# Government ‘considers lowering AAB threshold’

The previous story is more relevant to mathematics if one takes into account an earlier news, also from THE and also by  John Gill.

Delays to the annual grant letter may be down to government plans to announce an easing of the AAB rules that are to introduce competition for students between institutions.

From 2012-13, universities will be able to recruit as many students as they want provided they have grades of AAB or better at A-level, part of a two-pronged plan by the coalition to introduce competition into the sector. […]

AAB threshold has a potential to seriously affect uptake of Mathematics and especially of Further mathematics A levels by schoolchildren. Therefore the following news is of importance and needs a careful assessment. John Gill:

Now it has been suggested that the government, which has indicated a desire to extend the policy in future years, is planning to lower the grade limit to ABB in 2013-14.

The Times newspaper says the proposal had been due to be included in the grant letter, which had been expected to be sent out to institutions yesterday.

It reports that but that ministers have asked the Higher Education Funding Council for England for additional analysis on its potential impact, resulting in further delay to the letter.

The paper quotes an unnamed “government source” as saying: “Our view is that we would like to move to ABB.”

# HE bill ‘to be shelved indefinitely’

From THE, by John Gill:

David Cameron is reported to have made a dramatic intervention in the university reforms, shelving the higher education bill that was due this spring.

According to the Daily Telegraph, the bill, which would have introduced major regulatory reform including new legislation making it easier for private providers to enter the market, is now unlikely be published before 2015.

The paper quotes an unnamed Whitehall source as saying: “The Liberal Democrats were increasingly opposed to further reforms to universities after the recent decision to increase fees.

“But David Cameron was also unimpressed by the recommendations so the whole thing is now off the table.”

David Willetts, the universities and science minister, told the paper: “There’s going to be a further discussion in Cabinet in the next couple of weeks. There’s no final decision either way yet.” […]

However, many of the other reforms that have already been implemented, such as the increase in the tuition fee cap to £9,000 this autumn and the ‘core and margin’ and AAB plans, which will see student places removed from general allocations and thrown open to competitive bids, will not be affected.

[The Telegraph story is published under the title American-backed private universities plan dropped.]

# Turnitin in mathematics

The Turnitin tool gives a lot of false positives, e.g., the project of my UG student has a Turnitin score of 13% although no text is really copied from elsewhere. The student writes down 9 terms of the Baker-Campbell-Hausdorff formula, and 6 of them are “flagged” by Turnitin as matching two different sources.

# Mathematical Needs, a report by ACME: A brief review of the methodology of the report

All opinions expressed in the present post are of the author and no-one else. More specifically, all views expressed here may or may not represent the position of the London Mathematical Society which does not bear any responsibility for the content of this post.

So, in my opinion, the ACME policy document Mathematical Needs: Mathematics in the workplace and in Higher Education is a case of missed opportunities. Interesting data collected in workplace interviews appear to be compromised by methodologically flawed analysis.

For an example, one can look at the following case study.

6.1.4 Case study: Modelling the cost of a sandwich. The food operations controller of a catering company that supplies sandwiches and lunches both through mobile vans and as special orders for external customers has developed a spreadsheet that enables the cost of sandwiches and similar items to be calculated. It was necessary as part of this work to estimate the cost of onions in hamburgers, which was done by finding out how many burgers can be filled from one onion. The most difficult parameter to estimate for the model is the cost of labour.

This example illustrates one of the fundamental flaws of ACME’s approach: factually interesting case studies are interpreted via the the narrow prism of “modelling” agenda.

Meanwhile, anyone who ever did a spreadsheet of complexity of a sandwich should know that the key mathematical skill required is a basic ability of manipulating brackets in arithmetic and algebraic expressions, something that Tony Gardiner calls “structural arithmetic” and Michael Gove calls “pre-algebra”. (I have heard from a graduate of my University that his co-workers’ mastery of spreadsheets is inhibited by “brackets overload”; this expression is interesting because it has been coined at the actual workplace.) At a slightly more advanced level working with spreadsheets requires interiorisation  of the concept of functional dependency in its algebraic aspects (frequently ignored in pre-calculus).

To illustrate this point, I prepared a very simple spreadsheet. Look at the picture above: if the content of cell C14 is SUM(C8:C13) and you copy cell C14 into cell D14 (see the next picture),

the content of cell D14 becomes SUM(D8:D13) and thus involves change of variables. What is copied is an algebraic expression, not its value: notice that the value 85 became 130 when moved from cell C14 to cell D14!

Please notice that I am using the word “interiorisation” rather then “understanding”: people can manipulate brackets (or their cognitive equivalents) even if they are not able to clearly explain what they are doing; however, more basic principles like “every openning bracket should be matched by a closing one” perhaps can be formulated by anyone able to do a spreadsheet. Please notice and yet another qualifying remark: I am talking about “cognitive equivalents” of brackets: they have many forms, say, branching rules in tree-like structures, parsing, and primitive forms of recursion, to name a few.

Intuitive understanding that SUM(C8:C13) is in a sense the same as SUM(D8:D13) is best achieved by exposing a student to a variety of algebraic problems which convince him/her that a polynomial of kind $latex x^2 + 2x + 1$ is, from an algebraic point of view, the same as $latex z^2 + 2z + 1$, and that in a similar vein, the sum

$latex C_8 + C_9 + C_{10} + C_{11} + C_{12} + C_{13}$

is in some sense the same as

$latex D_8 + D_9 + D_{10} + D_{11} + D_{12} + D_{13}$ .

It looks as though ACME’s researchers never tried to look at the actual mathematical content of workplace activities, and therefore their recommendations for education are based on false premises. That the mathematical content is missing from their analysis is further confirmed by an important observation found on page 2 of the document:

Employers emphasized the importance of people having studied mathematics at a higher level than they will actually use. That provides them with the confidence and versatility to use mathematics in the many unfamiliar situations that occur at work.

In my opinion, here ACME missed a chance to ask the right question: why was indeed this happening? Instead, they appear to accept the employers’ vague hint that this is something about emotional maturity of their employees. But this is not about emotions at all; indeed, it is fairly obvious that a person’s “confidence” is directly linked to person’s understanding of what he or she is doing; meanwhile, the word “versatility” directly points to some mathematical skills involved in solving practical problems; the last point has been lost (or even never been looked at) in ACME’s analysis.

Next, I cannot avoid commenting on the intellectual vacancy of the concept of “modelling” as it is used by ACME:

6.1.2 Case study: Mathematical modelling developed by a graduate trainee in a bank […]
1. Modelling costs of sending out bank statements versus going online.

In the 19th century there was of course no option of going online, but in a similar situation they would simply say “comparing costs of sending out bank statements by post versus hiring an in-house courier”. Use of the trendy word “modelling” is superficial here, it only distracts from seeing the actual mathematical content of the activity.

# Gove on Computer Science — and Mathematical Logic

It seems that Mathematical Logic may be the next big thing in education, at least according to Michael Gove’s speechwriters. Here are quotes from his speech :

The best degrees in computer science are among the most rigorous and respected qualifications in the world. They’re based on one of the most formidable intellectual fields – logic and set theory – and prepare students for immensely rewarding careers and world-changing innovations […]

Instead of children bored out of their minds being taught how to use Word and Excel by bored teachers, we could have 11 year-olds able to write simple 2D computer animations using an MIT tool called Scratch. By 16, they could have an understanding of formal logic

previously covered only in University courses and be writing their own Apps for smartphones.

What follows at practical level is more sensational:

That’s why I am announcing today that the Department for Education is opening a consultation on withdrawing the existing National Curriculum Programme of Study for ICT from September this year.

The traditional approach would have been to keep the Programme of Study in place for the next four years while we assembled a panel of experts, wrote a new ICT curriculum, spent a fortune on new teacher training, and engaged with exam boards for new ICT GCSES that would become obsolete almost immediately.

We will not be doing that.

Technology in schools will no longer be micromanaged by Whitehall. By withdrawing the Programme of Study, we’re giving schools and teachers freedom over what and how to teach; revolutionising ICT as we know it.

# Early entry at GCSE

Have a look at a scan of the article that appeared in the Times Educational Supplement of 25 November last year.

Early entry at GCSE (Times Education Supplement 25 November 2011)

The worrying trend is that the % of GCSE A* grades is falling with early entry.

I am aware of schools that enter students early to ‘get it out of the way’.

Pupils get a C or better then do little or no mathematics in Year11.

What worries me is that some pupils may not then pick up the mathematics in Year 12 since some of the fire and passion for mathematics has gone out without having done much for a year. There is also a worry that pupils who would achieve an A* if they did GCSE Mathematics in Y11 may get an A or B at early entry and be content with that without realising (and I may be wrong in assuming this, so please correct me if I am wrong) that universities look at GCSE results as well when making offers. This could mean that entry to university courses in great demand is denied to those who do not achieve top grades at GCSE and pupils may not be aware of this.

Althoug his news is from USA, it  will add to controversy around school league tables and such.

From NYT, Big Study Links Good Teachers to Lasting Gain, by Annie Lowrey:

Elementary- and middle-school teachers who help raise their students’ standardized-test scores seem to have a wide-ranging, lasting positive effect on those students’ lives beyond academics, including lower teenage-pregnancy rates and greater college matriculation and adult earnings, according to a new studythat tracked 2.5 million students over 20 years.

And some sobering remarks:

Still, translating value-added scores into policy is fraught with problems. Judging teachers by their students’ test scores might encourage cheating, teaching to the test or lobbying to have certain students in class, for instance.

“We are performing these studies in settings where nobody cares about their ranking — it does not change their pay or job security,” said Jesse Rothstein, an economist at the University of California, Berkeley, whose work criticizing other value-added assessments unions frequently cite. “But if you start to change that, there is going to be a range of responses.”

I personally would propose an alternative way to assess school teachers: by their students’ performance at the next stage of education. For example, the best criterion to judge a GCSE level mathematics teacher is to look at numbers and academic performance of those his/her students who choose Mathematics/Further Mathematics as an A Level subject.

# Finland’s School Success

What Americans Keep Ignoring About Finland’s School Success, an article by Anu Partanen in The Atlantic.

A quote:

For starters, Finland has no standardized tests. The only exception is what’s called the National Matriculation Exam, which everyone takes at the end of a voluntary upper-secondary school, roughly the equivalent of American high school.

Instead, the public school system’s teachers are trained to assess children in classrooms using independent tests they create themselves. All children receive a report card at the end of each semester, but these reports are based on individualized grading by each teacher. Periodically, the Ministry of Education tracks national progress by testing a few sample groups across a range of different schools.

As for accountability of teachers and administrators, Sahlberg shrugs. “There’s no word for accountability in Finnish,” he later told an audience at the Teachers College of Columbia University. “Accountability is something that is left when responsibility has been subtracted.”