The Russell Group, which represents 24 leading institutions including Oxford and Cambridge, is to launch an immediate review of exam questions and course syllabuses [...] The sciences, maths and foreign languages could be subject to the biggest changes. [...] Maths professors have become increasing alarmed at the “overly structured” and “formulaic approach” to the subject at A-level [...]
Prof Nigel Thrift, vice-chancellor of Warwick, said it would form an independent company – [Alcab], the A-level Content Advisory Body – to represent the views of Russell Group universities and consult other higher education institutions and learned societies.
It will focus on the “facilitating subjects” seen as essential in the sixth-form – maths, further maths, English literature, physics, biology, chemistry, geography, history and both modern and classical languages.
In a letter to Mr Gove, Prof Thrift, who will lead the board, said it would review these A-levels between now and the autumn to “identify where changes are required to ensure the subjects are fit for purpose”.
It will mean delaying the introduction of new-style A-levels in these subjects from 2015 to 2016 if changes are needed, he said.
Prof Thrift also said that the advisory body would contribute to Ofqual’s “longer-term” monitoring of A-levels “to make sure that new qualifications are reviewed each year”.
Mr Gove welcomed the intervention, adding: “Strong leadership from Russell Group universities, and engagement across the wider higher education sector, is critical to the future development of A-levels.”
A highly unusual and original book for parents of young children, written by Yelena McManaman, Maria Droujkova, and Ever Salazar, and published under Creative Commons Attribution-NonCommercial-ShareAlike license. From promotional material:
How do you want your child to feel about math? Confident, curious and deeply connected? Then Moebius Noodles is for you. It offers advanced math activities to fit your child’s personality, interests, and needs.
Can you enjoy playful math with your child? Yes! The book shows you how to go beyond your own math limits and anxieties to do so. It opens the door to a supportive online community that will answer your questions and give you ideas along the way.
Learn how you can create an immersive rich math environment for your baby. Find out ways to help your toddler discover deep math in everyday experiences. Play games that will develop your child’s sense of happy familiarity with mathematics.
A five-year-old once asked us, “Who makes math?” and jumped for joy at the answer, “You!” Moebius Noodles helps you take small, immediate steps toward the sense of mathematical power.
You and your child can make math your own. Together, make your own math!
What follows is a translation of a fragment from Igor Arnold’s (1900—1948) paper of 1946 Principles of selection and composition of arithmetic problems (Известия АПН РСФСР, 1946, вып. 6, 8-28). I believe it is relevant to the current discussions around “modelling” and “real life mathematics”. For research mathematicians, it may be interesting that I.V. Arnold was V.I. Arnold’s father.
Existing attempts to classify arithmetic problems by their themes or by their algebraic structures (we mention relatively successful schemes by Aleksandrov (1887), Voronov (1939) and Polak (1944)} are not sufficient [...] We need to embrace the full scope of the question, without restricting ourselves to the mere algebraic structure of the problem: that is, to characterise those operations which need to be carried out for a solution. The same operations can also be used in completely different concrete situations, and a student may draw a false conclusion as to why these particular operations are used.
Let us use as an example several problems which can be solved by the operation
\[3 - 1 =2. \]
- I was given 3 apples, and I have eaten one of them. How many apples are left?
- A three meters long barge-pole reached the bottom of the river, with one meter of it remaining above the level of water. What is the depth of the river?
- Tanya said: “I have three more brothers than sisters”. In Tanya’s family, how many more boys are there than girls?
- A train was expected to arrive to a station an hour ago. But it is 3 hours late. When will it arrive?
- How many cuts do you have to make to saw a log into 3 pieces?
- I walked from the first milestone to the third one. The distance between milestones is 1 mile. For how many miles did I walk?
- A brick and a spade weigh the same as 3 bricks. What is the weight of the spade?
- The arithmetic mean of two numbers is 3, and half their difference is 1. What is the smaller number?
- The distance from our house to the rail station is 3 km, and to Mihnukhin’s along the same road is 1 km. What is the distance from the station to Mihnukhin’s?
- In a hundred years we shall celebrate the third centenary of our university. How many centuries ago it was founded?
- In 3 hours I swim 3 km in still water, and a log can drift 1 km downstream. How many kilometers I will make upstream in the same time?
- 2 December was Sunday. How many working days preceded the first Tuesday of that month? [This question is historically specific: in 1946 in Russia, when these problems were composed, Saturday was a working day --AB]
- I walk with speed of 3 km per hour; my friend ahead of me walks pushing his motobike with speed 1 km per hour. At what rate is the distance between us diminishing?
- Three crews of ditch-giggers, of equal numbers and skill, dug a 3 km long trench in a week. How many such crews are needed to dig in the same time a trench that is 1 km shorter?
- Moscow and Gorky are in adjacent time zones. What is the time in Moscow when it is 3 p.m in Gorky?
- To shoot at a plane from a stationary anti-aircraft gun, one has to aim at the point three plane’s lengths ahead of the plane. But the gun is moving in the same direction as the plane with one third the speed. At what point should the gunner aim his gun?
- My brother is three times as old as me. How many times my present age was he in the year when I was born?
- If you add 1 to a number, the result is divisible by 3. What is the reminder upon division of the original number by 3?
- A train of 1 km length passes by a pole in minute, and passes right through through a tunnel at the same speed — in 3 minutes. What is the length of the tunnel?
- Three trams operate on a two track route, with each track reserved to driving in one direction. When trams are on the same track, they keep 3 km intervals. At a particular moment of time one of them is at crow flight distance of 1 km from a tram on the opposite track. What is the distance from the third tram to the the nearest one?
These examples clearly show that teaching arithmetic involves, as a key component, the development of an ability to negotiate situations whose concrete natures represent very different relations between magnitudes and quantities. The difference between the “arithmetic” approach to solving problems and the algebraic one is, primarily the need to make a concrete and sensible interpretation of all the values which are used and/or which appear in the discourse.
This to a certain degree defines the difference of problems where is natural to request an arithmetic solution from problems which are essentially algebraic. For the latter, an arithmetic solution could be seen as a higher level exercise that goes beyond the mandatory minimal requirements of education. In many problems relations between the data and the unknowns are such that an unsophisticated normal approach naturally leads to corresponding algebraic equations. Meanwhile an arithmetic solution would require difficult, hard to retain in memory, algebraic by their nature operations over unknown quantities.
This happens, for example, in solution of the the following problem.
If 20 cows were sold, then hay stored for cow’s feed would last for 10 days longer; if, on the contrary, 30 cows were bought than hay would be eaten 10 days earlier. What is the number of cows and for how many days hay will last?
Some basic understanding of relations between the quantities appearing in the problem suffices for its conversion in an algebraic form. But to demand from pupils that they independently came to the formula
\[(200+300) \div 10\]
means pursuing a level of sophistication in operation with unknown quantities that is unnecessary in practice and unachievable in large scale education.
[With thanks to Tony Gardiner]
From The Independent (not in Hansard yet):
[Mr Gove, speaking to Education Select Committee on 15 May) indicated he was]
planning to scrap the present grading system entirely and replace A* and A grade passes with a one, two, three or four pass. [...]
He said it could well be the case that the “band of achievement that is currently A* and A” was replaced by a new one, two, three or four pass. The new-style GCSEs will start to be taught in schools in September 2015.
Graham Stuart, the Conservative chairman of the committee, also argued that Mr Gove could be “deliberately” paving the way for “grade deflation” in the exam system through the changes.
He said that the pass rate could also go down in the first year of pupils sitting the new exam (2017) – “because schools don’t know how to work the system”.
Students who previously were awarded an A grade pass could be awarded a four under the new system (a one or two would be roughly equivalent to an A* while three or four would equate to an A grade). Academics argue a four would not be seen by employers and universities as a top grade pass. Numbers are likely to replace grades throughout the system so instead of A* to G grade passes students would be awarded one to 10 passes.
However, Mr Gove replied that that the current exam system meant teachers were spending “too much time on exam technique and not enough on content”.
A musical rendition of such a complex and delicate subject matter stands a high chance of going very wrong. It is to the enormous credit of the Pit theatre company that it goes mostly very right. A few unnecessarily jarring comedic interludes aside, this is an engaging, nuanced and ultimately moving piece of theatre.
Read the review.
Schools in the Wirral, Devon and Buckinghamshire have provided the winning teams of codebreakers in this year’s Alan Turing Cryptography Competition.
Launched in 2012 as part of the Alan Turing Centenary, the Cryptography Competition is now an annual event in the School of Mathematics.
The story follows the adventures of Mike and Ellie, fresh from discovering the long-lost ‘Turing Treasure’ in last year’s competition, as they get caught up in a new cryptographic adventure around The University of Manchester, involving a mysterious ancient artefact – the Egyptian Enigma! Students were required to solve six codes to complete the competition.
This year’s winning teams were:
1st place Team ‘G15’ Calday Grange Grammar School, Wirral 2nd place Team ‘Room40’ Torquay Boys’ Grammar School 3rd place Team ‘SmileyFaces:)’ Sir William Borlase’s Grammar School, Marlow
Dr Charles Walkden from the School of Mathematics said: “Once again we – together with SkyScanner, the competition’s sponsor – have been delighted with the amount of excitement and enthusiasm that the competition has generated, with almost 2,000 young cryptographers from all over the UK taking part to solve some fiendishly difficult codes.
“We’ve also had people from Australia, South Africa and North America (as well as several European countries) following the competition, showing that there’s a global interest in the life of Alan Turing and his contributions to society. We’re already planning next year’s competition, starting in January 2014, which promises to be even bigger and better!”
Although the 2013 competition has now closed, you can still view the story and clues at:
Reposted from EdExec:
Funding for the Further Maths Support Programme is to be expanded to provide professional development for teaching staff.
Education minister Elizabeth Truss has announced that funding for the Further Mathematics Support Programme (FMSP) is being expanded to £25m over five years.
The aim of the FMSP is to increase the number of students studying further mathematics A level. Funding is used to target schools and colleges where no students are currently taking further maths, providing support to improve and extend their mathematics provision.
Read the whole story.
Look inside. Book description:
In the wrong hands, math can be deadly. Even the simplest numbers can become powerful forces when manipulated by politicians or the media, but in the case of the law, your liberty–and your life–can depend on the right calculation.
In “Math on Trial,” mathematicians Leila Schneps and Coralie Colmez describe ten trials spanning from the nineteenth century to today, in which mathematical arguments were used–and disastrously misused–as evidence. They tell the stories of Sally Clark, who was accused of murdering her children by a doctor with a faulty sense of calculation; of nineteenth-century tycoon Hetty Green, whose dispute over her aunt’s will became a signal case in the forensic use of mathematics; and of the case of Amanda Knox, in which a judge’s misunderstanding of probability led him to discount critical evidence–which might have kept her in jail. Offering a fresh angle on cases from the nineteenth-century Dreyfus affair to the murder trial of Dutch nurse Lucia de Berk, Schneps and Colmez show how the improper application of mathematical concepts can mean the difference between walking free and life in prison.
A colorful narrative of mathematical abuse, “Math on Trial” blends courtroom drama, history, and math to show that legal expertise isn’t always enough to prove a person innocent.
From the statement by Dr Wendy Piatt, Director General of the Russell Group:
“Results from AS-levels taken in Year 12 are useful to universities in the admissions process, especially in considering applications for the most competitive courses. [...]
“Whilst we have welcomed the Government’s review of the modular structure of the A-level, we do not believe this need be extended to the complete removal of the AS examination from the A-level.”
From The Telegraph:
Speaking at a Westminster Education Forum on maths, Stefano Pozzi, the assistant director of the national curriculum review division at the Department for Education, said [...] [r]eferring to the maths curriculum [...]: “Really, we are setting a much higher benchmark than we currently do now.
“How we’ve done that is in part through benchmarking against the expectations in high performing countries. Basically, politicians ask – and they’re right to – why we are expecting less of our young than they expect in other countries where kids do well?”
Speaking after the forum, [...] [h]e added: “If you look at what we’re expecting kids to do with fractions – that’s the most obvious thing that we’re doing and proportional reasoning. That stuff kids find hard and adults find hard.”