The National Numeracy Strategy Essay Example

The National Numeracy Strategy Essay The National Numeracy Strategy (DfEE 1999: part 1, p.12) requires teachers to identify mistakes, using them as positive teaching points by talking about them and any misconceptions that led to them. When dealing with a childs errors in their work it is not enough to simply mark them as wrong, the child must be given the opportunity to develop a greater level of understanding through correction. This may not simply be re-calculating a sum, but revising their ideas and concepts of the particular topic area. According to Skemp (1989) by the process of understanding, that which began as an error becomes a contribution to knowledge p.200. As identified in Pollard Tann (1993) it is also true that if a child is allowed to continuously make errors in the same subject or on the same topic the child can be caught in a vicious circle in which failure leads to anxiety which leads to further failure p. 68. Children too, experience frustration when they cannot reach their goals and repeated failure may result in loss of confidence and self-esteem. Teachers must provide the opportunity for the child to attain their targets. We will write a custom essay sample on The National Numeracy Strategy specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on The National Numeracy Strategy specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on The National Numeracy Strategy specifically for you FOR ONLY $16.38 $13.9/page Hire Writer Once the teacher realises the necessity to identify the misconstrued knowledge/concepts, they must discover underlying problems in the most accurate way. To simply study the childs work shows a self-important belief that the teacher can understand what the child is thinking. It is only by discussing with the child their ideas and perceptions that the true reasons for the misconceptions become evident. Alice states that multiplication makes numbers larger and division makes numbers smaller. Alices statements will be accurate when applied to the contexts of multiplication and division that she is most likely to be familiar with, for example positive integers. When children are first introduced to multiplication in school, they become familiar with the terms lots of and sets of, this then leads to an understanding of multiplication as repeated addition, which is often one of the first strategies introduced to children to tackle multiplication questions. One example of this is identified in Suggate et al (1998): Again the assumption could be made that because subtraction makes numbers smaller so too will division. So closely linking these four operations and not distinguishing the differences will map properties of one onto the other. Skemp (1989) identifies how introducing multiplication as repeated addition can lead to further problems, this [repeated addition] works well for the counting numbers, but it does not apply to multiplication of the other kinds of number which children will subsequently encounter; so to teach it this way is making difficulties for the future p.144. He goes on to identify the multiplication of negative numbers and fractions as being an area where children will develop problems. This thinking is reinforced by the Concepts in Secondary Mathematics and Science (CSMS) project where whole number computations and extensions to fractions and decimals were considered (Hart 1981); conclusions note that many children are still only groping towards ideas of multiplication a nd division. Alices teacher would need to discuss, with her, all the ideas and concepts she holds about multiplication and division. Only by exploring the childs understanding of underlying concepts and principles will the reason for the misconceptions become apparent. As already mentioned the teachers assessment of the reason for a childs errors may not be accurate purely by studying their work.  A starting point to rectify the misconception would be to identify in the NNS (DfEE 1999) what understanding Alice should have acquired by her age. Children, according to the NNS (DfEE 1999), do not encounter multiplication or division until year 2, and confirms my previous thinking that children are to understand the two operations as repeated addition and subtraction. It is not until year 4 that children multiply and divide decimals and fractions and examine related theory, such as the commutative law. Alice needs to be taught that multiplication and division are more than just complicated forms of addition and subtraction. There is more to multiplication and division than just computing sums. According to Nunes Bryant (1996) The child must learn about and understand an entirely new set of number meanings and a new set of invariants, all of which are related to multiplication and division, but not to addition and subtraction p.144. Research conducted by Hoyles, Noss Sutherland in 1992 showed an ingenious method to enable children to see that multiplication does not always make numbers bigger. The children were asked to reach a target number (e.g. 100) from a starting point (e.g. 13) through successive multiplications. The pupils easily overshot the target and therefore had to face the question: how do you make numbers smaller by multiplying them? The research identified this as a significant question, which helps pupils see the discontinuity between addition and multiplication. This type of activity along with one related to division could be used in school to highlight concepts children may not have realised. By addressing difficulties within topics early on children are prevented from forming certain misconceptions. The next stage for the teacher would be to decide how to prevent these sorts of misconceptions occurring in following years. It is apparent that Alices previous teaching has not allowed her to access the topic in a way that she can understand it. Teachers must consider both their teaching styles and childrens learning styles when approaching areas that children can easily misconstrue. The following years class should be given the opportunity to explore the concepts and theory behind multiplication and division, this may not be in line with the NNS (DfEE 1999)) order, but may provide those children with a greater comprehension of the operations they are carrying out. Once they are confident with the reasoning their manipulation and computation of numbers should be secure due to their underlying understanding. Emilys work shows four calculations with vulgar fractions. It is apparent that she is working horizontally to complete the sums either adding or subtracting the two numerators and the two denominators. The NNS (DfEE 1999) identifies that children from year 4 upwards should recognise the equivalence between fractions and at year 5 should be able to recognise from practical work simple relationships between fractions part 6 p.23. It appears from Emilys work that she does not understand the relationships. In the first question (shown below) she has to add two fractions with the same denominator.