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To What Extent Does the Teaching of Mental Calculation Strategies Support the Development of Formal Written Methods?

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Introduction

TO WHAT EXTENT DOES THE TEACHING OF MENTAL CALCULATION STRATEGIES SUPPORT THE DEVELOPMENT OF FORMAL WRITTEN METHODS? INTRODUCTION To answer the question to what extent does the teaching of mental calculation strategies support the development of formal written methods we should first of all consider what is meant by 'mental calculation'. I would consider it to be a way of finding solutions to problems using a knowledge of number facts and strategies, without using written algorithms or methods. This could be done either by 'visualising' the problem or simply 'just knowing' it. BACKGROUND Prior to the introduction of the National Curriculum, there was very little emphasis placed on teaching mental calculation strategies. The 'mental' aspect of mathematics was usually done in the form of recitation of multiplication tables or sometimes as twenty questions at the start of the lesson. These methods could certainly help to embed a body of facts within a child's mind, but it did not provide strategies or a knowledge of how to apply these facts to other mathematical problems. The Cockroft report (1982) stated that one reason it did not occupy a prominent position within most mathematics teaching was that ' It is difficult to find mental questions which are suitable for all the pupils in the classes', this was due to the fact that most primary classes contained pupils of a very wide range of abilities. ...read more.

Middle

It is because of this that a large emphasis of the curriculum is placed on teaching and developing mental strategies. This is to provide the child with all the 'tools' they will need to develop and be successful with formal written methods. The approach to mental calculation strategies begins with identifying the individual child's views and beliefs of how the number system works. It is irrelevant to try to teach children strategies for addition and subtraction if they lack a basic understanding of the principles of our number system. The key issues which we need to address are the basic principles of the base ten system and place values. Once a child has a firm grasp of these, they can provide a sound base for development of both mental and written calculations. Mental strategies which are fundamental to providing a sound base from which a child can progress are : - Counting on and counting backwards between 1 and 10. - Establishing number bonds and patterns between 1 and 10. - Doubling and halving. - Counting on in tens. These basic principles can then be expanded and applied to any place value which will secure a basis for the child from which they can progress. Thompson further identified the key strategies for young children as being: - Partitioning single digit numbers ( 7 = 5+2 or 4+3 ) ...read more.

Conclusion

This can only work if the child already has a sound knowledge of mental methods of subtraction. CONCLUSION It is now widely accepted that children need to have a secure knowledge of number facts and mental strategies in order for them to develop fully with number and be able to work competently with written calculations. This has now been exemplified by the fact that the Framework for Teaching Mathematics does not introduce formal written methods until the age of. We have to remember that there are many different strategies that can be used and that children can be extremely inventive. If we ensure we know which strategies children are using then we have a good indication of their level of ability or development and can help point out any inaccuracies. As Thompson said 'If teachers are to be successful in teaching mental strategies then they need, as a minimum requirement, to be familiar with the different methods that children use' If we are familiar with their methods then we can guide them towards more efficient and extended methods which can help them build a repertoire of facts which they can apply to almost any calculation, aiding their development and ability with numeracy. DIANE LYDIATE 01614442 4 DEREK KASSEM CM1101 ...read more.

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