Equals and equality

March 21, 2024 / chrishildrew / Leave a comment

Wikipedia tells me that the word “equals” derives from the Latin word “æqualis,” meaning “uniform”, or “identical”, which itself stems from aequus (“level”, “even”, or “just”). The equals sign – a pair of parallel lines, one above the other – apparently originated with a Welsh mathematician, Robert Recorde, in 1557. Bored of writing out “is equal to” again and again, he used a pair of parallel lines to stand instead.

Robert Recorde’s original explanation of the equals sign

Recorde wrote: “And to auoide the tediouſe repetition of theſe woordes : is equalle to : I will ſette as I doe often in woorke vſe, a paire of paralleles, or Gemowe lines of one lengthe, thus: =, bicauſe noe .2. thynges, can be moare equalle.” In modern English, this roughly translates to: “And to avoid the tedious repetition of these words: “is equal to” I will set as I do often in work use, a pair of parallels, or duplicate lines of one [the same] length, thus: =, because no 2 things can be more equal.”

The first recorded use of the equals sign in 1557. 14x + 15 = 71

Recorde called his new symbol – a much longer pair of parallel lines than we are now used to – “Gemowe lines.” The word “Gemowe” means “twin,” from the same root as the star sign “Gemini.” What Recorde has captured in his new symbol was the idea that the two lines are not the same – one is above the other, and one below – but they are of the same value. The are worth the same. They are equally valuable – equivalent.

This famous illustration has been used in training to help staff think about the ideas of inclusion and diversity

We have been thinking carefully about what equality means in education. We are not all the same – each of us is unique. Achieving equality of opportunity does not mean giving everyone the same treatment – as shown in the left hand picture above. Some people need extra help or support to achieve – as shown in the middle picture – and as a school we work hard to put that in place wherever it is needed.

Our ultimate goal is to remove the barriers that stand in the way of achievement and progress, so that our students can set no limits on what they can achieve. This is illustrated in the picture on the right. We know that this is challenging, and that some of the barriers are beyond our control. We know that we can’t always achieve it on our own – but that doesn’t mean we shouldn’t try.

I recently visited a maths lesson and saw another expression of “equality.” The teacher was guiding the students through solving algebraic equations to find the value of x. Something like this:

2x² + 12 = 44

Students volunteered to take the class through the process of solving the equation to find the value of x. The first step was to subtract 12, from both sides of the equation, to leave 2x² = 32.

The teacher asked: “why do you need to take 12 from both sides of the equation?” The answer emerged: because both sides have to equal the same amount. If you only took 12 away from the left hand side, then they wouldn’t be equal.

The Year 8 mathematicians went on to divide both sides of the equation by 2, leaving x²= 16, before taking the square root of both sides and concluding that x=4.

After I had visited the lesson, I kept thinking about the idea of equality – in mathematics, in education, in society. 2x² + 12 is not identical to 44 – the two sides of the equation look very different. But they have the same value. Our students are all different too, each with their own unique qualities, needs and circumstances. Their differences make them unique, and it is this uniqueness which provides the richness of our community. But every single child matters: they are all Churchill students. They are all part of the whole, all of equal value; they all belong equally.

Women in STEM: to the stars

February 14, 2019February 13, 2019 / chrishildrew / Leave a comment

Tuesday of this week was one of those days when the stars aligned and I saw the same issue from multiple angles all within 24 hours. The issue was gender inequality in Science, Technology, Engineering and Maths.

Attitudes to STEM subjects by gender

First thing in the morning, I received an email bulletin highlighting some research which had just been published on attitudes to STEM subjects by gender at KS4. The findings made for challenging reading:

Girls enjoy STEM subjects less than boys: The proportion of male pupils who ranked KS4 STEM subjects first for enjoyment was almost twice that for females: 59% vs. 32%.
Girls are less likely to say STEM is their best subject: When asked which subject they were best at, the proportion of male pupils who ranked a STEM subject first was 60%, which again was almost twice as high compared to females at 33%.
Boys are more likely to think STEM leads to a job: When asked about which subjects were most likely to lead to a future job, 69% of male pupils ranked a STEM subject first compared to 51% of females.
Girls and boys both name STEM as leading to highest paid jobs: When asked which would lead to the highest paid job, 81% of male pupils named a STEM subject compared to 77% of females.
Girls are less likely to pursue STEM at A level: When asked what they planned to study at A-Level, female pupils made up the minority of those naming STEM subjects. Particularly, in Engineering (14% / 86%), Computing (15% / 85%) and Physics (22% / 78%).

Combating gender inequality is a particular mission of mine, and it is one of the reasons we have named our new Science and Technology building after a prominent female scientist, Professor Dame Athene Donald. We are doing better than the national average at Churchill, where we have a 54% to 46% split of students taking Science and Maths courses in our Sixth Form. But there is still work to do, as there is considerable variation between subjects.

Dr Sue Black and Bletchley Park

Dr Sue Black

After school that same day, I was listening to an interview with Sue Black on my drive home. Sue Black is a prominent software engineer, keen to promote women in computer science. She was also instrumental in the campaign to save Bletchley Park, where ten thousand people (including Alan Turing, after whom another of our buildings is named) built some of the first computers and cracked the Enigma code used by the Nazis during World War Two. More than half of the people who worked there were women. No-one had any previous experience of computers. In 2019, there are fewer women working in tech than there were in the 1960s. How has this happened? Sue Black was an inspirational figure, challenging the stereotype of the software engineer and the systems analyst to show that women have a vital role to play in the future, as well as the history, of computer science.

Professor Jo Dunkley and Henrietta Swan Leavitt

Professor Jo Dunkley, OBE

Later that evening, I was driving back to school for governors’ meeting listening to a science podcast about how to measure the size of the universe. One of the guests was Professor Jo Dunkley, a physicist from Princeton University in America. Her research is in cosmology, studying the origins and evolution of the Universe, and she made this complex and challenging subject accessible and fascinating. She too described how, in her field, women make up 20% or less of the physicists looking at space, the stars, and cosmology, yet the women were every bit as talented and clever as any of the men. And she too had a tale of how, in the past, women made a huge contribution to the field of cosmology, astronomy and astrophysics.

Henrietta Swan Leavitt (1868-1921)

Professor Dunkley told the story of Henrietta Swan Leavitt, an astronomer working at Harvard University in the early 20th century. She was part of a group of women known as the “Harvard Computers“, hired to carry out calculations and process astronomical data in the days before electronic computers. In those days women were not allowed to operate the telescopes themselves – this was a male only environment. Instead, they studied the photographic plates produced by the telescopes. It was in doing this that Leavitt, who was profoundly deaf following an illness, made her ground-breaking discovery. She was studying a group of stars called the Cepheid variables. These stars pulsed at different rates, and Leavitt worked out a mathematical relationship between the brightness of these stars and the frequency of their pulses. This relationship, now known as “Leavitt’s Law,” allowed astronomers to measure the distance from Earth to faraway galaxies for the first time. It also enabled future astronomers such as Edwin Hubble to firmly establish that the universe was expanding.

Gender Equality

It was a freakish coincidence that, after reading about the inequality in perceptions of Science, Technology, Engineering and Maths between boys and girls in 2019, I should then be confronted with these fantastic examples of prominent women in STEM from the present day and the past. The majority of the code-breakers of Bletchley Park were 18 year-old women, just out of school, with no prior experience of computer science – yet they contributed to cracking the Nazi codes and saving millions of lives by shortening the Second World War. The very notion of computer science was, of course, invented by a woman – Ada Lovelace, back in the 1840s. In the present day, women like Dr Sue Black are blazing a trail for women in computer science and technology.

Ada Lovelace, painted in 1832

In the field of astronomy, cosmology and astrophysics, the foundations of our ability to measure the universe were laid by women – the Harvard Computers who were not even allowed to operate the telescopes. Prominent cosomologists such as Jo Dunkley continue their work today, including estimating the mass of the universe and studying distant galaxies.

Why is it, with this rich history and vibrant present of women in STEM, that so few girls go on to study Physics or Computing at A-level in this country? I don’t know, but I hope with examples like Lovelace, Leavitt, Black, Dunkley and Athene Donald to follow, we will see the trend reverse and true gender equality achieved.

Millicent Fawcett: a hero of Gender Equality

February 8, 2018February 20, 2018 / chrishildrew / 2 Comments

This week has been the centenary of the Representation of the People Act, the bill which finally gave women the vote on 6th February 1918. Even then, only women over the age of 30 who met a property qualification were able to vote, which enfranchised only 40 per cent of the total population of women in the UK. It was not until the Equal Franchise Act of 1928 that women over 21 were able to vote and women finally achieved the same voting rights as men. This act increased the number of women eligible to vote to 15 million.

Millicent Fawcett

One of the heroes of the suffrage movement was Dame Millicent Fawcett. Fawcett was born in 1847, and developed an interest in women’s rights at a young age. Her sister, Elizabeth Garrett Anderson, was the first female doctor in Britain. In 1866, at the age of 19, Millicent became the secretary of the London Society for Women’s Suffrage. She dedicated her life to campaigning for equal rights for women. Fawcett was a suffragist, not a suffragette. She distanced herself from the militant and sometimes violent activities of the suffragettes, preferring instead to work within the law.

Suffragettes Annie Kenney and Christabel Pankhurst

Fawcett spoke at her first public pro-suffrage meeting in 1869, and took over as the leader of the National Union of Women’s Suffrage Societies (NUWSS) in 1890. She held this position until 1919, a year after the Representation of the People Act finally achieved the aims she had been campaigning for over the past 53 years.

When the Equal Franchise Act of 1928 was to be signed into law, the 81-year-old campaigner, now a Dame Grand Cross of the Order of the British Empire, wanted to witness the historic moment. She made her way to the House of Lords in plenty of time for the ceremony, which was due to start at 6.30pm on 3rd July. Unfortunately, the House of Lords had completed their other business more quickly than anticipated, and brought the signing ceremony forward to six o’clock. After 62 years of campaigning, Dame Millicent arrived less than a minute too late to see the law conferring equal voting rights to women given royal assent.

Millicent_Garrett_Fawcett_2_Gower_Street_blue_plaque

Fawcett died the following August, in 1929, aged 82. She was born into an era where women were seen and not heard, where they had few rights, and where they were widely believed to be “the weaker sex.” Over her lifetime, the rights of women were transformed; by the time of her death women had the same voting rights as men. Little wonder, then, that Fawcett won the vote for “most influential woman” of the last 100 years run this week by BBC Radio 4, or that she has been chosen as the subject a commemorative statue to be erected in Parliament Square.

Artist Gillian Wearing with a model of the Fawcett statue

It is fitting that Fawcett continues to break new ground for women, even today: hers is the first statue of a woman to be erected in Parliament Square. The plinth will feature the names of 59 women and men who fought for women’s suffrage; it will be unveiled in April. In the statue, Fawcett holds a placard with a line from a speech she gave after the death of suffragette Emily Wilding Davison at the 1913 Epsom Derby: “courage calls to courage everywhere.”

Fawcett’s work remains incomplete, however: there are still significant gender inequalities at work in our society today. That is why Churchill Academy & Sixth Form has signed up to the Gender Equality Charter, with the aim of challenging and correcting gender imbalances wherever we find them. Click here to find out more.

Millicent Fawcett in 1870

If you want to learn more about the campaign for women’s right to vote and its impact on women’s rights and equality to the present day, you can join me in signing up for a free five-week online course (MOOC) called Beyond the Ballot: Women’s Rights and Suffrage from 1866 to Today run by Royal Holloway and the UK Parliament.