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Secondary Magazine - Issue 117: Building Bridges

Created on 25 November 2014 by ncetm_administrator
Updated on 16 December 2014 by ncetm_administrator


Secondary Magazine Issue 117'Infinity Bridge' by PauliCarmody (adapted), some rights resered

Building Bridges

The Roman god Janus and a Year 9 teacher have quite a lot in common at this time of year: both are looking back over the year that’s been, and also are looking ahead to the opportunities and possibilities of the future. Whether Janus had sufficient length of foresight to see the current changes to the GCSE specifications is not recorded by Virgil or Livy, but we’re sure that Year 9 teachers are very well aware of the decision that they have to make, and soon.

KS4 is, obviously, a bridge between KS3 and 5, but therefore it is also a bridge between thinking and doing mathematics largely in the concrete to largely in the abstract: GCSE study is the cognitive bridge from Cuisenaire rods to the Argand diagram. We therefore feel that this is the right place in the magazine to bring together some information and advice around making the best choice for your pupils. We hope it’s helpful; let us know @NCETMsecondary.

All the new GCSE specifications have been approved and published, along with specimen assessment materials: links to these were included in Issue 115. The exam boards have said that they will be producing further specimen materials, but with different timescales. They are also all offering information and training sessions. Many of the Maths Hubs have a workgroup focused on helping schools prepare for the new GCSEs, so if you’d like to find out more, or be involved directly, contact your local Maths Hub Lead School.

At the NCETM, we are committed to the principle of teaching for mastery: you can read the latest blog about this by Charlie Stripp, the NCETM’s Director, and also a very supportive response from Jane Jones, HMI and Ofsted National Lead for Mathematics. Teaching for mastery is entirely consistent with the aims and ethos of the new National Curriculum, namely that at all stages, ALL pupils

  • become FLUENT in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately;
  • REASON MATHEMATICALLY by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language;
  • can SOLVE PROBLEMS by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

with the expectation that

the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent should consolidate their understanding, including through additional practice, before moving on.

(the emphases are our own).

Please, therefore, scrutinise carefully the GCSE specification(s) and specimen assessment task(s) that are on your shortlist, and consider:

  • How will you teach the content: linear or spiral, or a blend?
  • How will you assess your pupils’ knowledge, now that the current National Curriculum level descriptors are obsolete?
  • How will you develop their mathematical fluency and reasoning and problem solving skills: “little and often” or “Fun Friday”, or a blend?
  • How will you assess their reasoning and problem-solving skills?
  • How will you challenge your high attainers: what rich and sophisticated problems are offered by the exam board(s)?
  • How will you support your low attainers: how will the exam board(s) help you provide effective additional practice?

What resources and support from the exam boards do you and your colleagues need to meet the National Curriculum aims and exemplify its ethos? What do your pupils need? How will the resources offered by your shortlisted exam board(s)

  • give all your pupils intelligent practice?
  • develop their procedural fluency?
  • and, develop their conceptual understanding?

And then, how will you assess your pupils’

  • procedural fluency,
  • conceptual understanding
  • and, their mastery?

Many of us are asking ourselves these and similar questions. Let’s share our answers and pool our thinking, either @NCETMsecondary or in the NCETM Secondary Forum.

Image credit
Page header by PauliCarmody (adapted), some rights reserved



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