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The English National Curriculum for the Foundation Stage is specifically developed for kids of 3-5 old ages ; major attending in the Curriculum is paid to such topics as literacy and numeracy. The Foundation Stage covers the undermentioned stepping rocks and early acquisition ends: 1 ) societal, emotional and personal development ; 2 ) literacy, communicating and linguistic communication ; 3 ) numeracy accomplishments ; 4 ) creative development ; 5 ) cognition of the existence and 6 ) physical development ( Lewis 2002 ) . In 1999 the English authorities created the National Numeracy Strategy ( DfEE, 1999 ) that was intended to better the quality of numeracy learning in primary schools. As Anghileri ( 2001 ) claims, inventions were expected to “develop [ children’s ] ability to ground mathematically and to reassign accomplishments to new situations” ( p.1 ) . The purpose of the present essay is to critically measure a child’s mathematical work, using to Early Learning Goals from the QCA Surestart Curriculum Guidance for the Foundation Stage ( 2000 ) . The appraisal standards are based on four attainment marks specified in the National Curriculum: 1 ) Target 1 – Using and using mathematics ; 2 ) Target 2 – Number and Algebra ; 3 ) Target 3 – Shape, infinite and steps ; 4 ) Target 4 – Handling information. The topic under the analysis is a kid from a primary school who is aged 5 old ages and who is traveling to come in a response category. Harmonizing to the National Numeracy Strategy, a kid from a primary school should hold appropriate cognition of steps and Numberss ( Thompson, 2000 ) . In peculiar, he/she should be able to understand the figure system and calculate with the aid of specific computation schemes ( Tymms, 1999 ) .

Actually, the appraisal of a kid was conducted in both written and unwritten signifiers within the primary scene ( in a Surestart baby’s room ) ; the environment was familiar to the kid and, hence, encouraged his originative thought and positively contributed to the overall public presentation. In the procedure of unwritten appraisal an appropriate feedback and supervising were provided to the kid. However, the written work was chiefly performed without external aid. In respect to the unwritten appraisal, a specific maths interview was initiated ( the transcript of the interview is given in the Appendix 1 ) ; some inquiries in the interview had an implicit or expressed mention to such topics as geographics, history and art. As a consequence, the kid demonstrated accomplishments in numeration, description of form, infinite, distance, length and apprehension of mathematical linguistic communication. In add-on, he appeared to be adept plenty in the computation of topographic point value. As SCAA ( 1997 ) points out, “Progression in understanding about topographic point value is required as a sound footing for efficient and right mental and written calculation” ( p.4 ) . In the written work the kid manifested some abilities in add-on and minus ( See Appendix 2 for inside informations ) , although such cognition is a rare phenomenon for kids of 5-6 old ages ( Bryant, Morgado & A ; Nunes, 1992 ) . Furthermore, the kid invariably drew a analogue between single mathematical symbols and acquired mathematical forms ; for Craft ( 2002 ) such originative method is widely spread among immature kids.

In position of these consequences, three attainment marks out of four were achieved by a kid ( See Appendix 3 that summarises the findings of the conducted appraisal ) . In peculiar, in Target 1 the kid attained Level 3, as he masterfully used and applied mathematics in different contexts ; for all that, the contexts were meaningful and reflected apprehension of symbols. For case, the kid was able to number from 1 to 50 ( both in sequence and out of sequence ) , recognise ordinal and central Numberss, evaluate objects’ measures and work out mathematical undertakings with the aid of mental callback ; the latter facet particularly respects figure equations ( e.g. 19 + 3 = 22 or 38 -5 = 33 ) . In Target 2 the kid attained Level 2, because he started to utilize some elements of minus and add-on, every bit good as computations of topographic point value. Refering the first facet, he demonstrated considerable accomplishments in minus and add-on equations, for illustration 8 + 2 = 6 + 4 or 12 – 4 = 10 – 2. Besides, the kid revealed unusual apprehension of mathematical forms which he recognised in Numberss, objects and forms. Finally, in Target 3 the kid attained Level 2, as he revealed apprehension of form, infinite and steps. As the child’s work showed, he recognised forms in images and analysed their belongingss, discussed measures of certain objects, evaluated clip and constructed simple forms. As for measurings, he was able to mensurate simple weight, length, temperature and money.

In this regard, the written and unwritten appraisals displayed that the kid well exceeded the mark criterions for his age-group, as he non merely gave accurate replies to mathematical undertakings, but besides easy coped with assorted logical issues. Therefore, the kid had good abilities in job resolution, communicating and logical thinking. As for job resolution, the informations presented in the appendices pointed out that the kid knew different problem-solving schemes and used them in appropriate contexts. Refering communicating, the kid truly employed the linguistic communication of Numberss and symbols. In respect to logical thinking, he managed to supply accurate consequences in an organized mode ( for illustration, see Task 2 of the child’s written work ) . Throughout the appraisal the kid used concluding to use his cognition to mathematical undertakings ; such logical thinking was surely based on clear logic. However, in some instances the kid seemed to utilize his ain thought alternatively of rigorous mathematical regulations and processs ; harmonizing to Thompson ( 1997 ) such attack consequences in less mistakes and better apprehension of mathematics. The same point of view is maintained by SCAA ( 1997 ) : “One ground that some students do non larn strategic methods for mental mathematics consequences from an over-reliance on numbering procedures” ( p.14 ) . As was stated above, the kid was non relied entirely on the taught mathematical processs ; on the contrary, he normally applied to certain mathematical artworks and drawings to happen a proper solution. In his hunt the kid deviated from the traditional mathematical constructs and procedures, but, however, provided right replies to both easy and complex undertakings.

In the procedure of appraisal it was found out that the kid demonstrated an unusual involvement in mathematics ; furthermore, his originative development positively influenced the child’s mathematical accomplishments. Using imaginativeness to construe new stuff, the kid managed to achieve appropriate cognition in a rapid manner ; in this respect, his attainment of cognition was non mechanical, but deliberate. It was obvious that a kid acquired figure sense through visual image, and in the point of view of Anghileri ( 2000 ) , it is impossible to understand mathematical forms and constructs without the acquisition of figure sense. In fact, today visual image of mathematical constructs is normally equated to such procedures as numeration or calculation, though traditional methods of maths learning continue to disregard the important function of visual image. Overall, the kid appeared to unite imaginativeness and visual image to construe mathematical undertakings ; such mixture of methods provides better consequences than a individual method. However, it is necessary to reenforce the survey of mental computation methods in the following stairss of child’s instruction, as there is a spread between written and mental computation methods. The kid successfully coped with written computations, while he had little troubles with mental computations, although no misconceptions were identified in the procedure of appraisal. Extra instructions in numeration and other mathematical operations will farther determine the child’s mathematical abilities. In the response category the kid will be taught to multiply and split Numberss and happen solutions to different mathematical jobs ( Munn, 1994 ; Carruthers & A ; Worthington, 2006 ) . Besides, he will larn how to understand mathematical artworks and do complex computations through dramas. The child’s cognition of mathematics may be enhanced by the usage of specific computing machine plans that help kids to understand assorted mathematical expressions and forms without troubles ( Noss, 1997 ) .


Appendix 1

The transcript of an interview

Question 1. Please, listen to a poetry and state me how many coneies appear in the poetry:

“One large bunny coney resiling merely like you,

Along came another one and so there were two.

Two large bunny coneies delving by a tree,

Along came another one and so there were three” .

Answer: Three coneies.

Question 2. Here is a cat. It will number to fifteen and you should rectify it, if it is incorrect.

“One pen, two books, four apples…”

Answer. The cat misses figure three.

“five dishes, six doors, seven autos, 10s dogs…”

Answer. The cat misses Numberss eight and nine.

“eleven pencils, twelve male childs, 14 lamps, 15 papers”

Answer. The cat misses figure 13.

Question 3. I will demo you cards with Numberss from 1 to 40 and you need to call them.

13, 18, 23, 40, 11, 15, 39, 2, 5, 8… .

Answer. 13, 18, 23, 40, 11, 15, 39, 2, 5, 8…

Question 4. Please name the monetary value of the undermentioned goods.


A book – 45p

A jumper – a‚¤15

A loaf of bread – a‚¤2

A chair – a‚¤50

An eraser – 35p

An album – a‚¤3

A pencil – a‚¤2

Question 5. What are Numberss between 11 and 13 and between 15 and 17.

Answer. 12 and 16.

Appendix 2

The sample of the child’s written work

Undertaking 1. What are the forms of the undermentioned figures? ( The figures are presented on images )


A circle

A square

An ellipse

A rectangle

Undertaking 2. Count the figure of books on the shelf ( See a image ) . How many books are ruddy and how many books are xanthous?

Answer. The figure is 17. There are 3 ruddy books and 7 xanthous books.

Undertaking 3. Here are some cards with different Numberss of lines. Identify which cards have more lines and which cards have less lines.

Answer. The cards 3 and 5 have more lines and the cards 1, 2, 4 have fewer lines.

Undertaking 4. Measure topographic point value of the undermentioned Numberss: 67, 34, 28, 83 and 72

Answer. 67 – 6 10s and 7 units ; 34 – 3 10s and 4 units ; 28 – 2 10s and 8 units ; 83 – 8 10s and 3 units ; 72 – 7 10s and 2 units.

Undertaking 5. Imagine a auto with three work forces. The auto makes a halt and one adult male gets out of it. How many work forces are in the auto now?

Answer. Two work forces.

Appendix 3

Attainment marks of the kid





Target 1

Using and using mathematics


1 ) Counts from 1 to 50

( in sequence and out of sequence ) ;

2 ) Solves mathematical undertakings that are instead complex for his age ;

3 ) Recognises ordinal and central Numberss ;

4 ) Evaluates objects’ measures.

Target 2

Number and algebra


1 ) Uses some elements of minus and add-on ( particularly minus and add-on equations ) ;

2 ) Reveals some cognition in topographic point value ;

3 ) Demonstrates understanding of mathematical forms.

Target 3

Shape, infinite and steps


1 ) Recognises forms in images ;

2 ) Discusses measures of certain objects ;

3 ) Constructs simple forms and steps infinite ;

4 ) Evaluates clip ;

5 ) Measures weight, length, money and temperature.


Anghileri, J. ( 2000 )Teaching Number Sense. London, Continuum.

Anghileri, J. ( 2001 )Principles and Practices in Arithmetic Teaching Innovative Approaches for the Primary Classroom. Buckingham, Open University Press.

Bryant, P.E. , Morgado, L. & A ; Nunes, T. ( 1992 )Children’s Understanding of Multiplication. Proceedings of the Annual Conference of the Psychology of Mathematics Education, Tokio.

Carruthers, E. & A ; Worthington, M. ( 2006 )Children’s Mathematics, Making Marks, Making Meaning. London, Sage Publications.

Craft, A. ( 2002 )Creativity and Early Old ages Education. London, Continuum.

DfEE ( 1999 )The National Numeracy Strategy. London, Department for Education and Employment.

Lewis, M. ( 2002 ) The Foundation Stage in England.Early Education, 38, 6.

Munn, P. ( 1994 ) The Early Development of Literacy and Numeracy Skills.European Early Childhood Education Research Journal, 2 ( 1 ) , 5-18.

Noss, R. ( 1997 )New Cultures, New Numeracies. London, Institute of Education.

QCA ( 2000 )Curriculum Guidance for the Foundation Phase. London, Qualification and Curriculum Authority.

SCAA ( 1997 )The Teaching and Assessment of Number at Key Stages 1-3. Discussion Paper No10. London, School Curriculum and Assessment Authority, MA/97/762.

Thompson, I. ( 1997 )Teaching and Learning Early Number. Buckingham, Open University Press.

Thompson, I. ( 2000 ) The National Numeracy Strategy: Evidence – or Experience-based?Mathematicss Teaching, 171, 23-27.

Tymms, P. ( 1999 )Baseline Assessment and Monitoring in Primary Schools: Accomplishments, Attitudes, and Value-Added Indexs. London, David Fulton.

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