Citizens’ Maths

Citizen’s Maths is a MOOC project funded by the Ufi Charitable Trust. It
is led by Calderdale College with CogBooks, the Institute of Education,
and OCR.

http://goo.gl/RexVLv is a call for maths teachers to express an interest
in working with Citizens’ Maths as “to camera” tutors.

The deadline for responses is Thursday 5/12/2013.

Please spread the call as widely as you wish.

Tony Gardiner: National curriculum – Comments and suggested necessary changes

Published today:

A. D. Gardiner, National curriculum (England), September 2013; Attainment targets and programmes of study (key stages 1–3). Comments and suggested necessary changes. The De Morgan Gazette 4 , no. 3 (2013), 13-57

From the Introduction:

The Education Order 2013 was “made” on 5 September 2013. The relevant details were “laid before parliament” on 11 September 2013, and will come into effect on 1 September 2014. Some of the details for GCSE were published on 1 November 2013. Further elaboration of GCSE assessment structure, and curriculum guidance for Key Stage 4 (Years 10–11, ages 14–16) are awaited.

It is generally agreed that the curriculum review process adopted over the last 3–4 years has been seriously flawed. Those involved worked hard, often under very difficult conditions. But the overall approach (of relying on civil servants and drafters whose responsibilities and constraints remained inscrutable) has merely demonstrated that drafting and maintaining curricula is a specialist task, requiring dedicated professionals with specialist experience.

Whatever flaws there may have been in the process, we will all have to live with the new curriculum for some years. So it is important to have an open discussion of the likely difficulties. This article is an attempt to indicate aspects of the National curriculum in England: mathematics programmes of study that will need to be handled with considerable care, and revised in the light of experience.

After three years of widespread unease about the process of the curriculum review and its apparent direction, it is remarkable that there has been almost no media coverage, and no clear professional response to the final mathematics programmes of study for ages 5–14. There is therefore a real danger that insights that emerged along the way will simply be forgotten, and that the same mistakes may then be made next time. [...]

The details laid before parliament are `statutory’; but they incorporate basic flaws, and significant contradictions between the statutory list of content (which could all-too-easily be imposed uncritically) and the declared over-arching “aims” (which could get forgotten, or ignored). Given these flaws, the fate of the new programmes of study will depend on how sensitively their implementation is handled—whether slavishly, or intelligently. Teachers—and Ofsted, senior management, etc.—need to be alert to those aspects of the stated programmes of study that incorporate predictable pitfalls.

We summarise here what seem to be the two most important flaws.

Some material in Key Stage 1 and 2 is very poorly specified (especially from Year 4 onwards).

Some items are listed unnecessarily and unrealistically early, and so may be introduced at a stage:

  • where they are not yet needed,
  • where they will not be understood,
  • where they will be badly taught, and
  • where – if the relevant requirements were relaxed – the premature material could easily be delayed without causing any subsequent problems.

The listing of content for Key Stage 3 is in some ways reasonable, but too many things are left implicit. The programme of study is less structured than, and contains less detail than, that for Key Stages 1 and 2. Hence the details of the Key Stage 3 programme need interpretation. At present:

  • the words of each bullet point are rarely elaborated;
  • the connections between themes are mostly suppressed; and
  • there is no mention of essential preliminaries.

In addition

  • the Key Stage 3 programme has no accompanying `Notes and guidance’.

In summary, if the declared goals for Key Stage 4 are to be realised,

  • we need some way of clarifying the specified content and relaxing the unnecessary and potentially damaging pressures built in to the Key Stage 1–2 curriculum as it stands; and
  • the centrally prescribed curriculum for Key Stage 3 needs to be much more clearly structured to help schools understand what it is that is currently missing at this level—initially by providing suitable non-statutory `Notes and guidance’.

MathJax v2.3 now available

From The MathJax Team:
After a successful beta run, we’re happy to officially release MathJax v2.3.

MathJax v2.3 is available on the CDN, and for download from GitHub or via the download page at http://www.mathjax.org/download/.

Version 2.3 is available on the CDN at

http://cdn.mathjax.org/mathjax/2.3-latest/MathJax.js

and starting today the files at the

http://cdn.mathjax.org/mathjax/latest/MathJax.js

address will be switched over the v2.3; it will take 24h-48h for the changes to propagate out to the distributed cloud servers.

Continue reading

GCSE: Higher level content

Reformed GCSE subject content includes three types of content: standard, underlined and bold. In the words of he document,

The expectation is that:

  • All students will develop confidence and competence with the content identified by standard type
  • All students will be assessed on the content identified by the standard and the underlined [here, for technical reasons, emphasised -- AB] type; more highly attaining students will develop confidence and competence with all of this content
  • Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

The distinction between standard, underlined and bold type applies to the content statements only, not to the assessment objectives or to the mathematical formulae in the appendix.

What follows is the list of items in the  Mathematics GCSE subject content and assessment objectives which contain bold type, higher content.I think this short lists clearly marks the boundaries of GCSE — AB

Continue reading

What exactly do student evaluations measure?

From a post by  Philip Stark on The Berkeley Blog:

●  student teaching evaluation scores are highly correlated with students’ grade expectations[10]

●  effectiveness scores and enjoyment scores are related[11]

●  students’ ratings of instructors can be predicted from the students’ reaction to 30 seconds of silent video of the instructor: first impressions may dictate end-of-course evaluation scores, and physical attractiveness matters[12]

●  the genders and ethnicities of the instructor and student matter, as does the age of the instructor[13]

Red the whole text.

Reformed GCSE subject content consultation – Government response

From the Department for Education:

Following the GCSE subject content consultation that closed on 20 August 2013, the Secretary of State has today published revised subject content for English language, English literature and mathematics, as well as the Government’s response to the consultation. The Secretary of State has also made a Written Ministerial Statement, which can be read here.

Ofqual has also published reforms to the design requirements for new GCSEs, including on arrangements for controlled assessment, tiering and new grading. Its summary of these reforms can be found here.

GCSE reform is finalised

Ofqual today (1st November 2013) [...]) announced a revised timetable for the reforms, meaning new GCSEs in English language, English literature and maths will take priority and will be introduced for first teaching from 2015.

The Department for Education will today be confirming the subject content for these subjects, following a separate consultation.

Key features of the new GCSEs in England will include:

  • A new grading scale that uses the numbers 1 – 9 to identify levels of performance, with 9 being the top level. Students will get a U where performance is below the minimum required to pass the GCSE
  • Tiering to be used only for subjects where untiered papers will not allow students at the lower end of the ability range to demonstrate their knowledge and skills, or will not stretch the most able. Where it is used [this apparently applie to maths -- AB], the tiering model used will be decided on a subject-by-subject basis
  • A fully linear structure, with all assessment at the end of the course and content not divided into modules. This is to avoid the disruption to teaching and learning through repeated assessment, to allow students to demonstrate the full breadth of their abilities in the subject, and to allow standards to be set fairly and consistently
  • Exams as the default method of assessment, except where they cannot provide valid assessment of the skills required. We will announce decisions on non-exam assessment on a subject-by-subject basis
  • Exams only in the summer, apart from English language and maths, where there will also be exams in November for students who were at least 16 on the preceding 31st August. Ofqual is considering whether November exams should be available in other subjects for students of this age.

Read the full statement from Ofqual.

Tony Gardiner: David Willetts and “Robbins Revisited”

David Willetts (Minister of State for Universities and Science) has just published a possibly significant pamphlet with the Social Market Foundation called Robbins Revisited:

Robbins was an LSE economist whose committee examined the future of the ish university system – reporting in 1963. The report was unusually perceptive and its recommendations influenced policy for the next 30 years. This report is interesting in that it indicates the relevant Minister’s desire to place current HE policy in a historical context. Half of the time the contextualising makes sense; but half of the time it seems to be influenced by the need for post hoc self-justification.

As so often with high level documents, the data are wilfully distorted (whether deliberately or through wishful thinking one cannot know) in order to fit a required political perspective. Willetts repeatedly interprets data as demonstrating “improvement” even where we know it does no such thing. And where the uncomfortable explanation is to hand, he prefers to express puzzlement – as on p.69 where he observes

“an apparent mismatch between the supply and demand for high-level computer skills. Employers currently say they cannot find the skills they need yet computer science graduates find it relatively hard to find graduate-level work”

but then fails to infer that perhaps many computer science undergraduates are accepted onto courses, and graduate, without the relevant “high-level skills”.

He makes no mention of the botched attempts to broaden studies at age 16-18 (e.g. Tomlinson), or of the fact that the A level ‘gold standard’ his colleagues defend makes sense only if it supports specialisation. He then misinterprets the English fudge of continuing with A levels while abandoning specialisation (Table 5.1) as if it were a move in the direction of the kind of breadth Robbins advocated.

However, he has a relevant qualification (pp.50-1):

“there is an important distinction to be made between the need for breadth in general, and the need for maths skills in particular. In an interview with The Listener in 1967 Robbins was asked why the numbers opting for applied and pure sciences had fallen below expectations. He blamed what he called “the terror of mathematics”, caused by poor teaching and a preoccupation in university maths departments with producing “aces”.

This issue has not gone away. Last year the Lords Science and Technology Committee expressed its shock that many Science, Technology, Engineering and Mathematics (STEM) undergraduates lacked the mathematical skills required to cope with their course at university. The National Audit Office has warned that this is an issue for student retention. Maths is a core part of science and engineering subjects – but it comes into many others [...] it is the universal analytical tool which matters more and more in today’s higher education.”.