Tony Gardiner: Teaching mathematics at secondary level

A. D. Gardiner, Teaching mathematics at secondary level. The De Morgan Gazette 6 no. 1 (2014), 1-215.

From the Introduction:

This extended essay started out as a modest attempt to offer some supporting structure for teachers struggling to implement a rather unhelpful National Curriculum.  It then grew into a Mathematical manifesto that offers a broad view of secondary mathematics, which should interest both seasoned practitioners and those at the start of their teaching careers.  This is not a DIY manual on How to teach.  Instead we use the official requirements of the new National Curriculum in England as an opportunity:

  • to clarify certain crucial features of elementary mathematics and how it is learned — features which all teachers need to consider before deciding `How to teach’.

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Programmes of study for Mathematics at Key Stage 4

Programmes of study for  Mathematics at Key Stage 4, which will be taught in schools from September 2015 alongside the new English and mathematics GCSEs, are published today. This appears to be the final pack of statutory documents:

Consultation on Key Stage 4 mathematics

The government response to consultation for key stage 4 English and mathematics on December 2nd 2013 can be found here; pdf.

DfE are now consulting on the draft Order and Regulations that will give effect to the new programmes of study for English and mathematics at key stage 4 from September 2015 and to extend the disapplication of the key stage 4 science programme of study for a further school year (2015/16).

Rebecca Hanson: 2014 Primary Mathematics Curriculum is Not Fit for Purpose

Re-posted from Authentic Maths.

Rebecca Hanson:

Following the writing of my first report on the 2014 Primary National Curriculum in December I have been corresponding with the key people involved in its development.

As a results of their comments I have written a second report which calls for the immediate suspension of the implementation of the 2014 Primary National Curriculum for Mathematics. This new report dated 6 Jan 2014 can be downloaded here: Fundamental Problems with the 2014 Primary National Curriculum for Mathematics.

The press release which accompanies this report can be downloaded here:
Call for Suspension of New Primary Mathematics Curriculum.

6 JAN FAULT: If you experience problems downloading the report an alternative version (without hyperlinks) can be downloaded from the Times Educational Supplement site.

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’.

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.

National Curriculum is published

The new National Curriculum is published today.

 A further consultation on the programmes of study for key stage 4 English, mathematics and science will follow, in line with the timetable for the reform of GCSE qualifications.

The majority of the new national curriculum will come into force from September 2014, so schools will now have a year to prepare to teach it. From September 2015, the new national curriculum for English, mathematics and science will come into force for years 2 and 6; English, mathematics and science for key stage 4 will be phased in from September 2015.

National Curriculum

From Department for Education:

The Secretary of State for Education, the Rt Hon Michael Gove MP, has today launched a statutory consultation on the draft legislative Order for the new national curriculum.

As you will know, the government has been reviewing the national curriculum in England since January 2011. In February of this year we published proposals […] Our formal public consultation, which closed in April, received over 17,000 submissions from a wide range of respondents. The summary report of those responses, along with the government response (which includes an update on the implementation of the new national curriculum), can be seen at https://www.education.gov.uk/consultations/index.cfm?action=conResults&consultationId=1881&external=no&menu=3.

[…] we have made a number of revisions to the national curriculum framework document and the draft programmes of study. You can view the new framework document and programmes of study, along with the consultation document on the Order for the new national curriculum and details of how to respond, at www.education.gov.uk/nationalcurriculum. The consultation will close on 8 August.

A local copy of the document file: The national curriculum in England: Framework document.

National Curriculum to be published today

From BBC:

The re-written national curriculum, to be published on Monday, will set out the framework for what children in England’s state schools should be taught between the ages of five and 14. […] However academies – which are now a majority of secondary schools – will not be required to follow the curriculum. […]

The changes will include fractions for five year olds […]

Education Secretary Michael Gove said the new-look curriculum would provide the “foundation for learning the vital advanced skills that universities and businesses desperately need – skills such as essay writing, problem-solving, mathematical modelling, and computer programming“.

In maths, there will be an expectation of a higher level of arithmetic at an earlier age. There will be a requirement for pupils to learn their 12 times table by the age of nine, rather than the current 10 times table by the age of 11.