View in EDS HTML Full Text PDF Full Text

Realizing the Cognitive Potential of Children 5-7 with a Mathematics Focus: Post-Test and Long-Term Effects of a 2-Year Intervention

Saved in:
Bibliographic Details
Title: Realizing the Cognitive Potential of Children 5-7 with a Mathematics Focus: Post-Test and Long-Term Effects of a 2-Year Intervention
Language: English
Authors: Shayer, Michael, Adhami, Mundher
Source: British Journal of Educational Psychology. Sep 2010 80(3):363-379.
Availability: British Psychological Society. St Andrews House, 48 Princess Road East, Leicester, LE1 7DR, UK. Tel: +44-116-254-9568; Fax: +44-116-227-1314; e-mail: enquiry@bps.org.uk; Web site: http://www.bpsjournals.co.uk
Peer Reviewed: Y
Page Count: 17
Publication Date: 2010
Document Type: Journal Articles
Reports - Research
Education Level: Elementary Education
Elementary Secondary Education
Grade 1
Grade 2
Descriptors: Foreign Countries, Intervention, Academic Achievement, Effect Size, Educational Strategies, Educational Theories, Achievement Gains, Educational Policy, Mathematics Instruction, Elementary School Students, Psychoeducational Methods, Learning Strategies, Intelligence, Pretests Posttests, Hypothesis Testing, Longitudinal Studies, Instructional Effectiveness, Cognitive Development, Cognitive Ability, Teaching Methods, Student Development, English, Piagetian Theory
Geographic Terms: United Kingdom
DOI: 10.1348/000709909X482363
ISSN: 0007-0998
Abstract: Background: In the context of the British Government's policy directed on improving standards in schools, this paper presents research on the effects of a programme intended to promote the cognitive development of children in the first 2 years of primary school (Y1 & 2, aged 5-7 years). The programme is based on earlier work dealing with classroom-based interventions with older children at both primary and secondary levels of schooling. Aim: The hypothesis tested is that it is possible to increase the cognitive ability of children by assisting teachers towards that aim in the context of mathematics. A corollary hypothesis is that such an increase would result in an increase in long-term school achievement. Sample: The participants were 8 teachers in one local education authority (LEA) and 10 teachers in another. Data were analysed on 275 children present at Year 1 pre-test in 2002 and at long-term Key Stage 2 post-test in 2008. Method: Two intervention methods were employed: a Y1 set of interactive activities designed around Piagetian concrete operational schemata, and mathematics lessons in both Y1 and Y2 designed from a theory-base derived from both Piaget and Vygotsky. Results: At post-test in 2004, the mean effect sizes for cognitive development of the children--assessed by the Piagetian test "Spatial Relations"--were 0.71 "SD" in one LEA and 0.60 "SD" in the other. Five classes achieved a median increase of 1.3 "SD". The mean gains over pre-test in 2002 for all children in Key Stage 1 English in 2004 were 0.51 "SD", and at Key Stage 2 English in 2008--the long-term effect - were 0.36 SD, an improvement of 14 percentile points. Conclusions: The main hypothesis was supported by the data on cognitive development. The corollary hypothesis is supported by the gains in English. The implications of this study are that relative intelligence can be increased and is not fixed, and that children can be led into collaborating with each other to the benefit of their own thinking, and that there does exist a theory-based methodology for the improvement of teaching.
Abstractor: As Provided
Entry Date: 2010
Accession Number: EJ897990
Database: ERIC
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
    Url: https://content.ebscohost.com/cds/retrieve?content=AQICAHj0k_4E0hTGH8RJwT4gCJyBsGNe_WN95AvKlDbXJGqwxwHi6JKclU1fgdfV34ICtvWxAAAA4jCB3wYJKoZIhvcNAQcGoIHRMIHOAgEAMIHIBgkqhkiG9w0BBwEwHgYJYIZIAWUDBAEuMBEEDL6Lp8ixMoDxVmca-gIBEICBmlh2Cv5haixPEUlW5BGe42Wl6UF2p9y4nM9hLttqVI6ze672Gao1IGnP8KcS8YwimxI2kOoMk6Ncf7ZRJOVbGLdp0MPMcpkTxCXXYoPkdh-I191bSDTgPJQxpwRaaEwsBSePF-HJ-wz5wsk6VJOEExLg9m9xnUJTKhQukAzxsw-aCIZNoATPeLuMGH28UxmWq14cqBWQ7A6OoJU=
Text:
  Availability: 1
  Value: <anid>AN0053883585;6kx01sep.10;2019May28.12:46;v2.2.500</anid> <title id="AN0053883585-1">Realizing the cognitive potential of children 5-7 with a mathematics focus: Post-test and long-term effects of a 2-year intervention. </title> <p>Background: In the context of the British Government's policy directed on improving standards in schools, this paper presents research on the effects of a programme intended to promote the cognitive development of children in the first 2 years of primary school (Y1 & 2, aged 5–7 years). The programme is based on earlier work dealing with classroom‐based interventions with older children at both primary and secondary levels of schooling. Aim: The hypothesis tested is that it is possible to increase the cognitive ability of children by assisting teachers towards that aim in the context of mathematics. A corollary hypothesis is that such an increase would result in an increase in long‐term school achievement. Sample: The participants were 8 teachers in one local education authority (LEA) and 10 teachers in another. Data were analysed on 275 children present at Year 1 pre‐test in 2002 and at long‐term Key Stage 2 post‐test in 2008. Method: Two intervention methods were employed: a Y1 set of interactive activities designed around Piagetian concrete operational schemata, and mathematics lessons in both Y1 and Y2 designed from a theory‐base derived from both Piaget and Vygotsky. Results: At post‐test in 2004, the mean effect sizes for cognitive development of the children – assessed by the Piagetian test Spatial Relations – were 0.71 SD in one LEA and 0.60 SD in the other. Five classes achieved a median increase of 1.3 SD. The mean gains over pre‐test in 2002 for all children in Key Stage 1 English in 2004 were 0.51 SD, and at Key Stage 2 English in 2008 – the long‐term effect – were 0.36 SD, an improvement of 14 percentile points. Conclusions: The main hypothesis was supported by the data on cognitive development. The corollary hypothesis is supported by the gains in English. The implications of this study are that relative intelligence can be increased and is not fixed, and that children can be led into collaborating with each other to the benefit of their own thinking, and that there does exist a theory‐based methodology for the improvement of teaching.</p> <p>This paper presents research on the effects of a programme intended to promote the cognitive development of children in the first 2 years of primary school (Y1 & 2, aged 5–7 years). Detail of its relation to previous intervention work with older children may be seen in [<reflink idref="bib22" id="ref1">22</reflink>] and [<reflink idref="bib27" id="ref2">27</reflink>].</p> <p>Earlier research on cognitive development of 10‐ to 16‐year‐olds had revealed that on Piagetian measures the levels of 11‐/12‐year‐olds entering secondary education spanned some 12 developmental years – i.e., from the average 6‐year‐old to the above‐average 16‐year‐old ([<reflink idref="bib30" id="ref3">30</reflink>]). On the other hand, research on 5‐ to 8‐year‐olds ([<reflink idref="bib28" id="ref4">28</reflink>]) had shown that 20% of the 7‐year‐olds were already at the mature concrete level (2B), the average level of 12‐year‐olds. A possible interpretation of these data – consistent also with data on 16‐year‐olds reported in [<reflink idref="bib31" id="ref5">31</reflink>] and the development charted in [<reflink idref="bib13" id="ref6">13</reflink>] – is that only 20% of the child population follow the complete developmental path described by Piaget. Bearing in mind that in Britain in 1945 only 20% of the population were deemed suitable for grammar school education, it seemed desirable to test whether an intervention at the outset of primary education might increase this proportion by the age of 7, thus increasing the potential for more children to benefit from the rest of their time in school. This intention was reinforced, after the start of the research project, by the data reported in [<reflink idref="bib29" id="ref7">29</reflink>] which showed that on the test of Piagetian conservations, <emph>Volume&Heaviness</emph>, the average performance of the 11‐/12‐year‐olds had slipped by 2004 to the level of the 8‐ to 9‐year‐olds in 1976.</p> <hd id="AN0053883585-2">The grounding of the RCPCM work in the maths education literature 1</hd> <p>The detailed specifics, and how they were used, are found in [<reflink idref="bib23" id="ref8">23</reflink>] and [<reflink idref="bib26" id="ref9">26</reflink>]. But from [<reflink idref="bib7" id="ref10">7</reflink>] and [<reflink idref="bib32" id="ref11">32</reflink>] were drawn the importance of concepts of <emph>measure</emph> in even 5‐year‐olds' development of their concept of number, neglected in much current teaching including the England and Wales National Numeracy scheme. From the work of [<reflink idref="bib6" id="ref12">6</reflink>] and [<reflink idref="bib8" id="ref13">8</reflink>] – and by implication from the early work of [<reflink idref="bib9" id="ref14">9</reflink>] – come the importance of multiple representations of number using both sides of the brain. From [<reflink idref="bib19" id="ref15">19</reflink>] comes the insight that even 5‐ and 6‐year‐olds have primitive concepts of multiplicative relations between numbers as well as additive, linking with measures, which are based on the ratio between the size of an object and the measure unit. And from much of the work of Nunes ([<reflink idref="bib17" id="ref16">17</reflink>]), and [<reflink idref="bib18" id="ref17">18</reflink>] detailed empirical research of how to promote multiplicative thinking was drawn on in the construction of thinking maths (TM) lessons, with the intention, by the end of Year 2, of evening up the balance in children's experience of number between the additive and multiplicative (ratio) aspects.</p> <p>In [<reflink idref="bib21" id="ref18">21</reflink>], one of the largest educational intervention effect sizes ever achieved – 2 <emph>SD</emph>s on mathematics achievement – is reported. The study describes work done in a single first year primary class in arithmetic (6‐ to 7‐year‐olds), the authors comment:</p> <p>The children with whom we have worked come disproportionally from among the least favoured of American families. Many of them are considered to be educationally at risk ... Yet these children learned effectively in a type of programme that, if present in schools at all, has been reserved for children judged able and talented–most often those from favoured social groups.</p> <p>This experiment, featuring a collaborative learning style for the children's mathematics work having much in common with that used in the realizing the cognitive potential of children 5–7 with a mathematics focus (RCPCM) classrooms, was also drawn on.</p> <hd id="AN0053883585-3">The Thinking Maths (TM) lessons</hd> <p>Insights into cognitive development from both Piaget and Vygotsky are used in the conduct of a <emph>TM</emph> lesson ([<reflink idref="bib3" id="ref19">3</reflink>]; [<reflink idref="bib4" id="ref20">4</reflink>]). Both believed in the virtues of collaborative learning. But Piaget himself made a seminal contribution to the mathematics literature in his book on number ([<reflink idref="bib19" id="ref21">19</reflink>]). From this and elsewhere ([<reflink idref="bib11" id="ref22">11</reflink>]; [<reflink idref="bib25" id="ref23">25</reflink>]), it was possible to assess all the statements in the England and Wales National Curriculum (NC) in terms of demand levels from early concrete through to concrete generalization. Similarly, the levels of the different agendas in a <emph>TM</emph> lesson were also assessed. Given the data in the monograph ([<reflink idref="bib28" id="ref24">28</reflink>]), the target aimed for in Year 2 (Y2) <emph>TM</emph> lessons, when the children would be 7, was mature concrete (for the Year 1 lessons it had been middle concrete). Each lesson started with an episode at a lower level, and the episodes – up to 3 – were designed so that children from a wide range of initial cognitive abilities could each make some progress from their present level during each lesson.</p> <p>Looking at the agenda of the <emph>TM</emph> lessons (and also the children) through Piagetian eyes is thus an essential aspect of the art. But Piaget's work tells us little (except the importance of 'cognitive conflict') about how to teach the lessons. For this, we turn to a view of Vygotsky's concept of the zone of proximal development (ZPD) that suggests that the mediating role of the teacher should be to maximize the collaborative processes through which the children can mediate each other's learning (see Appendix for an exposition of this view).</p> <p>Each episode of a <emph>TM</emph> lesson is a 3‐Act play. The first, called Concrete Preparation, introduces the context of the lesson agenda at a level where all in the class can participate (5–8 min). Here the 'argument within the collective' is begun. Several children are asked to describe their views of what the task ahead involves, and to suggest possible strategies of solving it. In some cases, the children are asked quickly in pairs, while sitting on the carpet, to attempt the easier parts of the task. Then different pairs are asked to offer their ideas, which others then discuss. In the second act, Construction, children, in groups from 2 to 4 or 5 are asked to go to their tables and attempt the first worksheet. In a few minutes time, they will be asked to present their ideas to the rest of the class, so they do not waste time in 'neat work': they discuss vigorously with each other, using pencils on papers, until they feel they have something worth saying or showing (typically, 7–12 min). Act 3, Reflection, is again communal – often on the carpet in front of the whiteboard again – where their different solutions are shown and shared with the whole class (8 min at least). Thus in Acts 1 and 2, the community of learning is created, in which children offer different insights, which are made available for all to work with. But Act 3, well managed by the teacher, gives maximum chances for the individual ZPDs of the children to be completed as they witness the ideas produced by the other groups. Typically Act 3 leads naturally to the next episode with agenda set usually at a higher level.</p> <hd id="AN0053883585-4">Method</hd> <p></p> <hd id="AN0053883585-5">The locations of the RCPCM research</hd> <p></p> <hd id="AN0053883585-6">The research team at Hammersmith and Fulham in 2001/2004</hd> <p>Hammersmith and Fulham (H&F) is a local education authority (LEA) in Inner London, with some areas of social deprivation in which the experimental classes were located. The initial task in 2001/2002 was to create the <emph>TM</emph> lessons for Y1 use in 2002/2003. Four teachers, previously selected to assist in professional development (PD) for the CASE@KS1 <emph>Let's Think</emph>2 lessons in H&F schools, were chosen as teacher‐researchers. The research team consisted of the two authors from King's College, an Advisory Teacher for H&F, and the four teacher‐researchers, and met for a whole afternoon working session every 3 weeks. Initially, the two authors would suggest mathematical contexts for a possible lesson, and then the whole team would work on how the lesson might be presented, and what worksheets, etc. were needed. Then one of the teacher‐researchers would offer to trial the lesson with a Y1 class, with the two authors in support. The first author would make detailed notes with a time line of the trial lesson, which would be written up for the next team afternoon. From that feedback, the whole team would then revise the initial lesson plan, and one or the other of the authors would produce all the materials needed for the project teachers. Often an amended version of the lesson was re‐trialled – sometimes more than once – before the team were satisfied with it. Later some of the ideas for the <emph>TM</emph> lessons came from the teacher‐researchers. Twelve <emph>TM</emph> lessons were generated for 2002/2003 (Y1) and 19 for 2003/2004 (Y2). Thus, the generation of lessons was based on the same processes of collaborative learning, with the teacher‐researchers, as the project teachers would be asked to use with their children.</p> <hd id="AN0053883585-7">The research team at Bournemouth in 2001/2004</hd> <p>Bournemouth is a town on the south coast of England with a school intake about the national average. The H&F and King's team had the responsibility of generating the <emph>TM</emph> lessons. But the Bournemouth LEA on the south coast of England offered to run a parallel replication of the RCPCM intervention in 2002/2004 in their schools – but taking the collaborative learning aspect of the classroom practice as their focus.</p> <hd id="AN0053883585-8">The research design: 2002–2004</hd> <p>In a recent research project CASE@KS1.H&F, in the LEA of H&F, [<reflink idref="bib2" id="ref25">2</reflink>] had reported for a 1‐year intervention with Y1 children (5/6 years of age) post‐test effect sizes in relation to control schools of 0.47 and 0.43 <emph>SD</emph>s on Piagetian tests. Children were given, every week, interactive and collaborative learning focused on the major concrete operational schemata – classification, seriation, spatial perception, time relations, and causality – described by Piaget. Their lessons were called <emph>Let's Think</emph> ([<reflink idref="bib1" id="ref26">1</reflink>]). Their interactive learning was conducted for some 20–30 min each day with groups of six children around a table with the teacher. Thus by the end of the week, every child had experienced the activity (given 30 children in the class) and the teacher had both been able to mediate the children into collaborative learning, and also learnt much about their individual learning difficulties. Yet the exercises in thinking had not been located within the context of any specific part of the National Curriculum (NC). This led to the design of the RCPCM Project that the H&F LEA agreed to participate in.</p> <p>In addition to experiencing the <emph>Let's Think</emph> activities, Year 1 (Y1) children would also receive whole‐class <emph>TM</emph> lessons in order to focus their thinking skills within one major subject of the NC. Then in Y2, the second year of full‐time education, the <emph>Let's Think</emph> work would have ceased but the children, already used to the learning strategies practised in the Y1 <emph>TM</emph> lessons, would now receive further whole class <emph>TM</emph> lessons at a rate of about one every 10 days. In addition, the teachers would be encouraged, where possible, to use the same teaching skills within the context of their ordinary numeracy work, and also to establish a link between the children's <emph>TM</emph> insights and the NC learning objectives.</p> <p>The RCPCM intervention featured 8 experimental classes in 8 H&F schools and 10 experimental classes in 4 schools in Bournemouth (mean age at Y1 pre‐test 5 years, 7 months, <emph>SD</emph> 3.9 months). H&F provided 5 control classes and Bournemouth provided 11. Table 1 shows the research design.</p> <p>Graph</p> <p>The schools were selected by the LEA Advisory Teachers in consultation with their Heads, on the assumption that the whole year group would be involved. The H&F schools were all one‐form entry: in Bournemouth all classes in the year group were involved. The selection was not random, but the samples are believed to be representative of the LEAs involved. In H&F the teachers received a 2‐day session of professional development (PD) twice each term in Y1 and Y2 up to and including the Spring term 2004. In Bournemouth, there were four 1‐day PD sessions from March to May 2002 on the <emph>Let's Think</emph> teaching, seven 1‐days of PD during Y1 for the <emph>TM</emph> lessons, and two 1‐day sessions in the first term of Y2.</p> <hd id="AN0053883585-9">Experimental and control groups</hd> <p>Table 2 shows data used frequently in the UK as a measure of socio‐economic status of families: the percentage of children in the schools allowed free school meals (%FSM). The control groups in each LEA were chosen as far as possible to cover the range of intakes of the experimental groups. For the difference between the mean of all controls and all experimentals <emph>t</emph> = −1.8; <emph>p</emph> =.088 for %FSM. Thus although the socio‐economic status of the intakes to the control schools is higher (%FSM are lower) the difference is not so great as to invalidate the study. It is convenient also to have control data that gives information on the higher levels of performance at post‐test. Details of all schools are shown in Table 2 in order to display the wide variation in both experimental and control schools' intakes.</p> <p>Graph</p> <p>H&F had been given by the Government in 1998 a 'Single Regeneration Budget' – that is, a considerable sum of money in recognition of the social disadvantage in the population supplying the LEA schools' intake. Some of it was spent in funding the previous CASE@KS1 project. The intention of the RCPCM project was to enhance the cognition and learning ability of the H&F pupils to at least the national average. At the same time, it was thought desirable simultaneously to replicate the intervention in an LEA with a quite different social composition. Table 3 compares the ethnic compositions of the two LEAs.</p> <p>Graph</p> <p>The details in both Tables 2 and 3 are of the whole schools in 2002/2003, so may not exactly describe the Y1 year groups. The contrast between the two LEAs can clearly be seen in Table 3, but inspection of Table 2 shows there is socio‐economic disadvantage comparable with that in H&F in the intake of at least two of the Bournemouth experimental schools.</p> <hd id="AN0053883585-10">The tests used</hd> <p>The Piagetian Spatial Relations test ([<reflink idref="bib16" id="ref27">16</reflink>]) was used in the original CSMS3 research covering the range early concrete (2A) through the concrete generalization (2B*) level. For the Y2 post‐test with the 7‐year‐olds, it was found possible to use it in its original form, as Piaget's original research featured children of this age. The two authors administered the test in H&F; in Bournemouth the first author tested the classes in one school as a demonstration for those testing the other schools. All the children's responses are given in the form of their own drawings: no reading or writing is involved. The first question involves them drawing a jam‐jar half‐full of water at the various orientations the teacher shows them (upright, tilted at 30° off vertical, and on its side: they have to imagine the water). The second gives them a drawn hill and asks them to draw a house on one side, and three trees on the other. The third repeats the agenda of question 1, but now with a jar containing a plumb‐line hanging from its lid. The fourth, permitting an assessment at the 2B* level as well as all levels going down to pre‐operational, asks them to imagine themselves standing in the middle of a road consisting of an avenue of trees, and to draw what they would see, covering the near distance as well as afar. Assessment of the children's responses consists of seeing how many aspects of the situation, how many relations, they can consider in the act of drawing. The scoring decisions are taken from the drawings in [<reflink idref="bib20" id="ref28">20</reflink>]. Thus with the hill, if they can handle one relation at a time only (early concrete, 2A) then they relate the orientation of the house just to the slope of the hill. But if they can handle two relations (mature concrete, 2B) then they will also bear in mind earth's horizontal, and they will draw the houses and the trees upright. In effect, the test measures the complexity of relations the children can handle in the moment, and thus acts as a test of fluid intelligence ([<reflink idref="bib24" id="ref29">24</reflink>]). The two authors assessed all the children's drawings from both LEAs. The test reliability is.82. Items 1 and 3 have four scoring levels, ranging from <2A (early concrete) to 2B (mature concrete). Item 2 has five scoring levels, ranging from <2A to 2B* (concrete generalization). Item 4 has six scoring levels, from <2A to the 2B*/3A (early formal) boundary. It is therefore equivalent to a 19‐item test, and was scored using the rating scale Rasch analysis to give an equal interval scale from 2.79 (just below 3 = 2A, early concrete) to >6.3 (higher range of concrete generalization).</p> <p>For the pre‐test at age 5, a modified version of the test designed by Adey for the CASE@KS1 project was used ([<reflink idref="bib2" id="ref30">2</reflink>]). Instead of requiring the children to draw all their answers, the apparatus was drawn for them (although still demonstrated by the teacher administering the test) so e.g., in the first question they were simply asked to draw in the water for each orientation of the jam‐jar. Adey cited a reliability figure of 0.74, but this lower figure is due to the restriction of range of the performance of the younger children.</p> <p>KS1 (Standard Assessment Tasks) (SATs) are Government tests taken by all children at the end of Y2, and used to assess schools' performance and are not published (KS1 is Key Stage 1 from 5 to 7 years, and Key Stage 2 is from 7 to 11). The Key Stages 1 and 2 test data were supplied by the schools after any appeals had been dealt with; the Y6 KS2 SAT results at the school level were published on 1 April 2009.</p> <hd id="AN0053883585-11">Results</hd> <p>Bearing in mind that long‐term effects data were obtained for Key Stage 2 SATs in both Maths and English the entire data analysis is conducted on only those children present at pre‐test in Y1 2002 and also in the 2008 SATs when they were 6<sups>1</sups>/<subs>2</subs> years older. In this way, all the effects are analysed on the same children. Although this is a 43% loss of sample for the experimental groups, it was thought this was an acceptable price to pay for a cleaner analysis of the data. In both LEAs, the mobility of children in the experimental schools is high.</p> <hd id="AN0053883585-12">Effects on cognitive development</hd> <p>For Figures 1–5, the mode of data analysis was first to obtain the residualized gain scores (RGS) in relation to the initial pre‐test scores on the Spatial Relations test on the 5‐year‐olds. For example for Figure 2, the regression for the KS1 Maths class mean scores on the class means for the Spatial Relations pre‐test was first computed for the control classes. The pre‐test mean score for each experimental class was then entered into the control's regression equation. The difference between the class KS1 Maths mean score and the score predicted from the control regression line is the RGS for the experimental class. The regression line averages all the controls, and the RGS shows the difference from what would have been expected had the experimental class been one of the controls. The correlation between pre‐ and post‐test scores is, of course, not perfect, so one should imagine the control class means lying scattered both above and below the regression line. In this way, in Figures 1–5, in addition to the experimental effect sizes, one sees also the extent to which the control classes vary above and below their own regression line; their class number weighted mean RGS sum to exactly zero. The RGS scores were then divided by the standard deviation of all the control children to convert them into effect sizes to allow for comparison from test to test.</p> <p>Graph: 5 Key Stage 2 English effects 2008.</p> <p>Graph: 4 Key Stage 2 Maths effects 2008.</p> <p>Graph: 3 Key Stage 1 English effects 2004.</p> <p>Graph: 2 Key Stage 1 Maths effects 2004.</p> <p>Graph: 1 Post‐test effects 2004 on the Spatial Relations test.</p> <p>Figure 1 shows the effect sizes at post‐test for all the classes for the Spatial Relations test. An important variable in this study's data is the variation between teachers, both in the experimental and the control groups, so it was thought important to display this in the figures to follow.</p> <p>The distribution of experimentals' effects is hardly normal. It can be read as tri‐modal, with one median about 1.3 <emph>SD</emph> showing what can be achieved by those who grasp the whole model; a second median about 0.6 <emph>SD</emph> for those trying a method with some success for the first time; and a third median around 0 <emph>SD</emph>. The average effect sizes are equivalent to raising a set of schools initially at the 50th percentile to the 70th percentile.</p> <p>In a similar way, the post‐test results for Y2 KS1 Maths and English were analysed in relation to children's Y1 Piagetian pre‐test data. Figure 2 shows the effect sizes in 2004 for each class for KS1 Maths in relation to the original pre‐test data. Figure 3 gives the KS1 English data.</p> <p>A recent book – [<reflink idref="bib12" id="ref31">12</reflink>] – summarizing all the meta‐analytic evidence there is available in educational research literature lists 'prior achievement' of students as the major general factor affecting student achievement in schools. The general effect of 'teachers' is about half as large. While Figure 1 shows data mainly in terms of 'prior achievement' of students, effects of 'teachers' can already be seen as well in the wider variation among the control classes in Figure 2.</p> <p>When the long‐term effects for Key Stage 2 are inspected, it needs to be born in mind that in the 4 years between KS1 and KS2 children have usually experienced learning with four different teachers, none of them using the teaching strategies which are the subject of this paper, so an even greater source of variation in achievement is seen. Figures 4 and 5 shows the 2008 KS2 effects for Maths and English.</p> <p>In both KS2 graphs, it can be noticed that the H&F control classes have shown a net improvement in relation to the Bournemouth controls. As a guide to the statistical significance of these data, and also as a guide to LEAs that wish to judge whether an investment in the PD required to deliver these effects would be justified, an alternative data analysis is presented in Table 4. Here, the means of the data for all the individual children in the experimental and control groups were first computed and then converted into effect sizes using the standard deviations of the groups. Then, using the formulae described in McNemar ([<reflink idref="bib14" id="ref32">14</reflink>]) for the difference between the difference scores, the magnitudes of statistical significance required for <emph>p</emph> ≤.05 and.01 were computed.</p> <p>Graph</p> <p>The rows headed '<emph>SD</emph> difference' give the experimental/control differences in <emph>SD</emph> units. In the row headed '<emph>SD</emph> gain over pre‐test', the value for KS2 Maths for Bournemouth of 0.22 is the effect size. Such a value is usually regarded as small, but since it is greater than the 0.21 required for <emph>p</emph> ≤.01 it is still statistically significant.</p> <p>Inspection of Table 4 shows that, e.g., the experimental group in Bournemouth was initially 0.5 <emph>SD</emph> below the controls in terms of cognitive development. But by post‐test in 2004, they were actually 0.1 <emph>SD</emph> above the control group, an overall gain of 0.6 <emph>SD</emph>, compared with a figure of 0.17 <emph>SD</emph> required for significance at the 0.01 level. In KS1 English in 2004, their relative gain of 0.59 <emph>SD</emph> was just as high. For KS1 Maths, their relative gain was smaller (0.30 <emph>SD</emph>) but significant at the 0.05 level (0.24 required for <emph>p</emph> ≤.05). In this way, the performance of all groups can be interpreted.</p> <p>For Figures 6 and 7, the national average (obtained from published DfCFS4 statistics) was subtracted from the means, and the differences from the national average shown in <emph>SD</emph> units.</p> <p>Graph: 6 H&F means in relation to national averages.</p> <p>Graph: 7 Bournemouth means in relation to national averages.</p> <p>Here, it can be seen that both H&F experimentals and controls were below the national average at pre‐test, with controls 0.31 <emph>SD</emph> below experimentals. But for Bournemouth, the controls were about 0.3 <emph>SD</emph>s above national average at pre‐test, and the experimentals 0.2 <emph>SD</emph> below, a net difference of 0.5 <emph>SD</emph> as shown in Table 4.</p> <hd id="AN0053883585-13">Discussion</hd> <p>From Figure 7, it can be seen that for Bournemouth control schools the KS1 and KS2 performance is relatively the same, with a mean of the Maths and English results 0.17 <emph>SD</emph> above the national average at KS1 and 0.15 <emph>SD</emph> at KS2. The experimental group did gain over the controls by 0.30 <emph>SD</emph> (gain significant at the <emph>p</emph> ≤.05 level, Table 4) on KS1 Maths, but on KS1 English they had overcome an initial deficit of 0.5 <emph>SD</emph>. The mean of English and Maths for the controls at KS2 was 0.15 <emph>SD</emph> above the national average compared with −0.05 <emph>SD</emph> for the experimentals. Hence, the net improvement compared with pre‐test of the experimentals versus the controls was 0.30 <emph>SD</emph> (−0.50 compared to −0.20).</p> <p>From Figure 6, it can be seen that H&F controls were about the national average at KS1 for the mean of the Maths and English in 2004, whereas in 2008 the mean was 0.23 <emph>SD</emph> above average at KS2. The experimental group was well above the controls on both Maths and English at KS1, and at KS2 in 2008 was still giving the same mean attainment as the control schools. Here, there are two added values to be considered: in relation to the excellent performance of the control schools the experimental schools give a mean increase of 0.30 <emph>SD</emph>, but in relation to national statistics the added value is around 0.65 <emph>SD</emph>.</p> <p>Four years is a very long time – in children's lives – between carrying out an intervention in schools and looking for long‐term effects in school achievement. Remember that the organizing hypothesis of the RCPCM research is that increasing children's cognitive level should give a permanent improvement to their learning ability and hence later school achievement. With respect to the experimental classes there is confirming evidence in Figures 6 and 7 from the KS2 English results. But other factors can intervene subsequent to an initial intervention in schools, e.g., overall school ethos; excellent (or otherwise) teaching, etc.</p> <p>If [<reflink idref="bib12" id="ref33">12</reflink>] 'prior achievement' is what can be assessed by a test of intelligence or cognitive ability, then this has been raised by 0.71 <emph>SD</emph> for H&F and 0.6 <emph>SD</emph> for Bournemouth by 2004, with concomitant increases in achievement in English at both KS1 and KS2. But the Bournemouth results for Maths at KS2 require comment and will be discussed below under PD.</p> <hd id="AN0053883585-14">The process of Professional Development (PD)</hd> <p>Given the previous description of RCPCM classroom processes it follows that simply 'telling' teachers how to do it was not an option. Just as each pupil – in interaction with other children in their close environment – has to construct each cognitive concept in their own mind, so too the PD of teachers needs a parallel process. The teachers need that not only for the development of their own skills: undergoing the same process themselves also gives them insight into managing their pupils' learning. In the H&F 2‐day PD sessions, teachers were split into two groups of 4: each group was given the teachers' guides and materials for a new different <emph>TM</emph> lesson. They were to discuss the lesson content and produce a lesson plan sufficiently detailed so that they could then give and explain it to the others. After the groups had shown each other the lesson plans, and answered questions arising, each group would go to a different primary school class accompanied by a member of the research team, and team teach one of their lessons. Later at the Teacher's Centre each group would report how their lesson plan had been realized, what difficulties they had encountered, and further ideas for teaching the lesson. First thing next morning the two groups would teach the other lesson, and then return to the Teachers' Centre for feedback and other PD agenda.</p> <p>In addition, each school was visited by one of the teacher‐researchers to see <emph>TM</emph> lessons taught and give the teacher personal feedback. Subsequent PD sessions would begin with a detailed reporting by teachers of their experience of teaching the lessons to their own pupils, and then followed by further work on new lessons as before. Everything to do with the specifics of both the Piagetian and the Vygotskian aspect of the art would be explored both in context and in terms of the teachers' own experience.</p> <p>From what the two authors were able to see on visits to Bournemouth the PD for <emph>Let's Think</emph> in Y1 was well done: they did see the teaching in one school as well as attending PD sessions. The teachers seemed to have learnt a lot from working with groups of six children each day, and it may be that that the cognitive development of the children was largely due to this, together with the information on children's learning difficulties that they may have applied to their conduct of other lessons. The Bournemouth teachers found the mathematics more difficult to handle, and the two authors had no time to assist in this in Bournemouth. The funding from ESRC did not extend to paying for much of the PD in Bournemouth: thus less time was given to the PD for the <emph>TM</emph> lessons in Y1 & 2 than in H&F, and in particular the collaborative learning between teachers planning and visiting each other's lessons, practised in H&F, was not provided in Bournemouth. In addition, those attending the PD sessions were the school Head and the lead teacher. Even had funding been available it would still have been impossible for the 4 teachers from school D or the 3 teachers from school B (see Figure 1) to be absent together on the PD days. Even so the experimentals did gain over the controls in KS1 Maths: the subsequent 4 years of teaching from Y3 to Y6 in the experimental schools appear to have favoured learning in English rather than mathematics: this is probably Hattie's 'teacher effect'.</p> <p>The research presented in this paper bears on two issues: the practice of PD and also the practice of mathematics teaching. Evidence has been produced that government hopes for the improvement of standards in schools could be realized by focus on and funding of the methods utilized in the research presented in this paper. In the paper by Shayer, Ginsburg, and Coe (2007) referred to earlier children's grasp of physical conservations at entry to secondary school – mainly related to their learning experiences between the ages of 5–8 – had deteriorated by an average of 0.79 <emph>SD</emph> in comparison with 1976. The data in Table 4 and Figures 1–5 show the possibility that this anti‐Flynn effect could be reversed.</p> <p>While it is true that the context of mathematics was used with the intention of making the children better thinkers, as shown by the results for English for both H&F and Bournemouth, it is claimed that the insights derived from the work both of Piaget and Vygotsky into the learning difficulties of children is also a contribution to mathematics education itself. But the contrast between the results in mathematics between H&F and Bournemouth also shows that, without a simultaneous investment in a collaborative style of PD, teachers are unlikely to construct, between each other and for themselves, both the new insight into mathematics and also the teaching skills they need to produce the better learning of their children.</p> <hd id="AN0053883585-15">Appendix</hd> <p>The interpretation of Vygotsky's concept of the ZPD used here is different from a view currently held widely, and evident in [<reflink idref="bib15" id="ref34">15</reflink>]. They say (p. 59):</p> <p>... the individual is not the most useful unit of analysis</p> <p>and that (p. 61):</p> <p>We will use the more general interpretation of ZPD in these discussions, referring to the zone as a location – in the teacher–child interaction – in which new understandings can arise</p> <p>It is not denied that this approach usefully extends the Brunerian concept of 'scaffolding' in the direction of a general theory of instruction, but that it is a valid interpretation of Vygotsky is questioned. Moreover, it is inadequate to address the deeper levels at which cognitive deficits are present in children. The individual child is the <emph>only</emph> focus of the theory of ZPD, and unless this is understood Vygotsky's thinking on the social origins of much individual development cannot properly be utilized.</p> <p>The notion of the ZPD arose as Vygotsky developed a practice of dynamic assessment of individual children intended to reveal far more of their current spectrum of thinking that can be revealed in a static psychological test. 'Mediation' here means that, when the psychologist finds that on some aspect of thinking the child does not succeed, he gives the child various signals intended to direct the child's perception to aspects of the task he needs to attend to before succeeding. The <emph>more</emph> mediation that is required the <emph>less</emph> the child is on the path towards achievement, and yet if success is attained a measurement of the child's present position of partial attainment has been recorded. By conducting this testing over important parts of the psychological spectrum, the child's individual ZPD can be mapped in addition to what he can do without mediation. Although Vygotsky left no detailed records one can see ZPD specifics in all the published works of Piaget. By working with a <emph>sample</emph> of children Piaget and his co‐workers had recorded the many alternative steps through which the ZPD of an <emph>individual</emph> child might move in the process of achieving a concept. This process of dynamic assessment was extended by [<reflink idref="bib10" id="ref35">10</reflink>] and utilized in this country, in a replication of Feuerstein's <emph>Instrumental Enrichment</emph> programme, to assess the changes of children's ZPDs over a 2‐year period ([<reflink idref="bib5" id="ref36">5</reflink>]).</p> <p>Thus, in addition to what can be revealed of children's present competencies by a psychometric test, the ZPD concept reminds us that each child has, in addition, a spectrum of partially achieved competencies, some perhaps only a quarter others three‐quarters already completed. Vygotsky claimed that his ZPD measure better predicted the next 2 years' success of pupils than their psychometric test results ([<reflink idref="bib33" id="ref37">33</reflink>], chap. 6). Only this view of the individual children enables us to appreciate this widely quoted statement ([<reflink idref="bib34" id="ref38">34</reflink>]):</p> <p>We could formulate the general genetic law of cultural development as follows: any function in the child's cultural development appears twice, or on two planes. First it appears on the social plane, and then on the psychological plane. First it appears between people as an interpsychological category, and then within the child as an intrapsychological category. This is equally true with regard to voluntary attention, logical memory, the formation of concepts, and the development of volition.</p> <p>   Vygotsky' own gloss on this was:</p> <p>Functions are first formed in the collective as relations among children and then become mental functions for the individual. ([<reflink idref="bib34" id="ref39">34</reflink>]).</p> <p>and</p> <p>Research shows that reflection [by the individual] is spawned from argument [in the collective]. ([<reflink idref="bib34" id="ref40">34</reflink>], p. 165, 5 lines later).</p> <p>Thus in thinking about the social process of shared cognition that a group of children can work within, while working on a problem, most if not all jumps in children's cognitive development are made when they witness a successful performance in a child like themselves in their social milieu, and towards which they may themselves have contributed. At that point, they complete their ZPD by a process of internalization, and then perform as if they had always known that concept. The conduct of the <emph>TM</emph> lessons is made so as to promote this process. The teacher is not a psychologist and so cannot be asked to mediate in the style of a ZPD tester (even if she were she could not possibly know all the pupils in this way). Instead she has a different mediation role. Knowing that it is the acts and words of the other children in the class that are closest to each child's ZPD her mediating role is to maximize the collaborative learning in the lessons – 'reflection [by the individual] is spawned from argument [in the collective]' – intervening only to give touches to the rudder as she sees the children going off course or failing to address some important aspect of the task.</p> <ref id="AN0053883585-16"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref26" type="bt">1</bibl> <bibtext> <sups>1</sups> <emph>Realizing the Cognitive Potential of Children 5–7 with a Mathematics focus</emph>: research project funded by the Economic and Social Research Council at King's College, London 2001–2004.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref25" type="bt">2</bibl> <bibtext> <sups>2</sups> <emph>CASE@KS1.H&F</emph> (1997–2000) research project based at King's College funded as part of a Single Regeneration Budget granted to the H&F LEA by the DfES.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref19" type="bt">3</bibl> <bibtext> <sups>3</sups>CSMS: Concepts in Secondary Science and Mathematics. Research programme funded at Chelsea College by the SSRC 1974–1979.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref20" type="bt">4</bibl> <bibtext> <sups>4</sups>Department for Children, Schools and Families: the Government Education Department for England and Wales.</bibtext> </blist> </ref> <ref id="AN0053883585-17"> <title> References </title> <blist> <bibtext> Adey, P., Robertson, A., Venville, G. Let's think! Windsor: nferNELSON 2001.</bibtext> </blist> <blist> <bibtext> Adey, P., Robertson, A., Venville, G. Effects of a cognitive stimulation programme on Year 1 pupils British Journal of Educational Psychology 72 1 – 25 doi:10.1348/000709902158748 2002.</bibtext> </blist> <blist> <bibtext> Adhami, M., Shayer, M., Robertson, A. Let's think through maths!: Developing thinking in mathematics with five and six‐year‐olds London: nferNelson 2004.</bibtext> </blist> <blist> <bibtext> Adhami, M., Shayer, M., Twiss, S. Let's think through maths! 6–9 London: nferNelson 2005.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref36" type="bt">5</bibl> <bibtext> Beasley, F., Shayer, M. Learning potential assessment through Feuerstein's LPAD: Can quantitative results be achieved? International Journal of Dynamic Assessment and Instruction 1 2 37 – 48 1990.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref12" type="bt">6</bibl> <bibtext> Butterworth, B. The mathematical brain London: Macmillan 1999.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref10" type="bt">7</bibl> <bibtext> Cable, J. (1997). A constructivist theory of quantities or in praise of ratio. PhD thesis, University of London.</bibtext> </blist> <blist> <bibl id="bib8" idref="ref13" type="bt">8</bibl> <bibtext> Dehaene, S. The number sense London: Allen Lane 1997.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref14" type="bt">9</bibl> <bibtext> Dienes, Z. P. An experimental study of mathematics learning London: Hutchinson 1963.</bibtext> </blist> <blist> <bibtext> Feuerstein, R., Rand, Y., Hoffman, M. B. The dynamic assessment of retarded performers: The learning potential assessment device: Theory, instruments, and techniques Baltimore, MD: University Park Press 1979.</bibtext> </blist> <blist> <bibtext> Hart, K. Children's understanding of mathematics: 11–16 London: John Murray 1981.</bibtext> </blist> <blist> <bibtext> Hattie, J. A. C. Visible learning: A synthesis of over 800 meta‐analyses relating to achievement London: Routledge 2008.</bibtext> </blist> <blist> <bibtext> Inhelder, B., Piaget, J. The growth of logical thinking from childhood to adolescence London: Routledge 1958.</bibtext> </blist> <blist> <bibtext> McNemar, Q. Psychological statistics 4th ed. New York: Wiley 1969.</bibtext> </blist> <blist> <bibtext> Newman, D., Griffin, P., Cole, M. The construction zone: Working for cognitive change in school Cambridge: Cambridge University Press 1989.</bibtext> </blist> <blist> <bibtext> NFER Science reasoning tasks Windsor: Author 1979.</bibtext> </blist> <blist> <bibtext> Nunes, T. The role of systems of signs in reasoning Brown, T., Smith, L. Reductionism and the development of knowledge 133 – 158 Mawah, NJ: Erlbaum 2002.</bibtext> </blist> <blist> <bibtext> Nunes, T., Bryant, P. Children doing mathematics Oxford: Blackwells 1996.</bibtext> </blist> <blist> <bibtext> Piaget, J., Inhelder, B. The child's conception of space London: Routledge & Kegan Paul 1956.</bibtext> </blist> <blist> <bibtext> Piaget, J., Szeminska, A. The child's conception of number London: Routledge 1952.</bibtext> </blist> <blist> <bibtext> Resnick, L. B., Bill, V., Lesgold, S. Developing thinking abilities in arithmetic class Demetriou, A., Shayer, M., Efklides, A. Neo‐Piagetian theories of cognitive development 210 – 230 London: Routledge 1992.</bibtext> </blist> <blist> <bibtext> Shayer, M. Cognitive acceleration through science education II: Its effects and scope International Journal of Science Education 21 8 883 – 902 1999.</bibtext> </blist> <blist> <bibtext> Shayer, M. Not just Piaget; not just Vygotsky, and certainly not Vygotsky as alternative to Piaget Learning and Instruction 13 465 – 485 2003.</bibtext> </blist> <blist> <bibtext> Shayer, M. Intelligence for education: As described by Piaget and measured by psychometrics British Journal of Educational Psychology 78 1 – 29 doi:10.1348/000709907X264907 2008.</bibtext> </blist> <blist> <bibtext> Shayer, M., Adey, P. S. Towards a science of science teaching London: Heinemann Educational Books 1981.</bibtext> </blist> <blist> <bibtext> Shayer, M., Adhami, M. Realising the cognitive potential of children 5–7 with a mathematics focus International Journal of Educational Research 39 743 – 775 2003.</bibtext> </blist> <blist> <bibtext> Shayer, M., Adhami, M. Fostering cognitive development through the context of mathematics: Results of the CAME Project Educational Studies in Mathematics 64 256 – 291 2007.</bibtext> </blist> <blist> <bibtext> Shayer, M., Demetriou, A., Pervez, M. The structure and scaling of concrete operational thought: Three studies in four countries Genetic, Social and General Psychological Monographs 114 3 309 – 375 1988.</bibtext> </blist> <blist> <bibtext> Shayer, M., Ginsburg, D., Coe, R. Thirty years on – a large anti‐Flynn effect? The Piagetian test volume and heaviness norms 1975–2003 British Journal of Educational Psychology 77 25 – 41 doi:10.1348/000709906X96987 2007.</bibtext> </blist> <blist> <bibtext> Shayer, M., Küchemann, D. E., Wylam, H. The distribution of Piagetian stages of thinking in British middle and secondary school children British Journal of Educational Psychology 46 164 – 173 1976.</bibtext> </blist> <blist> <bibtext> Shayer, M., Wylam, H. The distribution of Piagetian stages of thinking in British middle and secondary school children II: 14–16 year‐olds and sex differentials British Journal of Educational Psychology 48 62 – 70 1978.</bibtext> </blist> <blist> <bibtext> Vergnaud, G. Multiplicative structures Lesh, R., Landau, M. Acquisition of mathematics concepts and processes chap. 5 127 – 174 New York: Academic Press 1983.</bibtext> </blist> <blist> <bibtext> Vygotsky, L. S. Mind in society Cambridge, MA: Harvard University Press 1978.</bibtext> </blist> <blist> <bibtext> Wertsch, J. V. The concept of activity in Soviet psychology Armonk, NY: M. E. Sharpe 1979.</bibtext> </blist> </ref> <aug> <p>By Michael. Shayer and Mundher. Adhami</p> <p>Reported by Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib22" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib27" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib30" firstref="ref3"></nolink> <nolink nlid="nl4" bibid="bib28" firstref="ref4"></nolink> <nolink nlid="nl5" bibid="bib31" firstref="ref5"></nolink> <nolink nlid="nl6" bibid="bib13" firstref="ref6"></nolink> <nolink nlid="nl7" bibid="bib29" firstref="ref7"></nolink> <nolink nlid="nl8" bibid="bib23" firstref="ref8"></nolink> <nolink nlid="nl9" bibid="bib26" firstref="ref9"></nolink> <nolink nlid="nl10" bibid="bib32" firstref="ref11"></nolink> <nolink nlid="nl11" bibid="bib19" firstref="ref15"></nolink> <nolink nlid="nl12" bibid="bib17" firstref="ref16"></nolink> <nolink nlid="nl13" bibid="bib18" firstref="ref17"></nolink> <nolink nlid="nl14" bibid="bib21" firstref="ref18"></nolink> <nolink nlid="nl15" bibid="bib11" firstref="ref22"></nolink> <nolink nlid="nl16" bibid="bib25" firstref="ref23"></nolink> <nolink nlid="nl17" bibid="bib16" firstref="ref27"></nolink> <nolink nlid="nl18" bibid="bib20" firstref="ref28"></nolink> <nolink nlid="nl19" bibid="bib24" firstref="ref29"></nolink> <nolink nlid="nl20" bibid="bib12" firstref="ref31"></nolink> <nolink nlid="nl21" bibid="bib14" firstref="ref32"></nolink> <nolink nlid="nl22" bibid="bib15" firstref="ref34"></nolink> <nolink nlid="nl23" bibid="bib10" firstref="ref35"></nolink> <nolink nlid="nl24" bibid="bib33" firstref="ref37"></nolink> <nolink nlid="nl25" bibid="bib34" firstref="ref38"></nolink>
Header DbId: eric
DbLabel: ERIC
An: EJ897990
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Realizing the Cognitive Potential of Children 5-7 with a Mathematics Focus: Post-Test and Long-Term Effects of a 2-Year Intervention
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Shayer%2C+Michael%22">Shayer, Michael</searchLink><br /><searchLink fieldCode="AR" term="%22Adhami%2C+Mundher%22">Adhami, Mundher</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22British+Journal+of+Educational+Psychology%22"><i>British Journal of Educational Psychology</i></searchLink>. Sep 2010 80(3):363-379.
– Name: Avail
  Label: Availability
  Group: Avail
  Data: British Psychological Society. St Andrews House, 48 Princess Road East, Leicester, LE1 7DR, UK. Tel: +44-116-254-9568; Fax: +44-116-227-1314; e-mail: enquiry@bps.org.uk; Web site: http://www.bpsjournals.co.uk
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 17
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2010
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Elementary+Secondary+Education%22">Elementary Secondary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+1%22">Grade 1</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+2%22">Grade 2</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Intervention%22">Intervention</searchLink><br /><searchLink fieldCode="DE" term="%22Academic+Achievement%22">Academic Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Effect+Size%22">Effect Size</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+Strategies%22">Educational Strategies</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+Theories%22">Educational Theories</searchLink><br /><searchLink fieldCode="DE" term="%22Achievement+Gains%22">Achievement Gains</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+Policy%22">Educational Policy</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Elementary+School+Students%22">Elementary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Psychoeducational+Methods%22">Psychoeducational Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Strategies%22">Learning Strategies</searchLink><br /><searchLink fieldCode="DE" term="%22Intelligence%22">Intelligence</searchLink><br /><searchLink fieldCode="DE" term="%22Pretests+Posttests%22">Pretests Posttests</searchLink><br /><searchLink fieldCode="DE" term="%22Hypothesis+Testing%22">Hypothesis Testing</searchLink><br /><searchLink fieldCode="DE" term="%22Longitudinal+Studies%22">Longitudinal Studies</searchLink><br /><searchLink fieldCode="DE" term="%22Instructional+Effectiveness%22">Instructional Effectiveness</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Development%22">Cognitive Development</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Ability%22">Cognitive Ability</searchLink><br /><searchLink fieldCode="DE" term="%22Teaching+Methods%22">Teaching Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Development%22">Student Development</searchLink><br /><searchLink fieldCode="DE" term="%22English%22">English</searchLink><br /><searchLink fieldCode="DE" term="%22Piagetian+Theory%22">Piagetian Theory</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22United+Kingdom%22">United Kingdom</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1348/000709909X482363
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0007-0998
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Background: In the context of the British Government's policy directed on improving standards in schools, this paper presents research on the effects of a programme intended to promote the cognitive development of children in the first 2 years of primary school (Y1 & 2, aged 5-7 years). The programme is based on earlier work dealing with classroom-based interventions with older children at both primary and secondary levels of schooling. Aim: The hypothesis tested is that it is possible to increase the cognitive ability of children by assisting teachers towards that aim in the context of mathematics. A corollary hypothesis is that such an increase would result in an increase in long-term school achievement. Sample: The participants were 8 teachers in one local education authority (LEA) and 10 teachers in another. Data were analysed on 275 children present at Year 1 pre-test in 2002 and at long-term Key Stage 2 post-test in 2008. Method: Two intervention methods were employed: a Y1 set of interactive activities designed around Piagetian concrete operational schemata, and mathematics lessons in both Y1 and Y2 designed from a theory-base derived from both Piaget and Vygotsky. Results: At post-test in 2004, the mean effect sizes for cognitive development of the children--assessed by the Piagetian test "Spatial Relations"--were 0.71 "SD" in one LEA and 0.60 "SD" in the other. Five classes achieved a median increase of 1.3 "SD". The mean gains over pre-test in 2002 for all children in Key Stage 1 English in 2004 were 0.51 "SD", and at Key Stage 2 English in 2008--the long-term effect - were 0.36 SD, an improvement of 14 percentile points. Conclusions: The main hypothesis was supported by the data on cognitive development. The corollary hypothesis is supported by the gains in English. The implications of this study are that relative intelligence can be increased and is not fixed, and that children can be led into collaborating with each other to the benefit of their own thinking, and that there does exist a theory-based methodology for the improvement of teaching.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2010
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ897990
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ897990
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1348/000709909X482363
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 17
        StartPage: 363
    Subjects:
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Intervention
        Type: general
      – SubjectFull: Academic Achievement
        Type: general
      – SubjectFull: Effect Size
        Type: general
      – SubjectFull: Educational Strategies
        Type: general
      – SubjectFull: Educational Theories
        Type: general
      – SubjectFull: Achievement Gains
        Type: general
      – SubjectFull: Educational Policy
        Type: general
      – SubjectFull: Mathematics Instruction
        Type: general
      – SubjectFull: Elementary School Students
        Type: general
      – SubjectFull: Psychoeducational Methods
        Type: general
      – SubjectFull: Learning Strategies
        Type: general
      – SubjectFull: Intelligence
        Type: general
      – SubjectFull: Pretests Posttests
        Type: general
      – SubjectFull: Hypothesis Testing
        Type: general
      – SubjectFull: Longitudinal Studies
        Type: general
      – SubjectFull: Instructional Effectiveness
        Type: general
      – SubjectFull: Cognitive Development
        Type: general
      – SubjectFull: Cognitive Ability
        Type: general
      – SubjectFull: Teaching Methods
        Type: general
      – SubjectFull: Student Development
        Type: general
      – SubjectFull: English
        Type: general
      – SubjectFull: Piagetian Theory
        Type: general
      – SubjectFull: United Kingdom
        Type: general
    Titles:
      – TitleFull: Realizing the Cognitive Potential of Children 5-7 with a Mathematics Focus: Post-Test and Long-Term Effects of a 2-Year Intervention
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Shayer, Michael
      – PersonEntity:
          Name:
            NameFull: Adhami, Mundher
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 09
              Type: published
              Y: 2010
          Identifiers:
            – Type: issn-print
              Value: 0007-0998
          Numbering:
            – Type: volume
              Value: 80
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: British Journal of Educational Psychology
              Type: main
ResultId 1