A view from USA: “Why can’t we teach math?”

From a post  The School CEO: Why can’t we teach math? by  Jeanne Whitmore in American Fork Citizen, 29 September 2012:

I had a parent ask me why we don’t teach Compass and Straight edge Geometry anymore. Thank goodness he gave me a link to the Wikipedia article to explain what it is. (Here it is if you are interested.) I would love to explain to him why we don’t teach this particular type of geometry, but I don’t know. I couldn’t teach it; I don’t know if I could learn it.

But why could we teach it at one point, and we can’t now? As a Charter School CEO, it is difficult to get math and science teachers. Math and science teachers can make a lot of money in the private sector and schools have difficulty competing.

Mathematicians can earn a median wage of $99,000 and people in Math and Science occupations earn a median income of $74,040. It’s no surprise that people with Math backgrounds don’t want to earn a starting salary of less than $30,000 per year at an elementary school or high school. Granted there are teachers who only desire to teach and love the atmosphere of the school, but these are few and far between. A school would be lucky to get a great mathematician who

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has already retired from a non-education career then decided to teach as a second career.

But, let’s assume that mathematicians have always earned a much higher income than the general population. Why was it possible to hire a mathematician in the 40’s and 50’s, but not now? Well, the jobs that can use mathematics have exploded. Whole classes of occupations didn’t exist in the 40’s that exist now.

Look at this list of occupations: Actuary, Computer programmers, Computer Systems Analyst, Database Administrators, Financial Analyst, Market Research Analyst, Nuclear Engineer, Operations Research Analyst, Statistician and Survey Researcher. Many of these classes of jobs didn’t exist in the 40’s and even if they did exist, the computer revolution and Internet have enabled massive data collection that have increased the number of jobs in every field related to data analysis and statistics.

A research paper published in the National Bureau of Economic Research in 1957 showed that 87.4% of mathematicians worked in colleges and universities. Now, only 16% work in education with 63% working in the Federal Government and Scientific Research.

We can’t compete with the increasing demand for mathematicians from the private sector in salaries, benefits or work environment. But, if we can’t teach math in elementary and high school to the same standards we did in the 40’s and 50’s where will our next generation of mathematicians come from?

It is almost like the worm eating its own tail. We are chewing up the mathematicians we created in previous generations and we are not creating the new generations of mathematicians to take their place.

Today we can’t have a math teacher teach “Compass and Straight edge Geometry” because they were not taught that by their teachers.

Jeanne Whitmore is the founder and CEO of American Fork charter school Aristotle Academy, and an education columnist for the American Fork Citizen. Here is the document cited in the post: Study of math profession occupations, 1957.

 

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Proof of concept

This blog was set up in October 2011. On 27 September 2012, less than a year later, the number of visits to the blog has reached a healthy 100,000 (look at the tiny dial at the top of the sidebar).

In my opinion, the blog serves as proof of the feasibility of a blog/journal hybrid for electronic publication: a free-flowing discussion blog for a professional community and a scholarly journal for more substantial contributions, cross-linked and providing ample opportunities for post-publication review and discussion.

At the time when the “author pays” model of open access publishing has become the focus of debate in academia (see the discussion on the sister blog, LMS Members) , The De Morgan Journal dispels  a few misconceptions. It positively proves that

• free for authors and for readers channels of distribution of (pre-publication and/or post-publication peer-reviewed)  research work are easily attainable even for relatively small academic communities (in our test case: the mathematics education community represented by the LMS Education Committee);
• achieving decent technical quality of texts is not a problem; this blog supports ( LaTeX ). For an example of sophisticated typesetting of mathematics, have a look at the paper by David Pierce;
• electronic internet publishing could be very cheap for people who run it (for this blog, the costs of hosting the blog are absorbed by the London Mathematical Society and are hard to quantify, but to give some idea of market prices, hosting of a similar blog on WordPress would cost 26 pounds per annum);
• the main costs of academic publishing are covered by unpaid work of authors, reviewers, editors;
• modern technology allows one to aggregate even small, 15 minutes at a time, contributions from authors  and commentators into a valuable and meaningful total;
• this low-cost aggregation of collective effort is possible, however, only when the venture is run on a strictly not-for-profit basis (in a for-profit model, running costs immediately jump by several orders of magnitude because of need for expensive business infrastructure, costs associated with regulatory compliance, accounting, payment of taxes, etc.)

But enough about economics.

Blogs grow organically, like trees; they need some maintenance, attention and care, not much, but regular, like the watering of a garden. But what matters is the quality of content, something which is beyond the control of a humble blog administrator like me.  Even when this blog was still a seedling, it already attracted support and high quality input from the community — this is why it was able to make useful contributions to education policy discourse (see, for example, A draft school mathematics curriculum for all written from a humane mathematical perspective: Key Stages 1–4 and papers on specialist mathematics schools — they played constructive role in policy discussions).  I use this opportunity to thank all content providers: authors, contributors, editors who helped this blog to reach maturity.

Alexandre Borovik

David Wells: Can mathematicians help?

D. G. Wells,  Can mathematicians help? The De Morgan Journal 2 no. 4 (2012) 1–4.

Abstract:

Professional mathematicians have not made the contributions to the teaching of mathematics in schools that might have been expected, in part, at least, because of their failure to appreciate the processes of conceptualisation and reconceptualisation that lie behind good maths teaching and lead young children from naïve concepts, objectionable perhaps to the professional, in time to more sophisticated and professionally acceptable interpretations. Illustrated

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by the idea that ‘Multiplication is repeated addition.’

Key Stage 4 qualification reform – Secretary of State’s announcement

From DfE:

In the core academic subjects that make up the English Baccalaureate – English, mathematics, sciences, history, geography and languages – the Government intends to replace current GCSE with new qualifications, to be called “English Baccalaureate Certificates”.  The Government will be moving away from the competition between Awarding Organisations to sell their qualifications in these subjects.  Instead of schools choosing between a number of competing GCSEs in these subjects, a competition will be held to identify a single suite of qualifications, offered by a single Awarding Organisation in each subject, for a period of five years.

 A public consultation on these reforms has been launched, which will run until 10th December.  This can be accessed [here].

Click here for quotes from the Consultation Document:

No A* grades, endless re-sits or marks for coursework?

From Daily Mail:

Michael Gove is to herald an end to a quarter of a century of ‘dumbed-down’ exams this week when he abolishes GCSEs and brings back a tough new O-level style system.

The Education Secretary will announce the new exams on Tuesday in a joint press conference with Liberal Democrat Deputy Prime Minister Nick Clegg […]

Under Mr Gove’s shake-up, the

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current system whereby nearly three in ten pupils get A or A* grades will go. Instead as few as one in ten will get the top mark, Grade 1. […]

Marks will depend on a traditional ‘all or nothing’ three-hour exam at the end of the two-year course […]

[…] questions in the new exam will be graded, starting with easy questions and building up to difficult questions which will stretch the cleverest pupils.

It means that less able pupils may be unable to complete the paper.[…]

In addition, the new exams will be run by a single exam board following complaints that competition between rival boards is driving down standards. Read more.

And from BBC:

But pupils will not start studying for it until September 2015, after the next general election. The first exams would be taken in 2017.

Watch this space: GCSEs to be set by just one exam board to halt decline?

From The Telegraph:

Competing exam boards will be abolished under sweeping reforms to GCSE-level qualifications to be set viagra soft out by the Coalition next week. […]

Mr Gove hinted at next week’s plans when he appeared before the Commons education committee this week.

The Commons Education  Select Committee’s records are still not published, so we have to wait for details.

Some descriptions of mathematics

I. Mathematics is an exact language for description, calculation, deduction, modeling, and prediction — more a systematic way of thinking than a set of rules.

Mathematics is the language in which it is impossible to make a nebulous or imprecise statement.

Using a legal analogy, mathematics is a language for writing contracts with Nature that Nature accepts as legally binding.

II. The practical importance of mathematics lies in its ability to describe the real world.

The real world consists of what matters. The word “matter” as a noun is used for what the physical world is made of. But if we ask, “What’s the matter with Anne?” we may be asking about a physical ailment, or we may be asking about an idea that is causing Anne to behave strangely. Ideas matter.

The whole point of mathematical education is to make ideas real for students, ideas that were not real for

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them before. Ideas like fractions, for example. The fact that 2/3 is smaller than 3/4 matters in the real world.

III. Mathematically educated people are stem cells of a technologically advanced society. Because of the universality of mathematics, mathematicians and well educated users of mathematics are flexible in applying and inventing tools for work in technological environments which never existed before.

IV. Learning mathematics involves the profound assimilation of intellectual and aesthetic criteria as well as practically orientated ones. The very difficulty in learning mathematics makes it a personality-enhancing experience.

[With contributions and borrowings from David Corfield, Tony Gardiner, Michael Gromov, Niall MacKay, Henri Poincare, Frank Quinn, David Pierce.]

Steven Strogatz: Singular Sensations

A masterpiece of popularisation of mathematics, by Steven Strogatz in the  NYT: fingerprinting, the index theorem and works by  L. S. Penrose, “Dermatoglyphic topology,” Nature, Vol. 205 (1965), pp. 544–546, and  R. Penrose, “The topology of ridge systems,” Annals of Human Genetics, Vol. 42 (1979), pp. 435–444.

Gove pushes on with plans for the return of O-levels

From Mail Online:

Michael Gove will this week press ahead with reforms designed to fix the ‘broken’ exam system as he vows to replace GCSEs with a more rigorous, O-level style of exam.

The Education Secretary is expected to unveil plans to introduce a new qualification before the next election in 2015, arguing that GCSEs ‘haven’t worked’. […]

The proposals will be put out for consultation before the new examination is introduced in 2014.

The Education Secretary says the Government will consult experts, teachers and parents on what the new examination, and its grades, should be called.

‘The aim is to ensure that we have an examination that recognises the genuinely academically gifted by making sure that top grade, an A or whatever it might be called, is clearly a sign of someone who is a high flier, but at the same time, this examination, we hope, will ensure that all children – we hope the majority will take it at 16, some may take it at the age of 17 or 18 – that all children can have their fluency in English, mathematics and other subjects like history and physics recognised.”

Read more

Few Indian students opt for mathematics in UK

From Hindustan Times:

The reduced number of Indian students this year has led to concerns in some British universities over the financial viability of courses andd departments particularly in the subjects of Science, Technology, Engineering and Mathematics (STEM). As universities report a drop of between 20% and 30% of Indian students in the forthcoming academic year starting later this month, the drop has caused much concern over the future of STEM courses that have been popular among postgraduate Indian
students.

In oral evidence presented to the Business, Innovation and Skills Committee of parliament, senior figures in higher education and industry noted the concern among vice-chancellors about the impact of less Indian students on the financial viability of STEM courses.

The committee, which published its report on ‘Overseas Students and Net Migration’ last week, recommended that Indian and other non-EU students should be removed from overall immigration figures since most of them return home after their courses.

The recommendation, however, was rejected by the government keen to cut immigration from outside the EU. Nicola Dandridge, chief executive of Universities UK, which represents varsities and higher education institutions,
told the committee that vice-chancellors were “concerned” about the impact of less Indian students on STEM subjects. She said: “I think it is too early to draw apocalyptic conclusions about the closures of departments.

It is apparent now, because of the reduction of Indian students — students coming from the Indian subcontinent to study STEM subjects — that is where there are already questions being asked about the sustainability of certain
subjects”.