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Alignment in Mathematics Education John Mason (& Anne Watson) Friday 29 th Nov 2013

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Alignment assessment curriculum pedagogy

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What to look for in mathematics lessons practitioner comments Conceptual understanding Procedural fluency Solving problems: Extending mathematical repertoire Developing identification and application Developing reasoning Mathematical Thinking?

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Alignment in mathematics lessons New ideas can be seen to build on prior knowledge when.... New ideas might confuse students when.... Teachers ask why? when... A range of representations might be used when..... Lesson will be stop-start rather than flow smoothly when.... Written work may be rough when... Students may appear to be off task when... Teachers may have to deviate from the lesson plan when.... A lesson might contain no direct instruction when.... Silent work might be used at the start when.... A short test might be used when...

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Sample task What do you notice? How might you account for it? Can you begin to predict what is coming?

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Source http://www.datapointed.net/visualization s/math/factorization/animated-diagrams/

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In that task....... assessment curriculum pedagogy

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Sample Task Please write down a decimal number lying between 3 and 4; and which does not use the digit 5; and which does use the digit 7; and which is as close to 3 as possible;

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In that task....... assessment curriculum pedagogy

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Thinkers who inform mathematics education Sociologists Anthropologists Psychologists Cultural and gender studies Philosophers Mathematicians Politicians

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Policy International comparisons (assessment/pedagogy) EBacc EBC (assessment/curriculum) Curriculum nature and content (curriculum/pedagogy) Teacher recruitment and retention (pedagogy) Expenditure

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Aaarrrggghhh! Help I cannot take the problems of the country onto my shoulders It is easier to appear to make maths teachers act in certain ways than to appear to make Amazon act in certain ways

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Teachers research-informed change Small changes in practice Collaboration Task design Development of personal enquiry Ownership of short and medium term planning (pedagogy/professionalism)

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Opportunity To seek alignments in your own situation To probe beneath the surface of some alignment or lack of alignment