals because they turned up nearly two weeks late as the 10th July in Russia, was the 23rd July in the UK. The Russians were using a different calendar.

Lottery complications

Another example is of human confusion with maths. A UK lottery scratch card had to be taken off the market within a week due to players having problems with negative numbers. The card was called Cool Cash, and had a temperature printed on it. If you scratched a temperature lower than the target, you won. But lots of people playing didn’t understand negative numbers… “On one of my cards it said I had to find temperatures lower than -8. The numbers I had uncovered were -6 and -7 so I thought I had won, and so did the woman in the shop. But when she scanned the card, the machine said I hadn’t. I phoned Camelot and they fobbed me off with some story that -6 is higher, not lower, than -8, but I’m not having it.” These players didn’t know how negative numbers worked, so looked for the numbers that were usually lower when they were positive.

Maths is important in everyday lives as we all use it, sometimes without being aware of it. However, it is important that checks are made to ensure the correct figures and calculations are used. After all, our lives may depend on it.