More on A Level reform

From THE:

[T]he group of 24 large research-intensive universities will seek to establish an advisory body on 10 A-level subjects to help maintain standards.

The working group on the new standards body will be chaired by Nigel Thrift, vice-chancellor of the University of Warwick, and will focus on A levels in maths, the sciences, languages, geography, history and Classics.

Read the full article.

A major A-level overhaul

From The Telegraph, by  :

[…] on Wednesday Mr Gove will set out a further reform of the qualification – effectively turning the clock back to the 90s before exams were overhauled by Labour.

[…] under the new plan:

• AS-levels will become a standalone qualification with results no longer counting towards final A-level marks;

• Pupils will be able to take new-style AS-levels over one or two years, with qualifications covering exactly half the content of the full version;

• Full A-levels will be completely separate from AS and turned into “linear” qualifications, with all exams sat at the end of the two-year course.

[…] The move is likely to prove controversial among some universities because it will stop them using AS marks to award provisional places on degree courses.

[…] the Russell Group […] would form a new academic board to advise Ofqual on the content of A-levels.

Read the full article.

Children to be marked up for using long division in maths

By   in The Telegraph:

Long division and multiplication will make a return to maths exams as part of a Government drive to boost standards in primary schools, it will be announced today.

Pupils aged 11 will be given extra marks for employing traditional methods of calculation in end-of-year Sats tests, it emerged.

Children who get the wrong answer but attempt sums using long and short multiplication or adding and subtracting in columns will be rewarded with additional points.

Ministers insisted the changes – being introduced from 2016 – were intended to stop pupils using “clumsy, confusing and time-consuming” methods of working out. […]

Elizabeth Truss, the Education Minister, will outline the plans in a speech to the North of England Education Conference in Sheffield on Thursday.

Speaking before the address, she said: “Chunking and gridding are tortured techniques but they have become the norm in recent years. Children just end up repeatedly adding or subtracting numbers, and batches of numbers.

“They may give the right answer but they are not quick, efficient methods, nor are they methods children can build on, and apply to more complicated problems.

“Column methods of addition and subtraction, short and long multiplication and division are far simpler, far quicker, far more effective and allow children to understand properly the calculation and therefore move on to more advanced problems.”

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

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

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

 

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.

Read full article

Ofqual: Recruitment of Key Stage 2 subject experts

A colleague brought to my attention to the following advertisement from Ofqual:

“Recruitment of Key Stage 2 subject experts

[…] We are keen to hear from you if you feel you have a suitable level of experience in Key Stage 2 education and assessment, specifically in reading, writing, mathematics or science. You might be a current or ex-teacher or marker, or have other relevant experience in developing or delivering Key Stage 2 assessments. […]”

He has also raised his concerns:

“I have a gut feeling that any set of minimal requirements for “Key Stage 2 subject experts” invited to  work on “developing Key Stage 2 assessments” should include (at least in case of mathematics) some experience of teaching and assessment not only at KS2, but also at KS3 level. For otherwise how can they ensure the continuity and cohesion of pupils’ study?”

My opinion is that there are few people who will have the necessary experience of both KS2 and KS3 teaching experience and assessment development. They are more likely to find people with the KS2 experience only – of course KS3 experience as well would be a bonus, but most people (I should probably say teachers here) are primary or secondary, not both. People in middle schools (ages 9-13) would have bridged the KS2/3 divide, but perhaps would not have seen the curriculum through to the end of KS3. I think that if they stipulated the KS2/3 requirement then they would be faced with a dearth of applicants!

I was always amazed that pupils who came into secondary education with level 5 mathematics at KS2 never really seemed to have a grasp of the topics at that level – even many of those with level 4 struggled with level 4 in KS3. Now this could have been the 6  week lay-off they had over the summer, or the fact that they had been crammed for the KS2 mathematics SAT tests to get the best results for their primary school data. However there seemed to be little correlation between the algebra at level 5 which was tested at KS2 and the algebra at level 5 for KS3, the latter always seemingly the harder. Unfortunately I do not have any hard data to back up my opinion – it is just a gut reaction. One has to believe in the integrity of the powers that oversee these tests (QCA, QCDA, Ofqual or whatever) and that continuity did and will take place.

What should be the priorities of Ofqual A Level Reform Consultation?

Having read the Ofqual A Level Reform Consultation I suggest that DfE:

  1. Be wary of changes which may lead to a reduction in numbers taking Mathematics and Further Mathematics.
  2. Accept that there MUST be a common core in at least the pure parts of Maths and Further Maths.
  3. Accept that if the country/government is serious about wanting a more numerate population then the maths curriculum must be drawn up to do the job, not fitted into an unsuitable mould for the sake of ‘consistency’ across subjects.
  4. Accept that, at A level, no one exam can test satisfactorily the whole ability range in mathematics.
  5. For minimum disruption, redesign something like AEA or STEP to stretch the top ability range with problems (where students are not led through to the solution) and where rigour and good style are recognised and rewarded. Fund it and make it more accessible than the present AEA/STEP, with on-line support as for Further Maths. (I imagine HE are not so unhappy with the content of Maths and Further Maths but with the lack both of rigour and of problem solving.)

[Related posts: Universities to set A-levelsA Level Reform ConsultationCommons Select Committee on Education: Introduce National Syllabuses]

Stephen Huggett: Multiple choice exams in undergraduate mathematics

S. Huggett, Multiple choice exams in undergraduate mathematics, The De Morgan Journal, 2 no. 1 (2012), 127-132.

From the Introduction:

In addition to a rigorous practical test called the general flying test, candidates for a private pilot’s licence have to pass written exams in subjects including meteorology, navigation, aircraft, and communications. These written exams are multiple choice, which seems appropriate. The trainee pilots are acquiring skills supported by background knowledge in breadth not depth, and this can be tested by asking them to choose the right option from a limited list under a time constraint. It is not necessary, of course, for pilots to understand the underlying theoretical concepts.

In contrast, students of mathematics are certainly expected to understand underlying theoretical concepts. To a certain extent, this understanding can also be tested using multiple choice exams. Clearly, mathematicians need skills too, of which one of the most important is the ability to perform calculations accurately. This can also be tested using multiple choice exams.

Given that no one method of assessment is good for all of the understanding and skills expected of a student, one should use a variety of different assessment methods in a degree programme, including things such as vivas, projects, and conventional written exams. There is no claim here that multiple choice exams can do everything!

Read the rest of the paper.