By Niçaise

Nicaise S. examine numerique et equations aux derivees partielles (Dunod, 2000)(fr)(ISBN 2100049410)

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2 = 20% 10 is not a prime number There are many ways to teach long multiplication, each with their merits and pitfalls. However, the following approach can be very useful in the development of conceptual understanding. Consider the calculation 38 × 42: 30 8 40 1200 320 2 60 16 Leading to 38 × 42 = 1200 + 320 + 60 + 16 = 1596. This can now be applied to algebraic calculations, often with little or no input from the teacher. For example, consider the expansion of (n + 8)(n + 2): n 8 n n2 8n 2 2n 16 Leading to (n + 8)(n + 2) = n2 + 8n + 2n + 16 = n2 + 10n + 16.

Both of these strategies provide pupils with opportunities to self-regulate, and be responsible for, their learning. Sometimes, a pupil is heard to say to the teacher, ‘When I am stuck and ask you a question, you don’t tell me the answer. ’ This is often a sign of a skilful teacher, whose questions are helping to get to the bottom of what the pupil is thinking and hence what the difficulty is. Carefully constructed questions can enable the pupil to resolve the difficulty themselves. Ofsted (2008a: 48) Setting great homework is one of the best ways to get children learning independently.

The exercises allowed pupils to progress from routine practice of skills to twostep questions, where the method was not immediately apparent, and questions with unusual twists that required some adaptation to the standard method. Ofsted (2012a: 23) Independence, then, is what really connects the teaching with the learning. Direct instruction on the part of the teacher (that is, deciding the learning objectives, modelling the learn42 hapter 3 C ing, monitoring and evaluating understanding and tying the learning together – see Hattie, 2009: 206) is essential if students are to make progress.

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