Specialist mathematics free schools

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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.
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).

Preparedness of new undergraduates for degree level study

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At Cambridge Assessment, which is a department of the University of Cambridge and the parent organisation of three awarding bodies, researchers have been exploring the perceived preparedness of new undergraduates for degree level study.

Three strands of research have been completed:

  • A questionnaire survey of 633 university lecturers (including 179 mathematics lecturers) on the impacts of qualifications for 16 to 19 year olds on higher education
  • Focus groups on lecturers’ views about the effectiveness of curricula for 16 to 19 year olds as preparation for university
  • A literature review on the pedagogical differences between A Level and university.

The research focuses primarily on mathematics, biology, and English. Both qualitative and quantitative methods were used as part of a ‘mixed methods’ approach.

Summaries of the research are available at:

http://www.cambridgeassessment.org.uk/ca/Viewpoints/Viewpoint?id=139723

Full reports can be requested from the same website.

There are several key findings relating to mathematics:

  • There is a healthy appetite among mathematics lecturers for engagement in research exploring the transition from A level to higher education.
  • Over half of mathematics lecturers think that mathematics undergraduates are underprepared for degree level study.
  • ICT, teamwork, intellectual curiosity are the skills and attributes likely to be considered strengths of typical mathematics undergraduates when they begin degree level study.
  • Most lecturers think that academic writing, self-directed study, independent inquiry and research, and critical thinking skills are weaknesses of typical undergraduates when they begin degree level study. Depth of subject knowledge is also a concern for most mathematics lecturers.
  • Mathematics, further mathematics, and physics are the A level subjects considered by mathematics lecturers to provide the best preparation for a mathematics degree.
  • Biology, chemistry and mathematics are the A level subjects considered by biology lecturers to provide the best preparation for a biology degree.
  • More generally, history, English and mathematics are the A level subjects considered to provide the best preparation for degree level study by lecturers across a wide range of subjects.
  • According to almost 60% of mathematics lecturers, their institutions provide additional support classes for underprepared 1st year undergraduates.
  • Over 60% of mathematics lecturers have had to adapt their teaching approaches to teach underprepared 1st year undergraduates.

The research received considerable media attention at the start of April, when emerging findings were presented at a UCAS conference in Birmingham. The presentation coincided with an exchange of letters between the Secretary of State for Education and the national regulator, Ofqual, setting out a new policy in which Higher Education is to have more influence on the development of future A levels.

The three strands of research form part of a wider research programme which extends over several years. This work is an important means of restoring and strengthening links between qualifications developers and HE.

Ofqual: Comparison of A Levels with International Qualifications

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Report published by Ofqual purports to address, among others, the following issues:

Issue 3: Different levels of demand within mathematics – The number of different mathematics assessments at a variety of levels available to students in many education systems was also in contrast to A level Mathematics. Is there a need for A level Mathematics to have further lower-level options in addition to AS?

Issue 4: Breadth versus depth within mathematics – Within the more challenging mathematics courses considered, A level Mathematics is unusual in covering both pure mathematics and the application of mathematics in the same course. While this means that more fields within mathematics are available to study, other education systems include more demanding mathematics which an A level student can only access through additional A level courses. Would a more focused A level mathematics course better serve the needs of more capable mathematicians?

Issue 5: Specialism within mathematics – A level Mathematics includes optional routes. This means students with the same grade in the qualification may not be equally well prepared for a specific further course of study. Would distinct qualifications, building on a mathematical core but emphasising the different specialisms, better serve students and those seeking to match them to appropriate further opportunities?

Pdf file of the report: Comparison of A Levels with International Qualifications.

A report on the pilot of the linked pair of GCSEs in mathematics

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AlphaPlus Consultancy prepared for DfE The independent evaluation of the pilot of the linked pair of GCSEs in mathematics (MLP): Second Interim Report. This is the third of seven formative evaluation reports on the pilot of the linked pair of GCSEs in mathematics (MLP). A final summative evaluation report will be presented in December 2013.

A quote from p.6:

Problem solving and functionality are central to mathematics at Key Stage 4 (KS4). The previous reports on the MLP [Mathematics Linked Pairs] have identified the lack of a shared understanding by centres of what problem solving and functionality mean in relation to mathematics teaching and learning generally and in particular in relation to the revised assessment objectives (AOs) for GCSE mathematics. The fact that stakeholders have no common definition for these terms across the range of instances and contexts in which they use them, such as the two MLP qualifications, is problematic. An absence of clear definitions might lead stakeholders to fail to recognise and understand the different types of problem solving which the structure of the MLP promotes. The two previous MLP reports indicated that both effective teaching and assessment of problem solving and functionality are still in relatively early stages of their development. This is not an issue specific to the MLP: centres offering the MLP together with the single GCSE, awarding organisations and wider stakeholders all suggest that the issues regarding the teaching of problem solving are also evident for the single GCSE in mathematics.

Ofqual – Standards Review

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Ofqual published Review of Standards in GCSE Mathematics 2004 and 2008. Principal findings:

  • The major change that affected all GCSE mathematics examinations between 2004 and 2008 was a move from a three-tier examination system of foundation, intermediate and higher tiers to a two-tier system, comprising foundation and higher only. These changes had a significant effect on the demand of the examination by changing the balance of questions focused on each grade.
  • The spread of grades to be covered in each tier increased and in some awarding organisations this resulted in a rise of structuring within questions. In addition question design showed an increasing trend towards structuring of questions. Both factors made examinations less demanding over time.
  • The increasing numbers of centres entering students for specifications with modular examinations highlighted a mixed effect on demand. OCR’s modular assessment design minimised the effect of the changes and allowed standards to be maintained over time, whereas AQA’s modular design (also available in 2004) fragmented the assessment and increased structuring in questions, making the examinations less demanding.
  • The layout of question papers, the language used and the clarity of graphs and diagrams had all improved over the time period reviewed, providing a better quality assessment in mathematics.

Wolfram Alpha, a year later

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On 1 April 2011 I wrote to Wolfram Research:

I had a look at Wolfram Alpha and was slightly surprised that [it] returned, among many useful information about the matrix

12
01

the assertion that it had eigenvectors

(1,0) and (0,0).

You and I, of course, understand how to interpret the answer, but it could be quite confusing for a first year student.

I tried it again today, I got the same answer; see for yourself.

Eigenvectors as returned by Wolfram Alpha

GCHQ releases two Turing papers

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From ZDNet UK:

GCHQ has released two mathematical papers written by cryptographer Alan Turing after keeping the works secret for over half a century.

The intelligence agency believes the handwritten papers were produced by Turing during his time at Bletchley Park, the World War Two code-breaking centre, GCHQ said in a press release on Thursday. [...]

One of the papers, the informal ‘Paper on Statistics of Repetitions‘, seeks a means to tell whether two enciphered messages with different plaintext and an overlap of characters used the same encipherment key during the overlap.

The second paper, ‘The Applications of Probability to Cryptography‘, was possibly written between April 1941 and April 1942, as it contains the reference ‘Hitler is now of age 52′. The paper uses probability analysis to look at four problems: ‘Vigenère’, ‘A Letter Substitution Problem’, ‘Theory of Repeats’, and ‘Transposition Ciphers’, said GCHQ. [...]

The two papers have not been digitised, and only currently exist in handwritten form. People wishing to read the papers need to travel to the National Archives at Kew with the reference numbers of the papers, and two forms of ID — a picture ID, and proof of address. People who do this will probably be given a reader ticket number, which will then allow them to request the papers for viewing.

Programming project comes to primary schools

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BBC about the Code Club project. A quote:

Volunteers have kicked off a project to set up after-school clubs that teach young children how to programme computers.

Called Code Clubs, the sessions will aim to instil the basics of computer programming into children aged 10-11.

The clubs will be built around practical hands-on tasks that will include children making games and eventually controlling robots.

It aims to have 25% of the UK’s primary schools running a Code Club by 2014.

And more from BBC: Learning to code. A quote:

Alasdair Blackwell, our main tutor and the co-founder of Decoded, is an impressive evangelist for the open web, and the need to give ourselves the tools to make best use of it.

He argues that today’s teenage iPad users, far from being digital natives, actually have less understanding of what makes computers tick than his generation, who got their hands dirty with machines like the BBC Micro. “The children playing on iPads, I actually despair for them because they’re just using software, not creating software for themselves.”

Meanwhile, First Raspberry Pi computers to be delivered.

Cultures of Mathematics and Logic (China)

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9-12 November 2012
Institute for Logic and Cognition
Sun Yat-Sen University
Guangzhou, China
http://www.math.uni-hamburg.de/home/loewe/Guangzhou2012/

All researchers working on various aspects of “Cultures of Mathematics and Logic”, including, but certainly not limited to, philosophers, sociologists, historians of mathematics, mathematicians, and researchers in mathematics education, are cordially invited to submit their one page abstracts by the submission deadline of 30 June 2012 (see below for details).

DESCRIPTION OF THE CONFERENCE. Mathematics and formal reasoning are fundamental building blocks of knowledge, essential for science, technology, policy-making and risk-management. Mathematical practice is a rich phenomenon of human activity, with subtle differences between various cultures: here, the word culture can refer to national cultures, but also cultural differences in different historical periods, in different strata of a given society, in different social settings.

And yet, the public perception of mathematics is of an apersonal subject with little or no human interaction, based on a false picture of a science of pure thought and deduction, with almost no interaction or visible activity.

In a move away from these traditionalist positions, philosophers and social scientists have recently become more interested in studying mathematical and logical practice, or, to be precise, different mathematical and logical practices. Our conference will focus on this plurality of viewpoints, studying the various cultures of mathematics and logic, and involve several disciplines such as philosophy, sociology, psychology, cognitive science, history of mathematics, mathematics education, and linguistics.

KEYNOTE SPEAKERS.

* Andrea Bender. Universität Freiburg, Freiburg, Germany.
* Karine Chemla. Equipe Recherches Epistémologiques et Historiques sur les Sciences Exactes et les Institutions Scientifiques (REHSEIS), Paris, France.
* Christian Greiffenhagen. University of Manchester, Manchester, United Kingdom.
* Shirong Guo. Inner Mongolia Normal University, Hohhot, China.
* Juan Pablo Mejía Ramos. Rutgers University, Piscataway NJ, United States of America.
* Reviel Netz. Stanford University, Stanford CA, United States of America.
* Zhaoshi Zeng. Sun Yat-Sen University. Guangzhou, China.

IMPORTANT DATES.

Abstract submission deadline: 30 June 2012
Notification of authors: 30 July 2012
Conference: 9-12 November 2012

ABSTRACT SUBMISSION. All researchers are encouraged and invited to submit their abstracts until the deadline of 30 June 2012 via the easychair submission page at

https://www.easychair.org/conferences/?conf=cml2012

Please submit the abstract either in the “abstract” field of the easychair submission site or as a one-page PDF submission.

POST-CONFERENCE PUBLICATION. All authors of papers presented at the conference will be encouraged to submit a full version to a post-conference publication volume. The deadline for submission of full papers will be in early 2013. All papers submitted to the post-conference proceedings will be refereed to high journal standards, and acceptance as a presentation is no guarantee that the post-conference paper will be published.

PROGRAMME COMMITTEE. Mihir Chakraborty, Jadavpur University, India; Shuchun Guo, Chinese Academy of Science, China; Joachim Kurtz, Ruprecht-Karls-Universität Heidelberg, Germany; Brendan Larvor, University of Hartfordshire, United Kingdom; Benedikt Löwe, Universiteit van Amsterdam, The Netherlands; Martina Merz, Universität Luzern, Switzerland; Dirk Schlimm, McGill University, Canada; Ju Shier, Sun Yat-sen University, China

LOCAL INFORMATION. Guangzhou, known historically as Canton, is located in southern China on the Pearl River, about 120 km north-northwest of Hong Kong. With over 12 million inhabitants, it is the third largest city in China (after Shanghai and Beijing) and the largest city of southern China.
In the month of November, expected temperatures are between 15 and 24 degrees. Baiyun International Airport is a major transportation hub with many national and international airlines (for instance, Air France, China Southern Airlines, Emirates, Lufthansa, etc.). In addition, Guangzhou is easy to reach from Hong Kong with its international airport.