Westminster Hall debate: 16-to-18 Mathematics Education

Westminster Hall debate  27 March 2012, 16-to-18 Mathematics Education. [Hansard source (Citation: HC Deb, 27 March 2012, c334WH)]

As reported in The Guardian:

Social mobility being hampered by lack of maths teachers, says Tory MP

Liz Truss says comprehensive pupils are only half as likely as privately educated children to study maths.

Pupils educated at comprehensive schools are half as likely to study mathematics as their counterparts in the private sector, creating a “massive problem” with social mobility, a Tory MP has warned.

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Imaging study reveals differences in brain function for children with math anxiety

Scientists at the Stanford University School of Medicine have shown for the first time how brain function differs in people who have math anxiety from those who don’t.
A series of scans conducted while second- and third-grade students did addition and subtraction revealed that those who feel panicky about doing math had increased activity in brain regions associated with fear, which caused decreased activity in parts of the brain involved in problem-solving.

The paper itself: Christina B. Young, Sarah S. Wu, and Vinod Menon. The Neurodevelopmental Basis of Math Anxiety. Psychological Science OnlineFirst, published on March 20, 2012 as doi:10.1177/0956797611429134. A pdf file is avalable here.

Reward maths with more cash

An article by Elizabeth Truss MP in the The Telegraph. Some quotes:

With a lower proportion of students studying the subject in sixth form than any competitor nation, our next generation of maths teachers, city quants and rocket scientists is in danger of extinction. This feeds into all areas. There is a shortage of teachers at primary and secondary levels.[…]

Yet maths graduates are in demand. After medicine and dentistry, it is the highest-earning degree, with maths graduates earning twice that of a non-graduate. Those with a maths A-level have a 10 per cent earning premium. So why aren’t students queuing up to take maths?

One reason is the perverse funding incentives. More is paid to a school with a student getting an A in media studies than one getting a C in further maths. This is nonsense when the value to the student and the economy is considered. Further, A-level media studies, psychology and physics receive a 12 per cent funding premium, ostensibly due to equipment requirements. Consequently, only half of comprehensive sixth forms offer further maths, yet nearly 60 per cent offer media studies. Subjects such as psychology are catching up in popularity with maths, for the same reason.

Read the rest of the article.

Circle in Box: quality books for mathematical circles

A nice series of books for mathematical circles (both for students and for teachers!) published by the American Mathematical Society.

Mathematical Circles originated in Eastern Europe in the 1930s, spreading to Western Europe, Asia, and, eventually, to North America. Student circles are usually run by college professors, schoolteachers, or even enthusiastic parents wishing to share their appreciation of and love for mathematics.

The idea of teacher mathematical circles is more recent. Such circles are gatherings for elementary and secondary school teachers where they may develop effective approaches to teaching mathematics, with a particular emphasis on problem solving.

  

 

GAP in teaching

From GAP Forum: I got feedback [on use of GAP in teaching] from about 25 individuals.

GAP is used for teaching in at least the following institutions (in no particular order):

• University of Porto, Portugal
• Universidade Aberta, Portugal
• RWTH Aachen, Germany
• ZetaTrek expedition
• University of Braunschweig, Germany
• Colorado State University
• Ghent University, Department of Mathematics, Belgium
• United States Naval Academy at Annapolis, USA
• Auburn University Montgomery, USA
• University of Trento, Trento, Italy
• Nanyang Technological University, Singapore (www.ntu.edu.sg)
• Universidade de Brasilia, Brasil
• Rose-Hulman Institute of Technology, Terre Haute, USA
• Benedictine University, Lisle, USA
• University of Vlora, Albania
• University of Technology and Economics, Budapest, Hungary
• University of Western Australia, Perth, Australia
• University of Western Sydney, Australia
• Universitat Politecnica de Valencia, Spain
• University of St Andrews, Scotland, UK

The topics of the courses/teaching that were mentioned (many repeatedly) were:

•  Algebra
• Group Theory
• Representation Theory
• Number Theory
• Cryptography
• Computer Algebra
• RSA cryptosystem
• Semigroup Theory
• Coding Theory
• Information Security
• Computational Group Theory
• Computational Representation Theory
• Experimental Mathematics
• Groups and Symmetry

The levels of courses/teaching that were mentioned were:

• 2nd-3rd year
• Master
• Bachelor
• Graduate Education Majors
• Maths Majors
• Honours students
• PhD students

The following specific GAP packages have been mentioned in the feedback:

•   factint
•  automata
• data collections

It was pointed out that GAP was used in various workshops happening all over the world.

The following publicly available resources with respect to teaching material were mentioned:

• http://www.gap-system.org/Doc/Teaching/teaching.html
• http://www.math.colostate.edu/~hulpke/CGT/education.html
• http://cage.ugent.be/~jdebeule/teaching.html
• “Contemporary Abstract Algebra” by Joseph A. Gallian has GAP exercises
• “Sage for Abstract Algebra“, A Supplement to Abstract Algebra, Theory and Applications by Robert A. Beezer Department of Mathematics and Computer Science University of Puget Sound, http://abstract.ups.edu/sage-aata.html
• Applied Abstract Algebra, by David Joyner, Richard Kreminski, Joann Turisco

GAP is of course used in Sage, so the following collection of uses of Sage in teaching is relevant as well:

http://wiki.sagemath.org/Teaching_with_SAGE

The following translations of tutorials or material to other languages were mentioned:

• GAP tutorial in Spanish, by Ramon Esteban Romero
• “Algebra and number theory with GAP” in Russian by Alexander Konovalov

Exam boards in ‘race to the bottom’

From The Telegraph:

Exam boards are competing in a “race to the bottom” where they profit by setting pupils easier tests, the head of the Wellcome Trust will say next week.

Sir Mark Walport will argue that the competitive market between the three leading exam boards has pushed standards even lower since he led a critical review of science and mathematics teaching two years ago. [The rest of the article]

Amol Rajan: An educational landmark with striking implications

From a article by Amol Rajan in The Independent:

An educational landmark has just been passed that has rather striking implications for our school system. Over the weekend, reports confirmed that pupils who speak English as an additional language (EAL) – that is, not their first – are now outperforming their native, English-speaking counterparts for the first time.

Government data, based only on results in England,shows that 80.8 per cent of EAL pupils achieved five A*-C GCSEs last year. That compares with 80.4 per cent of pupils for whom English is a mother tongue. Native English speakers are still just ahead on the five A*-C GCSEs if Maths and English are included – but EAL pupils have closed the gap since 2008, and will probably overtake them in the next couple of years.

 

Gender biases in early number exposure to preschool-aged children

A paper by Alicia Chang, Catherine M. Sandhofer, and Christia S. Brown. Journal of Language and Social Psychology, December 2011 vol. 30 no. 4 440-450. Published online before print August 25, 2011, doi: 10.1177/0261927X11416207.

Abstract

Despite dramatically narrowing gender gaps, women remain underrepresented in mathematics and math-related fields. Parents can shape expectations and interests, which may predict later differences in achievement and occupational choices. This study examines children’s early mathematical environments by observing the amount that mothers talk to their sons and daughters (mean age 22 months) about cardinal number, a basic precursor to mathematics. In analyses of naturalistic mother–child interactions from the Child Language Data Exchange System (CHILDES) database, boys received significantly more number-specific language input than girls. Greater amounts of early number-related talk may promote familiarity and liking for mathematical concepts, which may influence later preferences and career choices. Additionally, the stereotype of male dominance in math may be so pervasive that culturally prescribed gender roles may be unintentionally reinforced to very young children.

And this is from  a post in the NYT Blog, under the title Mothers Talk Less to Young Daughters About Math:

Even [when their children are] as young as 22 months, American parents draw boys’ attention to numerical concepts far more often than girls’. Indeed, parents speak to boys about number concepts twice as often as they do girls. For cardinal-numbers speech, in which a number is attached to an obvious noun reference — “Here are five raisins” or “Look at those two beds” — the difference was even larger. Mothers were three times more likely to use such formulations while talking to boys.

And this is from my collection of testimonies made by professional research mathematicians about their earliest exposure to mathematics (I collect such stories for my forthcoming book Shadows of the Truth):

My Mother told me the following story.  When I was about two and a half  a small flock of birds flew overhead.  I said: “Look, there are two and three birds”.  I didn’t yet know the number five but I understood simple counting.

What mattered was that Mother found this conversation significant.  And yes, of course, she was talking to a boy …

 

Half of maths teaching places vacant

From The Telegraph:

Figures show 46 per cent of places are empty around six months before courses start.

The Training and Development Agency for Schools, which administers the process, insisted numbers were up on last year but admitted there was “still an urgent need for even more high quality recruits”.

According to figures, some 70 per cent of places on physics courses are still unfilled.

The disclosure comes despite the introduction of generous bursary packages designed to pull graduates with top degrees into the teaching profession.

For the first time this September, £20,000 will be available for students with a first-class degree to teach maths, sciences and foreign languages. Students with a 2:1 degree are set to get £15,000 to teach the most important subjects, while those with 2:2s could receive £12,000.

Stephen Hillier, TDA chief executive, said: “Good teachers can make all the difference in bringing maths to life for pupils and raising standards.

“Mathematicians entering the profession can rest assured that they will receive rigorous training that will include strategies for managing pupil behaviour and provide them with very good preparation for the classroom.”

According to figures, 2,635 places are available on maths training courses starting in September. Some 1,432 – 54 per cent – have been filled already.

 

Specialist mathematics free schools

A special issue of The De Morgan Journal (vol. 2 no. 2) is devoted to discussion of specialist mathematics schools in various countries across the world.

• A. D. Gardiner, Introduction, pp. 1-4.
• M. Lemme, Utter elitism: French mathematics and the system of classes prépas, pp. 5-22.
• A. V. Borovik, “Free Maths Schools”: some international parallels, pp. 23-35.
• D. Yumashev, ZFTSh: A specialist correspondence school, pp. 37-41.
• P. Tanovic, Matematicka Gimnazija, pp. 43-46.
• P. Juhász, Hungary: Search for mathematical talent, pp. 47-52.
• F. Truong and G. Truc, ‘Studying in a prépa as surviving in hell’: untold episodes from a mythical media tale, pp. 53-61.
• D. Pierce, St. John’s College, pp.63-73.
• A. V . Borovik and A. D. Gardiner, Mathematical abilities and mathematical skills, pp. 75-86.
• … more papers are in the pipiline, including a paper on the specialist mathematics classes in the Fazekas Mihály School in Budapest.

Comments are welcome (just click on “Leave a reply” below). Actually, every post in this Blog is open to comments. We welcome testimonies about other schools (the Computer Science High School “Tudor Vianu” in Bucharest, for example).