Teachers Aren’t Dumb

An Op-Ed piece in the New York Times, by

Mediocre teacher preparation extends to mathematics. An international study of new middle school teachers showed that Americans scored worse on a math test than teachers in countries where kids excelled, like Singapore and Poland. William Schmidt of Michigan State University identified the common-sense explanation: American teachers take fewer math classes. Instead, they take more courses in general pedagogy — coursework, that is, on theories of instruction, theories of child development and the like.

Can anyone give references to “an international study of new middle school teachers”? What was UK’s results in the study?

Merryn Hutchings,  Exam Factories? The impact of accountability measures on children and young people. Report for NUT Full text.

From the summary:

Professor Hutchings finds that:

  • The Government’s aims of bringing about an increased focus on English/literacy and maths/numeracy and (in secondary schools) academic subjects, has been achieved at the cost of narrowing the curriculum that young people receive.

  • Recent accountability changes mean that in some cases secondary schools are entering pupils for academic examinations regardless of aptitudes or interests. This is contributing to disaffection and poor behaviour among some pupils.

  • The amount of time spent on creative teaching, investigation, play, practical work and reading has reduced considerably and there is now a tendency towards standardised lesson formats. Pupils questioned for this study, however, say that they learn better when lessons are memorable.

  • Teachers are witnessing unprecedented levels of school-related anxiety, stress and mental health problems amongst pupils, particularly around exam time. This is prevalent in secondary schools but also in primaries.

  • Pupils of every age are under pressure to learn things for which they are not ready, leading to shallow learning for the test and children developing a sense of ‘failure’ at a younger and younger age.

  • Pupils’ increased attainment scores in tests are not necessarily reflected in an improvement in learning across the piece. Teaching can be very narrowly focused on the test.

  • The Government and Ofsted’s requirement that schools target pupils on Free School Meals with Pupil Premium money is prompting some schools to take the focus away from special educational needs (SEN) children. Accountability is discouraging schools from including SEN children in activities targeted at Free School Meals children even when children with SEN need the support more.

  • Accountability measures disproportionately affect disadvantaged pupils and those with SEN or disabilities. Teachers report that these children are more likely to be withdrawn from lessons to be coached in maths and English at the expense of a broad curriculum. Furthermore, some schools are reluctant to take on pupils in these categories as they may lower the school’s attainment figures. Ofsted grades are strongly related to the proportion of disadvantaged pupils in a school.

  • Ofsted is not viewed as supportive. It is seen as punitive and inconsistent, with the ability to cause a school to “fall apart”. In their analysis of a school, the inspectors also have a tendency not to take on board the way that individual circumstances affect outcomes.

  • The legacy effect of past Ofsted requirements means that these practices are still “drilled in” despite no longer being measured or required. These include the focus on marking of pupils’ work in a standardised manner and the monitoring of lesson structure.

David Singerman: X + Y the movie

[To appear in the LMS Newsletter]

There are now an increasing number of movies where mathematics plays an important role. Usually we are let down by the parts featuring the maths because the makers of the film have little knowledge about our subject. So it is a real pleasure to review x+y a beautiful film where the mathematics is carefully done but not in a way that will put off a non-mathematical audience. The director is Morgan Matthews who also made the BBC4 documentary Beautiful Young Minds about the Mathematical Olympiad and the film is clearly based on this documentary. This documentary can be seen on Youtube.

The main character is Nathan. From the BBC synopsis

Preferring to hide in the safety of his own private world, Nathan struggles to connect with people, often pushing away those who want to be closest to him, including his mother, Julie. Without the ability to understand love or affection, Nathan finds the comfort and security he needs in numbers and mathematics.

Even though there are similarities between this film and the documentary, the main story line is totally fictitious. Near the beginning, Nathan, who has Asperger’s syndrome, is involved in a car crash which kills his father to whom he was very close. He is then mentored by his maths teacher Martin Humphreys, who when young had taken part in the Mathematics Olympiad. He was diagnosed with multiple sclerosis but also has other problems to do with self worth and soft drugs and ended up being a secondary school teacher.

Humphreys recognizes Nathan’s abilities and persuades him to enter for the Olympiad. He goes to the preliminaries in Taipei.

One of the scenes where there is actual maths is when Nathan is brought to the board to explain how to solve a problem. This involves playing cards which can be face up or face down.

Nathan’s solution is to model this with binary arithmetic involving 0s and 1s and he then turns the problem into an arithmetic one which is easy to solve.

In Taipei he meets Zhang Mei, a girl on the Chinese team. The film concentrates on two relationships. One between Nathan and Zhang Mei and the other between Martin Humphreys and Julie.

The scene moves from Taipei to Cambridge where the Maths Olympiad takes place.

There is real pathos in the final scenes. One where Nathan finally opens himself up to his Mother, and another when Nathan and Zhang Mei while travelling back from Cambridge by train see a rainbow and the viewer feels that their relationship will last. At last, Nathan feels and understands love and affection. Some critics have thought that this ending is too soapy, but if you see the documentary on which this film is based, the rainbow really was there!

One should also mention the excellent cast. Nathan was played by Asa Butterfield, Martin by Ralf Spall, Julie by Sally Hawkins and Zang Mei by Jo Yang. A lovely film where mathematics plays a central role.

Geoff Smith on X + Y

Reposted from the UKMT’s Newsletter:

In March 2015, the film  X + Y  will appear in cinemas all over the UK. This is a romantic drama, and explores a collection of intense personal relationships. One of the main characters is a teenaged boy (played by Asa Butterfield) who competes enthusiastically in UKMT competitions, and who dreams of going to the International Mathematical Olympiad. Several leading actors decorate the cast (Sally Hawkins, Eddie Marsan, Rafe Spall, Jo Yang). The film was made with the co-operation of UKMT and the IMO, and logos and flags appear accordingly. The film has secured international distribution contracts, and will be seen in many countries, and on airlines.

This film grew out of the BBC2 documentary “Beautiful Young Minds”, and the common director is Morgan Matthews. If UKMT were to make such a film (an exceptionally bad suggestion), the emphasis would be much more on the mathematics and less on the relationships. Morgan Matthews has become very interested in the way people on the autistic spectrum can prosper in mathematics. There has been a natural concern in the maths community that portraying some mathematicians as being less than socially fluent is dangerous, because it could lead to the misapprehension that mathematicians are all strange.

My personal view is that the prefix “mis” in the previous sentence can be deleted. All mathematicians are strange because they place such an exceptional value on thought, ideas and understanding. I think that the maths community should be proud of the way it embraces people on the basis of their enthusiasm for and interest in mathematics. University maths departments are happy places, where the socially adroit rub along in harmony with people who live in more private spaces. The trick is mutual respect and affection. This is equally true of UKMT maths camps. Most students are relaxed and outgoing, with the full set of skills that allow them to prosper in the teenage social maelstrom. Some others are not, but everyone gets along almost all of the time, united by a passion for ideas and ingenuity. We all know maths people who sometimes appear confused and nervous, but who have beautiful mathematical insights.

Things would be even better if women and all racial groups were richly represented in the maths community, and UKMT has done excellent work on the gender issue by founding the European Girls’ Mathematical Olympiad and running the annual talent search examination, the UK Maths Olympiad for Girls. The mentoring schemes make an excellent education in mathematical problem solving available to all social groups. However, while social inclusion is very much “work in progress”, the incorporation of people on the autistic spectrum into the wider maths community seems to be a great success, and in my view, a cause for celebration.

Geoff Smith, Chair of the BMO and the IMO, University of Bath.

Disclaimer: Geoff was involved in assisting to make X + Y, so his views are not impartial.

Steven Strogatz: Whi Pi Matters

Our American colleagues celebrate today Pi Day, although, technically speaking, it is American Pi Day: for the rest of the world, today is 14/03/14. A brilliant article by Steven Strogartz in The New Yorker, a brief quote:

What distinguishes pi from all other numbers is its connection to cycles. For those of us interested in the applications of mathematics to the real world, this makes pi indispensable. Whenever we think about rhythms—processes that repeat periodically, with a fixed tempo, like a pulsing heart or a planet orbiting the sun—we inevitably encounter pi. There it is in the formula for a Fourier series: […]

Read the whole article.

Cameron’s £15,000 for maths and science teachers

From BBC:

David Cameron is to announce a £15,000 university bursary for teenagers with good A-level maths and science grades, if they commit to enter teaching.

This “golden hello” for teenagers is an attempt to recruit more maths and physics teachers for England’s schools. […]

These will begin with pilot projects, with a so far unspecified number of places, which will see incentives for young people to sign up for teaching before going to university.

The £15,000 over three years for potential teachers would help with living costs and would be repayable if students did not go on to teach for three years after graduating

Read full article.

David Mumford on Grothendieck and magazine “Nature”

Can one explain schemes to biologists

December 14, 2014

John Tate and I were asked by Nature magazine to write an obituary for Alexander Grothendieck. Now he is a hero of mine, the person that I met most deserving of the adjective “genius”. I got to know him when he visited Harvard and John, Shurik (as he was known) and I ran a seminar on “Existence theorems”. His devotion to math, his disdain for formality and convention, his openness and what John and others call his naiveté struck a chord with me.

So John and I agreed and wrote the obituary below. Since the readership of Nature were more or less entirely made up of non-mathematicians, it seemed as though our challenge was to try to make some key parts of Grothendieck’s work accessible to such an audience. Obviously the very definition of a scheme is central to nearly all his work, and we also wanted to say something genuine about categories and cohomology. Here’s what we came up with:

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