Dominic Cummings on Standards in English Schools

A few posts from Dominic Cumming’s Blog touching on issues of mathematics education policy.

Standards In English Schools Part 0: Introduction

Standards In English Schools Part I: The introduction of the National Curriculum and GCSEs

Bureaucratic cancer and the sabotage of A Level reform

A random quote from Bureaucratic cancer …

Some have asked ‘how much confidence did you have in ALCAB doing a good job?’ Answer? Initially not much. They are all under huge pressure to say everything is fine. Initially for example, despite physics departments across the country  complaining about the removal of calculus from Physics A Level (complaints that practically none of them will repeat publicly because of fear of their VC office), it did not look like ALCAB would be much use and they rejected calls from various professors I know on this subject. There is massive political pressure to focus exclusively on the numbers taking an A Level rather than the quality  of the A Level.

But my hope was that by creating something that would be seen as the ‘voice of the university subject experts’, they would have to listen and adapt in order to maintain credibility and avoid embarrassing challenges. There are more and more enraged academics fed up of VC offices lying to the media and misrepresenting academics’ opinions. I thought that creating something would push the debate in increasingly sensible directions where the emphasis would be on the skills needed on arrival at university. Now, everything to do with A Levels is dominated by political not educational concerns about the numbers doing them and ‘access’. This has helped corrupt the exam system. If we had professors of physics, French, music etc every year publicly humiliating exam boards for errors, this would soon improve things from a low base and make it much harder for MPs and Whitehall to keep corrupting public exams.

Maria Droujkova: Multiplication Explorers Online Course

Multiplication Explorers Online Course

What’s so special about multiplication? To begin with, it is universal and therefore unavoidable. We all had to learn it. And our children will have to learn it too, in some shape or form. Here’s something else – the way you will help your children learn multiplication will mirror the way you learned it yourself, unless you take steps to change that. So how did you learn?

Did you spend hours repeating “the facts” with chants, flashcards, and seemingly endless drills? A lot of things have changed since we were children. There must be more effective ways of mastering multiplication! And there must be ways to make it relevant to our lives!

Let’s dig deeper. Do you remember how you felt studying the multiplication tables? For so many people we meet, the dislike and fear of math can be traced all the way back to their struggles to understand (and not just memorize) multiplication. Can we change this pattern so our children, approaching multiplication, feel not fear but curiosity, not anxiety but joy, not alienation but affinity? Can multiplication be more about smart play, rich mathematical thinking and usefulness everywhere in life?

This is what our Multiplication Explorers course is all about. It explores holistic approach to learning multiplication. Memorization based on smart number patterns is a part of it. The course also includes bridges between multiplication and natural world, as well as links to many virtual and imaginary worlds in books, music, technology, art, and games.

We invite you to boldly go beyond the familiar representations of multiplication such as skip counting and repeated addition, to explore many more meaningful, beautiful, and fun models. This course is a launch pad to adventures across the universe of multiplication.

Register Button

Carter review of initial teacher training

Report from Sir Andrew Carter, chair of the independent review of the quality and effectiveness of initial teacher training (ITT) courses. [pdf] The report sets out how the ITT system is performing and highlights examples of good practice as well as areas for improvement. The government’s response to the review is also available.

Some recommendations of the report relevant to mathematics departments in universities:

  • Recommendation 1a: Subject knowledge development should be part of a future framework for ITT content.
  • Recommendation 1b: Issues in subject-specific pedagogy, such as pupil misconceptions, phases of progression in the subject as well as practical work, should be part of a framework for ITT content.
  • Recommendation 3: Schools should include subject knowledge as an essential element of professional development.
  • Recommendation 4: DfE should make funded in-service subject knowledge enhancement courses available for new primary teachers to access as professional development.
  • Recommendation 5: Universities should explore offering “bridge to ITT” modules in the final years of their subject degrees for students who are considering ITT programmes.
  • Recommendation 8: There are many universities that are home to world-leading research and assessment organisations – yet in our experience it can be the case that these organisations are either not involved in ITT or are involved in a superficial way. ITT partnerships should make more systematic use of wider expertise outside university departments of education.
  • Recommendation 13: All schools should, whenever practically possible, seek out and participate in robust local partnership arrangements. In a school-led system, this recommendation is naturally the responsibility of schools.

The Government response to the Carter review of initial teacher training (ITT) is difficult to interpret. Department for Education has no control over universities (the only serious providers of “subject knowledge”), and is therefore is unable to formulate a coherent policy of improvement of teachers’ subject knowledge. The deliberate attempt to shift ITT away from universities – towards a school-based, apprentice training model is a very recent and peculiarly English idea, whose (real and potential) flaws do not seem to be recognised in either the report or the government response.

Disclaimer: writing for this blog, I act in my personal capacity; the views expressed here are my own and do not necessarily represent position of my employer, or the London Mathematical Society, or any other organisation or institution.

Mathematical practice: Job opportunity

I am seeking to fill two research assistant posts, one in Oxford, one in Edinburgh.
The description in the job-ad is fairly open, as I am looking for flexibility in thinking about new ideas, and ability to deliver on written work,  rather than any particular technical specialism. The survey paper is the best guide to the thinking.
Professor Ursula Martin CBE
Professor of Computer Science
University of Oxford

Yagmur Denizhan: Performance-based control of learning agents and self-fulfilling reductionism.

Yagmur Denizhan: Performance-based control of learning agents and self-fulfilling reductionism. Systema 2 no. 2 (2014) 61-70. ISSN 2305-6991. The article licensed under the Attribution-NonCommercial-NoDerivatives 4.0 International License. A PDF file is here.

Abstract: This paper presents a systemic analysis made in an attempt to explain why half a century after the prime years of cybernetics students started behaving as the reductionist cybernetic model of the mind would predict. It reveals that self-adaptation of human agents can constitute a longer-term feedback effect that vitiates the efficiency and operability of the performance-based control approach.

From the Introduction:

What led me to the line of thought underlying this article  was a strange situation I encountered sometime in 2007 or 2008. It was a new attitude in my sophomore class that I never observed before during my (by then) 18 years’ career. During the lectures whenever I asked some conceptual question in order to check the state of comprehension of the class, many students were returning rather incomprehensible bulks of concepts, not even in the form of a proper sentence; a behaviour one could expect from an inattentive school child who is all of a sudden asked to summarise what the teacher was talking about, but with the important difference that –as I could clearly see– my students were listening to me and I was not even forcing them to answer. After observing several examples of such responses I deciphered the underlying algorithm. Instead of trying to understand the meaning of my question, searching for a proper answer within their newly acquired body of knowledge and then expressing the outcome in a grammatically correct sentence, they were identifying some concepts in my question as keywords, scanning my sentences within the last few minutes for other concepts with high statistical correlation with these keywords, and then throwing the outcome back at me in a rather unordered form: a rather poorly packaged piece of Artificial Intelligence.
It was a strange experience to witness my students as the embodied proof of the hypothesis of cognitive reductionism that “thinking is a form of computation”. Stranger, though, was the question why all of a sudden half a century after the prime years of cybernetic reductionism we were seemingly having its central thesis1 actualised.

Ivor Grattan-Guinness obituary

From The Guardian, by Tony Crilly

Energetic historian of mathematics and logic

When Ivor Grattan-Guinness, who has died aged 73 of heart failure, became interested in the history of mathematics in the 1960s, it was an area of study widely considered to be irrelevant to mathematics proper, or something that older mathematicians did on retirement. As an undergraduate at Oxford, he found that mathematics was presented drily, with no inkling of the original motivations behind its development. So Ivor set himself the task of asking “What happened in the past?” – as opposed, he said, to taking the heritage viewpoint of asking “How did we get here?”

Read in full.

Ivor Owen Grattan-Guinness, historian of mathematics and logic, born 23 June 1941; died 12 December 2014

MBE to a maths clubs volunteer

From BBC:

A man who runs free maths classes for primary age children has been recognised in the New Year Honours list with an MBE.

Gbolahan Bright has been running the Bright Academy maths clubs for primary age children in London and Essex for the past 20 years.

“I have gained a lot from this society. I have been blessed and it would have been ungrateful of me if I did not give back,” he said.

Of the 500 or so children who have taken the classes, about 50 gained their GCSE while still at primary school.

Read more.

Retraining 15,000 teachers?

Philip Nye writes in a paper  Cameron needs to rethink maths and science plan (12 Dec 2014) that

Under No 10’s plan, 15,000 teachers of other subjects will also retrain as maths or physics teachers, as part of a “major push” to boost maths, science and technology skills.

However, Professor Alan Smithers, director of the Centre for Education and Employment Research at the University of Buckingham says: “It’s really easy to say ‘well, physics is science, so therefore there’ll be people teaching biology, or who have done medicine or engineering [degrees] that we can retrain as physics teachers’. But biology is really as different from physics as, say, history is.”

Perhaps the same skepticism can be applied to mathematics.

Mathematics Resilience – making it happen

The Shard Symposium

16th January 2015 10am – 4pm

Evidence is accruing that Mathematical Resilience is fundamental to developing a numerate, empower society. You are cordially invited to attend a symposium designed to explore the next steps to be taken in enabling learners to become Mathematically Resilient.

The symposium is convened to bring together practitioners, funders and researchers to discuss what is happening in enabling learners to develop Mathematical Resilience. It is a precursor to an international conference that will be held jointly by University of Warwick and Open University in November 2015.

The symposium will be held at the Warwick University Business School Offices in The Shard, 32 London Bridge Street, London, SE1 9SG, nearest underground station London Bridge.

A small charge of £20 is payable for registration, this will be made to cover refreshments throughout the day. You can register for the event here.