Some Mathematicss Educators argue that Standard Written Algorithms for the Four Rules need non be taught to Children as Part of the Primary Curriculum
Although some mathematics pedagogues believe that standard written algorithms should non be taught to primary age kids, the National Numeracy Strategy, together with the Primary National Curriculum clearly province that these methods should be taught. Although it is stated that these methods should be taught, The National Numeracy Strategy does emphasises the importance of mental computations ; emphasizing the significance of mental methods in the early old ages. It is besides recognised that non all kids do mental computations in the same manner and that treatment and comparing of different methods is of import. Many research workers believe that these mental methods, which allow intuitiveness, should hold more accent placed on them, as Pound notes:
‘Many of the troubles encountered by older kids in get bying within the formal regulations of mathematics could be prevented if instructors built upon the children’s current mathematical apprehension and methods of computation’ ( Pound, 1999, p43 ) .
By recognizing that mental methods of computation are of import for children’s mathematical development the National Numeracy Strategy aims to help the soft patterned advance from mental, intuitive computations on to the usage of standard written methods.
The National Numeracy Strategy states that standard written algorithms are ‘reliable and efficient procedures’ but besides stresses that they are merely utile if used accurately and by kids who can ‘judge whether the reply is reasonable’ ( DfES, 1999, p7 ) . In her survey of Year 5 students Anghileri found that ‘when taught an algorithm to happen an reply, they do non utilize their intuition to see if the reply “feels about right”’ ( Anghileri, 2001, hypertext transfer protocol: //www.standards.dfes.gov.uk ) . Despite the National Numeracy Strategy saying the importance of being able to judge that an reply is sensible, it appears that some research workers have found that when utilizing standard algorithms kids do ignore their mental methods of computation.
Ian Thompson has written widely on the topic of mathematics concentrating on children’s computation methods. Within the article ‘Written methods of calculation’ he scrutinises this extremely debated topic of the instruction of standard written algorithms, analyzing children’s methods of mental and written computations. Thompson argues that standard written algorithms should non be taught within the primary school ; but that one time kids have an apprehension of informal methods of computation criterion algorithms could be introduced to older kids. He expands on this statement, asseverating that one time these older kids have been taught criterion algorithms they should merely hold to be used as a method of computation by ‘those who understood them and/or wished to do usage of them’ ( Thompson, p171 ) .
Thompson, and many other educational research workers, have studied children’s methods of mental computation and have come to the decision that ‘children’s mental methods operate really otherwise from standard written methods in several respects’ ( Thompson, p170 ) . It is this research that leads Thompson to his decision that standard written algorithms are non the optimum method of learning kids computations if entire apprehension is to be gained in all four basic operations. This theory is backed up by other research workers ; Anghileri states that ‘the usage of formal methods may suppress children’s apprehension of mathematical jobs unless it is underpinned by sound mental strategies’ ( Anghileri, 2001, hypertext transfer protocol: //www.standards.dfes.gov.uk ) ; she is in understanding with Thompson on the importance of mental methods of computations.
Throughout the article Thompson emphasises the importance of children’s mental methods of computation ; mental methods of computation make kids believe about the logical thinking behind a computation, whereas criterion methods take much of the ‘meaning’ of the Numberss and what they represent, as Blair and Hughes argue: their usage can ‘encourage passivity’ ( Blair and Hughes, 2001, p31 ) . Thompson farther argues that the phrases and descriptions used in the instruction of standard algorithms can be confounding and meaningless, he states that:
‘Phrases like “put down the five and transport the one” or “put the 1 on the doorstep” are non truly contributing to the development of relational apprehension in children’ ( Thompson, p175 ) .
In schools today kids are encouraged to utilize their imaginativeness and to spread out on their mental methods of computation, yet when being taught criterion written algorithms they have to suspend much of their ain intuitiveness, ‘the determination as to how to put out the computation, where to get down what value to assign’ ( Thompson, p173 ) are removed from the kid, they have to lodge to a set of mathematical regulations, which, Thompson believes is non a natural patterned advance from children’s mental thought and therefore inhibits mathematical acquisition.
Thompson emphasis the point that in his, and others, research he has found that both kids and grownups do non utilize standard algorithms when they perform computations in the existent universe. Many research workers are in understanding with Thompson that the instruction methods for standard algorithms, and other mathematical techniques, will hold a important consequence on whether there is understanding, Harries and Spooner note that if mathematics is presented as modus operandis to follow and facts to be remembered, so it ‘seldom consequences in the acquisition of accomplishments or cognition that can be applied ( Harries and Spooner, 2000, p78 ) . Thompson expands on this, underscoring the fact that ‘algorithms were developed long ago so that mundane arithmetic could be carried out with the lower limit of dither and the upper limit of speed’ ( Thompson, pp174-175 ) .
It is Thompson’s belief that standard written methods of algorithms are now out of day of the month, that modern methods of ciphering, based on children’s mental methods of computation should be taught in schools. It is his belief that these methods are more ‘user-friendly’ and are learnt ‘naturally’ as they allow intuition, and do kids ‘think’ about the computation they are transporting out, as mental methods of computation take the ‘automatic and unreflective use of abstract symbols’ ( Thompson, p182 ) .
The ability to cipher standard written algorithms in all four regulations are set results laid out in the current Primary National Curriculum for twelvemonth 6 students. But the National Curriculum besides notes that informal methods, both written and mental, should besides be taught, and that standard methods should be developed from informal methods. Many research workers argue that standard methods should non be taught at primary degree, yet the National Curriculum shows standard algorithms as a natural patterned advance from informal methods of computation. Askew and William in their research show that standard methods when used in concurrence with a child’s ain mental or informal methods compliment each other, they province that:
‘Pupils with entree to both recalled and deduced figure facts make more advancement because each attack supports the other’ ( Askew and Williams, 1995, p8 ) .
The instruction of mathematics demands to follow a logical and natural patterned advance, add-on, minus, generation and division is increasingly taught from the start of primary school, utilizing methods applicable to the phase of the children’s mathematical ability. Frobisher et al believe that one time ‘procedure is understood, when the different stairss make sense, so the extension to new spheres and complex illustrations is more consecutive forward’ ( Frobisher et al, 1999, p172 ) . It is this theory that is the footing for the National Curriculum’s inclusion of standard written algorithms within the primary model ; that standard algorithms are a natural patterned advance from informal methods and should hence be included within primary mathematics learning. As the national Curriculum provinces written methods should be developed for all four regulations, constructing on mental methods already learnt ( DfES, 1999, p48 ) .
Many research workers recognise that it is the manner that standard written algorithms have been taught that affects whether they are understood, it is now recognised that larning by rote and non giving intending to mathematics is non contributing to supplying kids with mathematical ability that they will go on to utilize and happen utile throughout their lives. Thompson asserts that ‘teachers need to be cognizant of the scope of available methods’ ( Thompson, 1999, p4 ) for learning computation to back up all children’s mathematical development. If the importance of mental and informal methods in the instruction of standard algorithms is recognised so the patterned advance to these standard methods should be natural.
By guaranting that standard written methods are merely taught one time informal methods have been developed, standard algorithms become meaningful to kids ( Frobisher et al, 1999, p193 ) . It can hence be argued that as informal methods of computation for all four methods are taught throughout primary school so it is merely natural to come on on to standard written algorithms at this early phase of a child’s mathematical acquisition.
Anghileri, J. ( 2001 )Development of Division Strategies for Year 5 Pupils in Ten English Schools, hypertext transfer protocol: //www.standards.dfes.gov.uk/research/themes/thinkingskills/ThuOct101531302002/implications, Date accessed 19/04/2007
Askew, M. and William, D. ( 1995 )Recent Research in Mathematics Education 5-16, London: Office for Standards in Education.
Blair, H. and Hughes, P. ( 2001 )Primary Mathematicss Curriculum Guide, London: David Fulton Publishers Ltd.
Department for Education and Skills, ( 1999 )The National Numeracy Strategy, Sudbury: DfEE Publications.
Frobisher, L. et Al. ( 1999 )Learning to Teach Number, Cheltenham: Stanley Thomas Publishers Ltd.
Harries, T. and Spooner, M. ( 2000 )Mental Mathematicss for the Numeracy Hour, London: David Fulton Publishers Ltd.
Pound, L. ( 1999 )Supporting Mathematical Development in the Early Old ages, Hymen: Open University Press.
Qualifications and Curriculum Authority ( 2005 )Mathematicss: 2004/5 Annual Report on Curriculum and Assessment, hypertext transfer protocol: //www.qca.org.uk/downloads/qca-05-2171-ma-report.pdf, Date accessed 20/04/2007
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