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Closing the Gap (Mission Impossible)

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Closing the Gap (Mission Impossible) The gap in educational attainment between students from wealthier and poorer homes in England has been widely reported for many years. Successive governments have railed against the stubborn existence of the gap and have ostensibly sought to close it through the use of various policy levers. Recently, governments from both major parties have placed a great emphasis on the responsibility which schools bear for closing the gap: Surely we must agree that good teaching will equate to good outcomes for all pupils? Fig.1. GCSE attainment gap 2011-2017 (Ofsted 2018) But schools will continue to fail to close the gap. They are but one element of a broader social framework. Within this social framework ‘the gap’ is created long before children arrive at school. Further, the schools system as a whole, through the way it is set up and managed, largely serves to perpetuat
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The two faces of Division

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W hen I teach beginning primary school teachers about division, I usually begin by asking them to come up with a ‘story’ for the calculation 12 ÷ 4. They tend to respond, as my secondary beginning mathematics teachers do also, with a story about sharing. Cakes and sweets are enormously popular. This response is also typical of secondary age schoolchildren in my experience and that of the Concepts in Secondary Mathematics and Science (CSMS) investigators, (Hart et al, 1981). I have a suspicion that this reveals something about the mental pictures, and movement schemes, people carry about division and I think that the root of a significant difficulty is hidden inside this mental picture. There are two forms of division which are distinct enactively, we act them out differently when we learn about them and when we ‘do’ them in our early lives, but equivalent numerically. That is that the ‘answer’ is the same number. This is why the distinction is hidden. The two forms
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