American Mathematical Society leads the way

American Mathematical Society leads the way in publication of high quality mathematics books for school mathematics teachers. Here are two latest examples:

Mathematical Circle Diaries, Year 1: Complete Curriculum for Grades 5 to 7
Anna Burago,
Prime Factor Math Circle, Seattle, WA

A co-publication of the AMS and Mathematical Sciences Research Institute.

Early middle school is a felicitous time for children to begin their mathematical circle education. Math circles expose children to the type of mathematics that stimulates development of logical thinking, creativity, analytical abilities, and mathematical reasoning — skills that, while scarcely touched upon at school, are in high demand in the modern world. This book contains everything that is needed to run a successful mathematical circle for a full year, distributed among 29 weekly lessons: detailed lectures and discussions, sets of problems with solutions, and contests and games, plus valuable know-how on the running of a circle. The book is based on the author’s extensive experience teaching math circles in the Seattle area and on the compilation of materials from these circles.

Integers, Fractions and Arithmetic: A Guide for Teachers
Judith D. Sally,
Northwestern University, Evanston, IL, and Paul J. Sally, Jr., University of Chicago, IL

A co-publication of the AMS and Mathematical Sciences Research Institute.

This book, which consists of twelve interactive seminars, is a comprehensive and careful study of the fundamental topics of K – 8 arithmetic. The guide aims to help teachers understand the mathematical foundations of number theory in order to strengthen and enrich their mathematics classes. Five seminars are dedicated to fractions and decimals, and the remaining seminars cover standard topics in detail, albeit in a slightly unconventional order. The book is intended for the professional development of teachers and is appropriate for teacher education programs, as well as for enrichment programs such as Mathematical Circles for Teachers.


A response to Aaron Sloman

A response to: Aaron Sloman, Is education research a form of alchemy?

David Wells

Aaron Sloman after a very distinguished fifty-year career is currently the still active Honorary Professor of Artificial Intelligence and Cognitive Science at the University of Birmingham. His conclusions in this article, as he admits,

“are not the theories of a specialist researcher in education or educational technology”

but are strictly from his own AICS perspective, plus his experience of teaching programming and AI and related subjects to undergraduate students.

My perspective is essentially that of a primary and secondary mathematics teacher who has long taken an interest in educational research, so I was immediately suspicious of his title, which he attempts to justify like this:

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Who wrote the KS 1-2 mathematics curriculum?

Adapted from ‘s article in The Guardian:

The coalition’s curriculum review, which began in January 2011 and in June 2012 produced draft proposals for English, maths and science in primary schools – the secondary version has yet to appear – has been dogged by

allegations of secrecy. […]

When it comes to the draft primary maths curriculum, most close observers of the review say that much of the writing was done by the late Richard Dunne […]

Survey for teachers of mathematics and science

This survey is part of the Institute of Education‘s work for The Royal Society project “Vision for Science and Mathematics Education 5-19”. A quote:

The Royal Society’s objectives include support for the development of a world class education system in science and mathematics as a contribution both to research and to UK economic competitiveness.  The current research is aimed at helping to redress identified shortcomings in current provision relating to teachers and the science and mathematics workforce, leadership and ethos within schools and colleges, infrastructure and accountability.

What surprises me is that such issues as subject knowledge and mathematical competence of mathematics teachers are not even mentioned in the survey. Look at relevant questions in the survey — they do not mention that!

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More on ban of calculators in tests for 11-year-olds

Press release from DfE and discussion of underlying statistics in A table from

based on Trends in International Mathematics and Science Study (TIMSS):

From TIMSS 2007: England rank bottom of all sampled countries for restricting calculator use in the maths classroom


Colors of Math

Documentary filmmaker Ekaterina Eremenko is famous for unique, innovative documentaries. Her new film Colors of Math (The Russian title, Чувственная математика – Sensual Mathematics – is better) is an intellectually stimulating and beautifully shot film invites us to look at mathematics from a new angle – as the arena of the senses. To most people mathematics appears abstract, mysterious. Complicated. Inaccessible. But math is nothing but a language to express the world. Mathematics can be sensual. In this documentary, the beauty of mathematics, its sounds, colors, taste, and texture are revealed through the eyes of contemporary mathematical geniuses Cédric Villani, Aaditya V. Rangan, Jean-Michel Bismut, Günter Ziegler, Maxim Kontsevich, and Anatoly Fomenko.

Get more information on the film at, and watch the trailer here. Judging by the trailer, the film deserves promotion by mathematicians.

A still from the film:

Ofqual announces changes to A levels

A press release from Ofqual:

Ofqual has today (Friday, 9 November) announced that from September 2013 students in England will no longer be able to sit A level exams in January, after the proposal received strong support following a three month consultation into A level reform. The change will also address recent concerns over how many times students can sit their exams by reducing resit opportunities. […]

Key findings from the consultation are published today and show support for:

  • the principle of higher education engagement with A level design, however there was less support for universities “endorsing” each A-level
  • students being assessed at the end of each of their first and second year of study
  • the removal of January exams and reduced resit opportunities
  • increasing synoptic assessment in A levels, allowing students to integrate and apply their skills, knowledge and understanding with breadth and depth
  • reducing internal assessment.

Full text of the press release. Related reports:


Calculators banned in primary school maths exams

By  in  The Telegraph:

Calculators are to be banned in primary school maths exams as part of a Government drive to boost standards of mental arithmetic, it was announced today.

Pupils will be required to complete sums using pen and paper amid fears under-11s in England are already more reliant on electronic devices than peers in most other countries.
The change – being introduced from 2014 – coincides with the publication of a draft primary school curriculum that recommends delaying the use of calculators as part of maths lessons.
Currently, children are expected to use them at the age of seven, but this is likely to be put back to nine or 10 under the Coalition’s reforms.
Elizabeth Truss, the Education Minister, said that an over-reliance on calculators meant pupils were failed to get the

rigorous grounding in mental and written arithmetic that they needed to progress onto secondary education.
Pupils should not use the devices until they know their times tables off by heart and understand the methods used to add, subtract, multiply and divide, she said.

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