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A Modest Proposal: Towards a Theory and Practice of Teaching Using Vygotsky's N + 1 Principle in Dialogic Learning

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Title: A Modest Proposal: Towards a Theory and Practice of Teaching Using Vygotsky's N + 1 Principle in Dialogic Learning
Language: English
Authors: Shayer, Michael
Source: Journal of Cognitive Education and Psychology. 2022 21(2):135-155.
Availability: Springer Publishing Company. 11 West 42nd Street 15th Floor, New York, NY 10036. Tel: 877-687-7476; Tel: 212-431-4370; Fax: 212-941-7842; e-mail: subscriptions@springerpub.com; Web site: https://connect.springerpub.com/content/sgrjcep
Peer Reviewed: Y
Page Count: 21
Publication Date: 2022
Document Type: Journal Articles
Reports - Evaluative
Education Level: Higher Education
Postsecondary Education
Elementary Secondary Education
Descriptors: Learning Theories, Sociocultural Patterns, Science Instruction, Dialogs (Language), Science Curriculum, Curriculum Development, Theory Practice Relationship, Piagetian Theory, Achievement Tests, Cooperative Learning, Outcomes of Education, Educational Change, Teacher Education Programs, Preservice Teachers, Science Teachers, Teaching Methods, Intelligence Quotient, Thinking Skills, Foreign Countries, Educational History, Elementary Secondary Education
Geographic Terms: United Kingdom (England)
ISSN: 1945-8959
1810-7621
Abstract: This article addresses the problem of "education for all," and offers a research proposal that replaces procedural learning by a learning practice whereby all are engaged. Although educational research since 1990 of dialogical learning (DL) and collaborative learning (CL) have shown that it is possible to promote the learning practices that they focus on, little evidence is available on long-term effects of school achievement. Teachers also face pressure from both the UK and USA governments having produced policy documents favouring procedural teaching. An exception is CASE, Cognitive Acceleration through Science Education (1984 onwards), and a 2-year course for 12-14 year-olds. This functioned by collaborative learning placed in highly structured theory-based science lessons based on Piagetian models of difficulty. Students consistently performed higher in National exams in science, maths and English at 16 (Shayer, 1999b). It is argued that a better way of changing teaching practice would be to place it in teachers' initial training. By assisting trainee science teachers, in designing their science curriculum lessons--assisted by DL and CL literature--to extract and use the same theory-base that had been used by CA staff for constructing CASE lessons, they would possess a valid theory and practice of teaching.
Abstractor: As Provided
Entry Date: 2023
Access URL: https://connect.springerpub.com/content/sgrjcep/21/2/135
Accession Number: EJ1368186
Database: ERIC
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  Value: <anid>AN0160064500;w0501oct.22;2022Nov09.01:18;v2.2.500</anid> <title id="AN0160064500-1">A Modest Proposal: Towards a Theory and Practice of Teaching Using Vygotsky's N + 1 Principle in Dialogic Learning </title> <p>This article addresses the problem of "education for all," and offers a research proposal that replaces procedural learning by a learning practice whereby all are engaged. Although educational research since 1990 of dialogical learning (DL) and collaborative learning (CL) have shown that it is possible to promote the learning practices that they focus on, little evidence is available on long-term effects of school achievement. Teachers also face pressure from both the UK and USA governments having produced policy documents favouring procedural teaching. An exception is CASE, Cognitive Acceleration through Science Education (1984 onwards), and a 2-year course for 12–14 year-olds. This functioned by collaborative learning placed in highly structured theory-based science lessons based on Piagetian models of difficulty. Students consistently performed higher in National exams in science, maths and English at 16 (Shayer, 1999b). It is argued that a better way of changing teaching practice would be to place it in teachers' initial training. By assisting trainee science teachers, in designing their science curriculum lessons—assisted by DL and CL literature—to extract and use the same theory-base that had been used by CA staff for constructing CASE lessons, they would possess a valid theory and practice of teaching.</p> <p>Keywords: teacher training; cognitive development; science education; difficult pupils</p> <p>This article argues that the only way to start to change the current and universal practice of procedural teaching in schools is to offer an alternative practice in the <emph>initial training</emph> of teachers <emph>that is powerful enough to displace it totally.</emph> The function of the teacher now changes to that of a guide and an assistant to children constructing their own knowledge collaboratively, including himself as a co-worker. This practice is far from earlier notions of allowing pupils to learn freely: The teacher has a very demanding role in controlling the events in the classroom based on his developing knowledge of the depths of the structure of learning involved. And as will be shown later, such skills lead to an important change in the concept of true learning.</p> <hd id="AN0160064500-2">BACKGROUND</hd> <p>After World War 2 both in the USA, UK and elsewhere it was felt necessary to include the whole population in the secondary education process. America had its High Schools taking everyone, and the UK British Education Act 1944 offered the solution of taking the top 20% by IQ tests as being considered worthy of education in Grammar schools for subsequent access to Universities. The rest would go to Secondary Modern schools and leave school at 14.</p> <p>During the 60s it was becoming increasingly obvious that there were too many children from the lower SES of society that the system of universal education was failing. Following the publication of <emph>The Growth of Logical Thinking</emph> by [<reflink idref="bib17" id="ref1">17</reflink>] there was a rush of cognitive intervention studies addressing early secondary schooling from North America and Australia ([<reflink idref="bib6" id="ref2">6</reflink>]; [<reflink idref="bib19" id="ref3">19</reflink>]; [<reflink idref="bib20" id="ref4">20</reflink>]; [<reflink idref="bib26" id="ref5">26</reflink>])—such studies became out of fashion by the late 80s. Perhaps further work in this line had been blocked by the general reaction against Piaget in psychology at the time.</p> <p>At the same time a research program was initiated in England—CSMS—intended to study the problems of teaching science and mathematics in secondary schools.</p> <hd id="AN0160064500-3">British CSMS Program, 1974–1979 Population Survey</hd> <p>In England in the mid-60s Comprehensive secondary schools with an all-ability intake began to be in instituted in place of the previous system of selective schools for the top 20% of the population. It soon became apparent that there were problems in handling the learning of the less able, as in the USA.</p> <p>As part of the work of the CSMS[<reflink idref="bib1" id="ref6">1</reflink>] program a survey of 10,000 children between the ages of 9 and 16 was conducted using three Piagetian tests covering all possible of levels of thinking of children between 6 and 16. Figure 1 shows the results ([<reflink idref="bib28" id="ref7">28</reflink>]; [<reflink idref="bib29" id="ref8">29</reflink>]). It was greeted with disbelief by most commentators, while some praised it for showing just why their tradition of teaching only for the elite—that is those already at the early formal (3A) level by 14—was correct. But many teachers said that it helped to explain the difficulties they already had in their new Comprehensive schools.</p> <p>Graph: FIGURE 1. Distribution of ability in British population in 1976.</p> <p>Unfortunately this article published in the British Journal of Educational Psychology in 1976, never reached general awareness. This is the "elephant in the room" never attended to as an important variable in the dialogic learning literature.</p> <p>Firstly this showed that formal cognitive development (3A & above) in children was much less universal than is inferred in [<reflink idref="bib17" id="ref9">17</reflink>]—only 30% attaining even early formal (3A) thinking by the age of 16. Looking at the age of 11/12 for entry into secondary school the range of mental age is far greater than previously conceived. In Science and Mathematics the curriculum in use at that time in England & Wales Grammar schools was well addressed to the development of the top 20%. Another study [<reflink idref="bib27" id="ref10">27</reflink>] had shown that one of the grammar school courses, Nuffield Chemistry, required early formal thinking (3A) in the first 2 years, and then a mixture of early formal and mature formal (3A/3B) for the next 3 years. As can be seen in Figure 1 it would only be the top 20% who could be able to succeed. So what about the rest?</p> <hd id="AN0160064500-4">Cattell on Intelligence</hd> <p>The great psychometrician [<reflink idref="bib7" id="ref11">7</reflink>], p. 145 et seq.) commentated, on finding that the standard deviation of fluid intelligence tests was 24 IQ units:</p> <p>It is the "spread" of I.Q., however, that has occasioned most comment and speculation. The magnitude of the spread, i.e., the standard deviation of adult mental ages, when it first became apparent, was a matter of astonishment to thinking people. Few other human characteristics (e.g., stature, blood pressure) show such a coefficient. ... As Burt, Terman and others were quick to realize, it meant that some members of the same adult community could be considered two or three times as "old," "mature," or "advanced" as others.</p> <p>Thus, even in the separate field of psychometric testing there was awareness of the tremendous range of cognitive development in adults that was later shown in Figure 1 for children. This did not reach the education literature.</p> <p>Figure 2 shows development curves for Boys' Height in England ([<reflink idref="bib38" id="ref12">38</reflink>], Boys) In the case of the Height curves it can be concluded that; generally, they express the genetic program for height in a representative Western environment. Thus the Height curves show the development pattern that was being looked for by Cattell and others when they looked at the spread in fluid intelligence scores, because the population in England by 1963 can be regarded as one with an adequate environment for the normal growth of height.</p> <p>Graph: FIGURE 2. Tanner curves for height (Boys).</p> <hd id="AN0160064500-5">The Problem in England</hd> <p>Figure 1 shows that the general environment today is most unfavourable to cognitive development. How has this come to be? For England one might speculate on the origins of some of the massive variation shown in the figure. One obvious phase is that of the Industrial Revolution[<reflink idref="bib2" id="ref13">2</reflink>] during C18/19: Squash workers in terraces of 2 up-2 downs, working 12 hours a day, 6 days a week, often with children also working (few in school), and the conditions for supporting cognitive development must have been very poor. The middle-classes were taken care of by the Grammar schools—in C18 and C19 taking 2% of the population or less at that time—and the cognitive development of those children could be taken as the genetic program as shown in Figure 2 for height. Indeed, if one takes only the top 20% of the current distribution of the data shown in Figure 1 for cognitive development, one gets a set of curves very similar to those in Tanner's Figure 2. These were the only children—the top 20% by IQ tests—who, in the British 1944 Education Act, were considered as worthy of education in Grammar schools.</p> <p>It was recognition of the problems following from this that in the 60s led to the setting up of Comprehensive schools with all-ability intakes and the closing of most of the grammar schools.</p> <hd id="AN0160064500-6">The Situation Following 1990</hd> <p>This year turned out to be pivotal. Suppose one take the view that [<reflink idref="bib7" id="ref14">7</reflink>] and the CSMS program (1974–1979) had between them acknowledged the size and existence of the "elephant in the room." In Ibsen's play <emph>Per Gynt</emph>, the hero, travelling through mist in the mountains, comes up against a massive enveloping barrier (the Bøyg) against which there is no way through. Out of the clouds the message "<emph>Go round about</emph>" is thundered. This is how the world of educational research seems to have responded following 1990: The bulk of educational research switched to collaborative and dialogic learning ("<emph>Go round about</emph>").</p> <p>From around 1990 there were four silos of work addressed to the problem of how to promote better learning in students: <emph>Feuerstein Instrumental Enrichment</emph> (FIE), <emph>collaborative learning</emph> (CL), <emph>dialogic learning (DL) and cognitive acceleration (CA)</emph>. Although CL and DL were closely related in their practices, their publication record has mostly proceeded in separate silos, although there are frequent cross-references. [<reflink idref="bib14" id="ref15">14</reflink>] is a convenient review of work on CL, and [<reflink idref="bib16" id="ref16">16</reflink>] a summary of DL. But in [<reflink idref="bib25" id="ref17">25</reflink>], after summarizing work on dialogical learning—including the concept of Accountable Talk—she says:</p> <p>This chapter has presented evidence that dialogic teaching is capable of enhancing learning to a remarkable degree. We have also shown that dialogic teaching is now a major focus among scholars in the learning sciences. Despite the growing and increasingly convincing evidence for the power of dialogic instruction, however, not very much of it is going on in most schools. There are plenty of professional development offerings that claim to help teachers learn dialogic teaching skills, but most are shallow and not empirically tested. Many school textbooks contain suggested "discussion" topics as an extension of the "basic" instructional material they offer. But efforts to seriously adopt dialogic teaching as a core (and constant) instructional method are not common. And even when a school or district takes up a plan for increasing this kind of instruction, it is rarely fully implemented. Why is this the case?</p> <p>With a methodology consisting of a system confined to minute-by-minute interactions between the students and interventions by the teacher—however good and effective in increasing learning behaviors it may be—it would be impossible to see "the elephant in the room." It has two-faces: It is not only the immense range of abilities among the children (Figure 1); it is also the equally large range of difficulties within the school curricula (Figure 3a). <emph>How can a lesson plan or research study be effective unless it addresses the relation between the difficulty range of the lesson content and the ability range of the children, D<subs>l</subs>/P<subs>l</subs>? How can teachers be assisted to improve their practice unless it is focussed on the actual science or mathematics they are presently teaching?</emph></p> <p>Graph: FIGURE 3A. Structure of a Pask learning plan for concepts.</p> <hd id="AN0160064500-7">FIE Feuerstein Instrumental Enrichment</hd> <p>Feuerstein as a young psychologist immigrating to Israel from Romania soon after WW2 found that younger fellow immigrants performed very poorly in Israeli schools, with very low results on psychometric tests. As a basis for designing lessons he covered the whole psychometric spectrum, choosing one at a time, e.g., spatial relations, as a context for the lessons. By analysing all the steps of difficulty in that part of the spectrum he would design up to 10 lessons of increasing levels of difficulty and complexity delivered at the rate of three a week. By the end of the second year of secondary school the students would have covered all 13 aspects of the psychometric spectrum.</p> <p>The conduct of the Feuerstein Instrumental Enrichment ([<reflink idref="bib9" id="ref18">9</reflink>]) (FIE) lessons featured some collaborative learning. In the initial 10 minutes the subject of the worksheets would be discussed with all the students, preferably placed in a U-shape of places so the students could see and hear each other. The teacher would facilitate student-student interaction rather than answering students' questions. Then for at least 25 minutes the students would work independently on the worksheets. Then the whole class would discuss all the problems and the successes together, again with the teacher operating as a mediator.</p> <p>Early research showed that the intention of re-integrating the holocaust survivors within normal Israeli schooling had been successful ([<reflink idref="bib9" id="ref19">9</reflink>]).</p> <p>An important source for Feuerstein was [<reflink idref="bib42" id="ref20">42</reflink>] original recommendations for learning/teaching, the N + 1 principle:</p> <p> <emph>Learning which is orientated toward developmental levels that have already been reached is ineffective from a point of view of a child's overall development. It does not aim for a new stage of the development process, but rather lags behind this process. ...The only good learning is that which is in advance of development.</emph> </p> <p>In addition there was Vygotsky's concept of the ZPD, Zone of Proximal development:</p> <p> <emph>The zone of proximal development of the child is the distance between his actual development, determined with the help of independently solved tasks, and the level of potential development of the child, determined with the help of tasks solved by the child under the guidance of adults and in cooperation with his more intelligent partners.</emph> </p> <p>This implies that in each child's mind there is not only his present competence but also a series of partially formed concepts from only a quarter, half or three-quarters of the way to full possession. Hence a recommendation for teaching:</p> <p> <emph>We propose that an essential feature of learning is that it creates a zone of proximal development, that is, learning awakens a variety of internal developmental processes that are able to operate only when the child is interacting with people in his environment and in cooperation with his peers. Once these processes are internalized, they become part of the child's independent developmental achievement.</emph> </p> <p>Hence in the design of the FIE lessons there is both the N + 1 principle, and some collaborative learning.</p> <hd id="AN0160064500-8">Gordon Pask on Learning</hd> <p>Back in the early 50s Pask began work on creating Machine Learning[<reflink idref="bib3" id="ref21">3</reflink>] ([<reflink idref="bib22" id="ref22">22</reflink>], [<reflink idref="bib23" id="ref23">23</reflink>]). He would take a major concept in chemistry or physiology, and then study all the various steps or routes by which that concept could be attained. Figure 3a shows a typical preliminary plan.</p> <p>At each of the steps a piece of learning is presented to the student on the screen. For the four possible starts shown in Level 1 there is enough detail shown to enable him to make a choice from the machine. Having succeeded in his reply he is then given a choice of one or two routes at the next level, and so on until he is shown the last task to achieve the major concept at Level 2. He may also succeed only at one of the intermediate levels.</p> <p>If this describes the learning system for one individual student, how much more, also, must it describe the learning system for a school class in science or mathematics?</p> <hd id="AN0160064500-9">The CASE Intervention</hd> <p>Following the CSMS program (1974–1979) at King's College, London, work began on an intervention in the context of science, a major school subject. As part of the CASE I project (1980–1984) [<reflink idref="bib31" id="ref24">31</reflink>] first replicated Feuerstein IE in a Special School[<reflink idref="bib4" id="ref25">4</reflink>] in England with children from 12 to 14, with effect sizes of 1.1 on Raven's Matrices and 1.2 by individual interview on a battery of Piagetian concepts. At the same time work was begun on the assumption that if one worked in the context of science it should be possible to further general thinking abilities as shown in Figure 1.</p> <p>Work began on designing <emph>Thinking Science</emph> ([<reflink idref="bib1" id="ref26">1</reflink>]) lessons based on a taxonomy of the difficulty of science concepts ([<reflink idref="bib30" id="ref27">30</reflink>], chapter 9) derived from [<reflink idref="bib17" id="ref28">17</reflink>] work, and constructed, as with FIE, to promote Vygotsky's <emph>N + 1</emph> thinking (Appendix B). The emphasis on collaborative learning used, at this point (1982/83), was simply due to the fact that one of the authors had taught chemistry earlier in an elite school by a heuristic method (van Praagh, <emph>Chemistry by Discovery</emph>, [<reflink idref="bib39" id="ref29">39</reflink>]). Obviously later the developing history of collaborative learning was consulted.</p> <p>This led to a second grant, CASE II (1987–1990), designed to accelerate the cognitive development of children in the first 2 years of secondary education, aged 12–14, CASE,[<reflink idref="bib5" id="ref30">5</reflink>] in the middle to lower part of the ability range ([<reflink idref="bib32" id="ref31">32</reflink>]; [<reflink idref="bib33" id="ref32">33</reflink>]).</p> <p>CASE addresses a system, as with Pask, that incorporates the whole lesson time and a model of the various difficulties leading to the major concept of the lesson. Lessons were created for use each 10 days for the first 2 years of secondary education. They incorporated the Vygotsky's <emph>N + 1</emph> principle which provided the directed aim of the collaborative learning involved. Instead of being constructed with a single aim to be achieved by the end of the lesson, as with procedural teaching, each child may at any point in the lesson experience a jump in his ZPD as his group finds a new insight. If the lesson may be viewed as structured as with the Pask diagram, Figure 3, many of these increases may only be only partly higher in the lesson's cognitive content, but still of value.</p> <p>Graph: FIGURE 3B. Procedural teaching plan.</p> <p>For each lesson an area of science involving one of the ten Piagetian formal operational schemata as shown in Table 1 would be used as the context of the lesson, with activities containing the various levels of understanding involved toward functioning at the formal operations level ([<reflink idref="bib17" id="ref33">17</reflink>]). The collaborative learning, as with FIE, involved firstly Concrete Preparation where the class were briefly shown the work ahead, but requiring only a low level of cognitive processing to ensure that all might begin participating. This is followed by a period of small-group activity by groups from 2 to 4 in number, and lastly for a whole-class discussion at the end where each group reported their findings and ideas, as in FIE. The function of the teacher changed to that of <emph>mediator</emph>: With the inner structure of the lesson in his/her head, the teacher's actions were those that directed pupils' attention to processing their common task. This required, and led to a 2-year professional development (PD) program offered to schools conducted over a 9-year period, from 1991 to 2000 from King's College, London.</p> <p>TABLE 1. Schemata Studied in the Growth of Logical Thinking</p> <p> <ephtml> <table frame="hsides" rules="groups"><colgroup><col content-type="1" width="50%" /><col content-type="2" width="50%" /></colgroup><thead><tr><th align="left">Biological and social science</th><th align="left">Physical sciences</th></tr></thead><tbody><tr><td align="left">Control of variables</td><td align="left">Coordination of frames of reference</td></tr><tr><td align="left">Exclusion of irrelevant variables</td><td align="left">Multiplicative compensation</td></tr><tr><td align="left">Probability</td><td align="left">Equilibrium of physical systems</td></tr><tr><td align="left">Correlation</td><td align="left">Proportional thinking</td></tr><tr><td align="left">Combinatorial thinking</td><td align="left">Physical conservations involving "models"</td></tr></tbody></table> </ephtml> </p> <p>In terms of the CSMS diagram in Figures 1, 4 shows the effect on one school (<emph>N</emph> = 150) whose intake at 12 was just at the National mean. Viewed against the heavy brown line showing the population average, the Post-effect average at 14—in heavy black—has moved up approximately 1.4 Piagetian levels (from mature concrete to just early formal). In addition, the intervention appears to have affected the below average more than the above average, which had been one of its intentions. <emph>But in terms of Tanner's curves for height</emph> (Figure 2) <emph>the post-intervention effect has only squeezed the distribution less than half the way towards being comparable.</emph></p> <p>Graph: FIGURE 4. Effect of a King's College CASE intervention.</p> <p>Each year, from 1991 to 1999, between 10 and 12 schools began the King's College 2-year PD program, with the Pre-test measured using the Piagetian test, Pendulum ([<reflink idref="bib21" id="ref34">21</reflink>]) and the post-test being the results in the National exam GCSE taken 3 years later at age 16. Schools promised PD the next year agreed to be controls for this year-group. Thus, over the 90s approximately 100 schools in England and Wales had received this training.</p> <p>For one cohort of the CASE PD program ([<reflink idref="bib34" id="ref35">34</reflink>]), <emph>N</emph> around 2,000, the average effect-size for science at the National exam at 16, GCSE, 3 years after the intervention, was 0.60 SD. For mathematics the effect-size was 0.50 SD. Given that the intention of the CASE program was to raise the general intelligence of the pupils, the fact that the mean effect-size for English was 0.57 is supportive.</p> <hd id="AN0160064500-10">The CAME intervention</hd> <p>Following the success of the CASE program at King's College, London, [<reflink idref="bib3" id="ref36">3</reflink>]; [<reflink idref="bib36" id="ref37">36</reflink>] switched to the context of mathematics.[<reflink idref="bib6" id="ref38">6</reflink>] For this purpose it was necessary to produce taxonomy of the difficulty levels of all the mathematics involved. Piaget contributes only a description of ratio and proportionality, so here use was made of previous work by the GAIM project.[<reflink idref="bib7" id="ref39">7</reflink>]</p> <p>Otherwise the same learning principles were used as had been used in the CASE project. On the National Exam at 16 (12 schools, <emph>N</emph> around 2,000) the effect-size on GCSE for maths was 0.44, for science 0.3, and for English 0.32. The lower effect-sizes compared with those for CASE is suggested to be that these were reported for the first time from the original research project, whereas those for CASE followed the experience of several years of the conduct of King's College PD programs. A recent use of CAME in Tonga ([<reflink idref="bib10" id="ref40">10</reflink>]) reported an effect-size of 1.25 on the Tonga Numerical Reasoning test.</p> <hd id="AN0160064500-11">The RCPCM Study</hd> <p>[<reflink idref="bib35" id="ref41">35</reflink>], [<reflink idref="bib37" id="ref42">37</reflink>] conducted a 2-year intervention for children aged 5–7[<reflink idref="bib8" id="ref43">8</reflink>] in the context of mathematics (<emph>N</emph> = 350 approx.), again using collaborative learning, as with CASE. At immediate post-test, using the Piagetian <emph>Spatial Relations</emph> test ([<reflink idref="bib21" id="ref44">21</reflink>]) there was an effect-size of 0.71. On the Government Key Stage 1 tests at seven there were effect-size of 0.65 for maths and 0.43 for English. At Key Stage 2 taken at 11, 4 years later, effect-sizes were, for maths 0.24, and for English 0.34. Appendix A shows a lesson plan for a Y2 (6/7 years) teacher with a Thinking Maths lesson with both National Curriculum levels (level NC 4 is designed as the desired level by Year 6, the end of Primary) and difficulty levels in Piagetian terms.</p> <p>This study is also noteworthy on account of the working group used fortnightly by the team: The two University staff plus four teacher-researchers. A possible lesson-plan would be offered to the team and discussed to the point where it could be re-written and made ready for testing. One of the teacher-researchers, who were also teaching in the project schools, would teach the lesson, and the University team would make lesson-notes with a time-line. At the next team meeting the lesson would be discussed, and any necessary changes would be made before it went out to the other project schools.</p> <p>The fact that the various CA programs had shown that the same principles could be applied successfully throughout schooling is important, but also was subject to two major deficiencies. Firstly they were separate thinking lessons and not obviously related to the lessons in the ordinary curriculum. Second, although they worked in the hands of the teachers, the theory behind the structured lessons was hidden from the teachers, and never became their possession. Lastly, as can be seen in Figure 4, they were only a beginning step to solving the problem shown in Figure 1.</p> <hd id="AN0160064500-12">The Finland Study</hd> <p>In the late 90s an attempt was made to see if CASE and CAME could feasibly be introduced into National programs for use in schools in Finland ([<reflink idref="bib13" id="ref45">13</reflink>]). The large-scale study included all the schools in the district of the town of Vihti: 14 Primary and 2 Secondary (<emph>N</emph> = 350) and was an intensive intervention in the last year of Primary (12+ yrs.). Instead of using the CA activities once every 10 days over 2 years, they were given at the rate of one a week, by the author, allowing up to 28 during the 1 year. Thereafter the cognitive development of the children was followed through secondary until the age of 16. Table 2 summarizes the results:</p> <p>TABLE 2. PRT III Test at Year-End for CASE and CASE Control</p> <p> <ephtml> <table frame="hsides" rules="groups"><colgroup><col content-type="1" width="10%" /><col content-type="2" width="10%" /><col content-type="3" width="10%" /><col content-type="4" width="10%" /><col content-type="5" width="10%" /><col content-type="6" width="10%" /><col content-type="7" width="10%" /><col content-type="8" width="10%" /><col content-type="9" width="10%" /><col content-type="10" width="10%" /></colgroup><thead><tr><th /><th colspan="3" align="center">Mean score</th><th colspan="3" align="center">% Early formal+</th><th align="center">Grade 6 effect</th><th align="center">Grade 9 effect</th><th align="center">Grade 7–9 gain</th></tr><tr><th align="left">School</th><th align="center">Grade 6</th><th align="center">Grade 7</th><th align="center">Grade 9</th><th align="center">Grade 6</th><th align="center">Grade 7</th><th align="center">Grade 9</th><th /><th /><th /></tr></thead><tbody><tr><td align="left">A</td><td align="center">7.10</td><td align="center">7.35</td><td align="center">8.38</td><td align="center">48.3</td><td align="center">55.6</td><td align="center">90.6</td><td align="center">1.35</td><td align="center">2.04</td><td align="center">1.05</td></tr><tr><td align="left">B</td><td align="center">6.92</td><td align="center">7.27</td><td align="center">7.5</td><td align="center">44.6</td><td align="center">54.1</td><td align="center">58.5</td><td align="center">1.16</td><td align="center">1.15</td><td align="center">0.23</td></tr></tbody></table> </ephtml> </p> <p>1 On the mean levels, 7 is early formal; 8 is mature formal; 6 is concrete generalization.</p> <p>As can be seen the immediate post-test effect at the end of Grade 6 was larger than any previous CA intervention and was in the context of mixed-ability teaching, universal for most Finnish Primary schools. But secondary school A continued to organize mixed-ability teaching, whereas school B graded all their classes on entry by ability measures. There was no further cognitive development of the students in school B, whereas between 14 and 16 school A showed a further gain of 1.05, giving a total effect-size of 2.04. Adding one extra standard deviation to the effects shown in Figure 4 would get them close to the range shown in the Tanner curves for height in Figure 2.</p> <p>The children in School A, without any further cognitive training in secondary—other than given mixed-ability teaching—have retained the collaborative learning process specific to what they had attained by the end of Grade 6, and subsequently used it in such a powerful way that by working in the context of normal secondary science and maths from 14 to 16, but within the style of mixed ability teaching, they increased the growth of their own intelligence far beyond what could have been expected; i.e., as well as learning they had also learnt to learn. This suggests that, rather than having separate thinking lessons it should be possible to teach the whole science or maths curriculum in the way that the CASE lessons were originally constructed, and further to extend this to all 5 years of secondary education.</p> <hd id="AN0160064500-13">Towards a Model of Learning</hd> <p>The CA process had developed a style of collaborative learning throughout the lesson, in addition to the FIE lessons that instead had the middle section with the children doing independent work on their worksheets. This learning appears to have <emph>inverted</emph> the implicit description of the curriculum in procedural terms. Instead of looking at learning in terms of immediate and describable terms, to be achieved who knows how, it focuses attention on desirable scientific or mathematical <emph>actions</emph> which, skilfully employed, would certainly result in procedural aims, but that is not their immediate intention. As with Pask's original work in Machine Learning the intention is to construct as many of the interlinks with other relevant actions as possible so as to increase the ability to practice in scientific or mathematic contexts. The practice recommended has the intention of rejecting the concept of "knowledge" as being that which results from procedural learning, and replacing it with the actual ability to <emph>practice</emph>, with understanding, <emph>the subject itself</emph>, in mixed-ability classes. "Doing-mathematics," "Doing-science." "Practicing mathematics;" "Practicing science." And this style of learning could begin from Y1, as shown in the RCPCM project, and continue throughout secondary school.</p> <hd id="AN0160064500-14">THE PROBLEM</hd> <p></p> <hd id="AN0160064500-15">Procedural Teaching</hd> <p>A teacher with a procedural model of teaching will prepare a lesson by thinking about where he thinks the students have got to at the present, level 1, and then sees a sequence of two simple procedural steps by which <emph>some</emph> right answers can be obtained at level 2.</p> <p>He plans to take the student through these steps during the lesson. His lesson plan inevitably short-cuts much of the cognitive content relating to the major concept. Figure 3b shows what is happening: The teacher has chosen just one path shown in red through the system of relations that underpin the cognitive field.</p> <p>It cannot be said strongly enough how powerful is the almost universal practice of procedural teaching in schools. That is how we were taught ourselves, that is what Governmental decrees in educational matters, in England and the USA, say either explicitly or implicitly—<bold>Teach</bold> (procedurally of course): That is what your job is. It is quite difficult to realize that is only <emph>one</emph> model, which only works, to some extent, to fit a situation where the students are all around the same level of ability.</p> <hd id="AN0160064500-16">Learning Practice</hd> <p>The social situation faced in the practice of universal secondary education, both in the American High School, and in the Comprehensive schools in England and in most European countries is radically different from that assumed implicitly by procedural teaching. As can be seen in Figure 1 at entry to secondary school at 12 the ability levels of the pupils range from that of the average 6 year-old to that of the top 15% of 16 year-olds {12-year gap}. Try to "<bold>Teach</bold>" at the average level and you will lose the bottom 30% because they can't follow, and you will lose the top 30% because they are bored, leading to trouble. The model of learning now has to shift to a <bold>Learning Practice</bold><emph>where all are engaged</emph>. This is what was used in all the CA projects.</p> <p>The desired teacher's skill then focuses on (a) designing contexts that cover several different levels of attainment within the same area of the subject, (b) showing the students from the beginning what there is about the context that will allow them to engage, (c) arranging students' collaborative learning groups so that each will cover a range of abilities that is not too wide, (d) monitoring the groups' performances with the expectation that he, the teacher, is also part of the collaborative learning of the whole class and may still find something new for himself, (e) intervening with groups only if he can see some action that he can suggest that will draw their attention to something they can do, or correcting their collaborative behavior, (f) from his attention to all of the groups' working making a plan for the whole-class discussion at the end that enables first the lower ability groups to show what they have constructed, and then turning to other groups where he seen them attain something they can show, and leaving to the last concepts at the highest levels within the lesson context.</p> <p>Developing Skill (d) is probably more analogous to how shooters learn to use a shotgun on moving targets ([<reflink idref="bib4" id="ref46">4</reflink>], p. 195; 200–202). It may take a year or two before teachers begin to reflect on their own practice over and above practicing competently. Provided that the teachers were already in possession of a common theory and practice of teaching, CPD (<emph>Continuing Professional Development</emph>) could later have a valuable place both within a school, and on a University course.</p> <p>This way of teaching, developed from the original way of accelerating cognitive development, would now become what Vygotsky had originally suggested, a better way of learning altogether.</p> <hd id="AN0160064500-17">THE MODEST PROPOSAL</hd> <p>This is the claim: The only way to start to change the current and universal practice of procedural teaching in schools is to offer an alternative practice in the <emph>initial training</emph> of teachers <emph>that is powerful enough to displace it totally.</emph> The function of the teacher now changes to that of a guide and an assistant to children constructing their own knowledge collaboratively, including himself as a co-worker.</p> <p>Continue that and schools would gradually fill up with teachers so trained until they become a majority, having a shared language within which to discuss their teaching. But that training has to be a complete and sufficient theory and practice of learning.</p> <p>A second claim: There already exists, in all the four silos following 1990, sufficient expertise to create that theory and practice: It is not a matter of choosing this silo over that. FIE can continue in the contexts for which it were designed. The various CA programs can provide an understanding of the learning in various school curricula, and both the DL and the CL expertise can contribute in the minute-by-minute collaborative learning processes required.</p> <p>Consider the process by which the CASE and FIE collaborative learning processes becomes the possession of the children. The teachers in receipt of PD are guided into changing their teaching practice into mainly that of mediating the children's collaborative learning so that, in combination of small group action and discussion, plus whole-class discussion, the children construct their learning for themselves. Certainly the teachers, with their own knowledge of the different levels that underlie the aims of each lesson, intervene from time to time to call the children's attention to things they may have missed. They also learn how to manage the whole-class discussions. And by watching and listening to the children the teachers, over a 2-year period, do learn something of what the originators put into their structured CASE lessons—<emph>but never enough to know how to create such lessons for themselves</emph>.</p> <p>Each step of the processes requires a systems theory description. The University Professional Development (PD) staff for CASE cannot <emph>know</emph>, and then <emph>tell</emph> the teachers what it is they are to learn. They arrange for sets of teachers, in small groups, to <emph>plan</emph> together a CASE intervention lesson. The teachers then teach it, and afterwards meet for collaborative discussion with the PD staff, who were present and made notes with a time-line of each lesson, and may also join the discussion. Thus the whole work of this process is that of the teachers constructing together, with feedback (their own) their practice of the CASE lessons. The same applies to their students: The teachers cannot <emph>know</emph>, and then <emph>tell</emph> the children what it is that they are to learn. Using the context of the well-constructed lessons, the students collaborate with each other in constructing their own N + 1 understanding of the concepts involved. Their success depends on the quality of the mediation given by the teacher, mediation that requires a greater degree of control, not less, than that of ordinary teaching.</p> <p>Thus to a teacher who then asks to be told how to do it in the practice of all his science lessons from Grade 7 to Grade 11, the reply has to be given "I can't <emph>know</emph> and then <emph>tell</emph> you how to do it: But I can show you how to construct it for yourselves." It is proposed to design a new research project by which trainee teachers would be able, collaboratively, to learn to design and practice their science lessons using the same theory base as was used by the King's College team who constructed the original CASE lessons. This would result in their having a N + 1 theory of teaching <emph>themselves</emph>, as recommended by Vygotsky, as opposed to merely using <emph>other's</emph> structured lessons.</p> <p>None of the originators of the CA projects are now available, and because of its complex design involving the whole spectrum of psychometrics, it would be very difficult to start from FIE. Instead the designers of the necessary initial research program would have to plan for learning <emph>themselves</emph> at the same time as setting up a system that allows the teachers, at the same time, to learn how to address the whole of the curriculum of science, or maths, using the same methodology as used by their originators in designing their CASE or CAME lessons.</p> <p>For CASE ([<reflink idref="bib30" id="ref47">30</reflink>], chapter 8) it was shown that teachers could be trained how to analyse the difficulty of any science concept—based on two taxonomies derived from the work of Piaget (see Appendix B)—from three sessions of practice, again by small group collaborative learning. This was one of the intellectual tools used in constructing the original CASE lessons, in addition to collaborative learning. The other is how to design for "cognitive conflict." That is to look at a context of various steps toward a science concept, and plan the lessons so that the children encountered the various paths relating to that science concept, each finding something at their level that they might experience as a "jump."</p> <p>To begin with, it would be necessary to set up a system involving both University PD staff, and teachers as their initial training. The teachers would teach perhaps four or five of the CASE lessons, but in addition to the usual planning and feedback sessions of collaborative learning by the teachers, there would be an attempt to deconstruct the content of each of the lessons so as to see the cognitive conflict at the heart of the lesson. By then they would already have the training in assessing the Piagetian level and difficulty of the science concepts they were working with, and would be ready to design lessons themselves.</p> <p>For use in the initial training of teachers it is essential that they work collaboratively: Remember that their University PD staff cannot "tell" them, but can provide training in the use of the taxonomy. By working in groups of three or four they create their own hypothesis of a lesson plan for the next step in the curriculum, and then test it by themselves teaching it, and then joining in with the University staff in collaborative discussion of how it went. By repeating this over the period of a year their expertise would develop until they were in possession both of a theory and practice of teaching within their own subject, and also a deeper understanding of that subject. Likewise the University staff would have much to gain in the development of their own understanding of the whole process.</p> <p>The research staff would need to attend each lesson, and make detailed notes, with a time-line, of the content of each of the lessons taught, and make these available for the teachers' feedback sessions, as in the original RCPCM (1997–2001) research for 5/6 year-olds ([<reflink idref="bib36" id="ref48">36</reflink>]).</p> <p>As the year went on the proportion of teacher-designed science lessons to CASE lessons would increase until the teachers became confident in planning the entire science curriculum in an N + 1 way. As the year progressed the function of the University staff would transform into focusing on the way teachers were conducting their mediation of the lessons. They could supplement their own lesson notes by having some lessons recorded visually as well. This would be where the research on Dialogic and Collaborative learning could be offered to the teachers for reflective discussion on their own mediating practice, with a multitude of teaching episodes made available through the recordings.</p> <p>It is important to realize the magnitude of the change from ordinary schooling that is implicit in this research proposal. <emph>Procedural Teaching</emph> is to be ousted by <emph>Learning Practice</emph>. The function of the teacher is to be changed from that of a conveyor of "knowledge" to the students to that of a mediator of the students' constructing their own science or maths practice. Both teacher and students become involved in a common pursuit of true learning.</p> <p>The same relation applies to the training process for the teachers where it is more obvious that the University PD staff will, at their level, find that they have as much to learn as participants with the teachers, from the process, as the teachers themselves with their children. Just the same applies to a teacher with a class of 6-year olds as they tackle the mathematics lesson shown in Appendix A. The teacher may not know the complex system of multiplicative relations between numbers that underlies the lesson content ([<reflink idref="bib41" id="ref49">41</reflink>]), but she will encounter it implicitly as she attends to the children and often understands more of it.</p> <p>The teacher cannot possibly anticipate all the fox-paths that may appear[<reflink idref="bib9" id="ref50">9</reflink>] (Figure 3a), but he can respond to them when they occur, taking some action that may shift the attention of a working group towards a higher level of processing. If his intervention is successful, then the teacher has, at his level, also learnt more about the complex web of relations, within the subject, that surrounds its major concepts. He also learns when he witnesses a group making a break-through in their thinking. The more he is co-active in the class's learning the better will his mediation be.</p> <p>At the end of the project, there would be a set of teachers armed with a theory and practice of teaching science, and a group of University staff competent to take control of other teachers' initial training. After another year, it should be possible to publish the system in sufficient detail to enable other Universities to adopt it for teacher training.</p> <hd id="AN0160064500-18">Expected Effects of Teacher Training</hd> <p>As can be seen in Figure 4 the effect of one well-structured lesson a fortnight for use of CASE for 2 years shifted the whole cognitive range up the figure, but less than half-way toward the range shown in Figure 2 for Height. Were each and all of the science lessons both constructed and mediated in a CASE way, the students may well enter Year 3 with the range shown considerably tighter than is shown in Figure 4. And the Finland study for Class A suggests that this could go further in the next 3 years.</p> <p>Perhaps more important: Both in the initial use of FIE in Israel and of the various CA courses (CASE; CAME; and iCAME with the 5 & 6 year-olds) there has been the experience of the atmosphere generated when such teaching has been practiced with the children. "My head hurts, but it was worth it" was the comment of one lower ability child after a CAME lesson. A 6-year old who had repeatedly only said in iCAME lessons, "I don't agree with Jacob," but refused to say more in spite of the teacher prodding for his reasons, 1 day excitedly jumped up and said "I <emph>agree</emph> with Mary, and, for <emph>two</emph> reasons."</p> <p>And most important: The change from teaching to the curriculum in a procedural way, to experiencing learning by the ability for the students to <emph>practice</emph>, with understanding, <emph>the subject itself</emph>, in mixed-ability classes is a great qualitative change in the concept of learning—what true knowledge is.</p> <p>This proposal is necessarily a modest one. Only if first this mode of Initial Training for teachers is shown to be successful by a University department, would it then be possible to explore further how to extend it to all years of secondary school and then report how it has affected the teachers' and student's concept of schooling and knowing, particularly by those whose present experience of schooling is negative.</p> <hd id="AN0160064500-19">Could the Same Methodology Be Used for the Teaching of English?</hd> <p>In order to achieve this in any main school subject it is essential first that a valid taxonomy be created (e.g., Appendix B for science) that contains everything that subject experts consider relevant to learning in their subject, with different levels of attainment of these. Without this it would not be possible to produce lesson plans. Work and practising in English covers a very different field of studying than the more obviously conceptual subjects of science and mathematics. Here the progression of practice is more in terms of depths of understanding of each of the aspects of learning that teachers regards as valuable.</p> <p>Two steps are needed: In order to achieve reliability it needs first to be tested on 20 or more teachers on questions containing all expected levels in all the taxonomy,[<reflink idref="bib10" id="ref51">10</reflink>] and revised accordingly. Then a similar range of questions need to be given to a suitable sample of all ability 14 year-olds, and any further adjustments made until it achieves validity ([<reflink idref="bib30" id="ref52">30</reflink>], chapters 8–10).</p> <p>Thereafter the research team could proceed in the same way as was suggested for science above. Some preliminary work in English has been done ([<reflink idref="bib11" id="ref53">11</reflink>], [<reflink idref="bib12" id="ref54">12</reflink>]). [<reflink idref="bib43" id="ref55">43</reflink>] reports, from currently running CA English for teachers in the first 2 years of secondary education, an initial taxonomy for English containing these five descriptors—Classification; Frames of Reference; Intentions and Consequences; Narrative Sequencing, and Symbolic Reasoning—covering four Piagetian levels of difficulty: Pre-operational, Mature Concrete, Concrete Generalization and Mature Formal. This is work in progress.</p> <hd id="AN0160064500-20">Disclosure</hd> <p>The authors have no relevant financial interest or affiliations with any commercial interests related to the subjects discussed within this article.</p> <hd id="AN0160064500-21">Funding</hd> <p>The author(s) received no specific grant or financial support for the research, authorship, and/or publication of this article.</p> <hd id="AN0160064500-22">APPENDIX A</hd> <p>The figure shows a lesson plan from [<reflink idref="bib2" id="ref56">2</reflink>] for a Y2 (6/7 years) teacher with a Thinking Maths lesson on multiplicative relations, ([<reflink idref="bib41" id="ref57">41</reflink>]) with both Piagetian and National Curriculum levels (level NC 4 is designed as the desired average level by Year 6, the end of Primary).</p> <p>Graph</p> <p>Initially, the children were told a story of a manufacturer of Jelly-Babies who wanted to have more variety in the sweets. The children were shown pictures of Jelly-Babies in Baby form and in Daddy form, and asked what form would a Sister have (children in pairs on the carpet). Then they would be asked, in groups of 2–4, to work on a sheet containing several pictures of each form, but varying in size so that e.g., they might see a Baby larger than a Daddy, or a Sister smaller than a Baby. Finally there is a whole class discussion of what each group had done. If time permits the groups would be asked to design a Giant Jelly-Baby.</p> <hd id="AN0160064500-23">APPENDIX B</hd> <p></p> <p> <ephtml> <table frame="hsides" rules="groups"><colgroup><col content-type="1" width="25%" /><col content-type="2" width="15%" /><col content-type="3" width="15%" /><col content-type="4" width="15%" /><col content-type="5" width="15%" /><col content-type="6" width="15%" /></colgroup><thead><tr><th colspan="6" align="left">Taxonomy 1: Different aspects of the development of the child's interaction with the world</th></tr><tr><th align="left">Function</th><th align="left">1 pre-operational</th><th align="left">2A early concrete</th><th align="left">2B mature concrete</th><th align="left">3A early formal</th><th align="left">3B mature formal</th></tr></thead><tbody><tr><td align="left">1.1 Interest and investigation style</td><td /><td /><td /><td /><td /></tr><tr><td align="left">1.2 Reasons for events</td><td /><td /><td /><td /><td /></tr><tr><td align="left">1.3 Relationships</td><td /><td /><td /><td /><td /></tr><tr><td align="left">1.4 Use of models</td><td /><td /><td /><td /><td /></tr><tr><td align="left">1.5 Type of categorization</td><td /><td /><td /><td /><td /></tr><tr><td align="left">1.6 Depth of interpretation (of descriptive passages)</td><td align="left">Does not look for contradictions in interpreting a descriptive account. Tends to pick on one feature only.</td><td align="left">Imposes a consistent interpretation, but builds it around one feature of the account. Nominal scale<sup>3</sup> level of interpretation.</td><td align="left">Takes several aspects of described situation, but separately, and in imposing cause-and-effects stays within the descriptions, and mostly redescribes it. Ordinal scale<sup>2</sup> level of interpretation. (Examine whether a concrete model (1.4—2A and 2B) is provided).</td><td align="left"><italic>Extended describer</italic> level. Still stays within the descriptive account, but considers more than one aspect at once (trees removed; rain on soil; soil washed away).</td><td align="left"><italic>Explainer thinking</italic>. Not only are all the relevant features of the description accounted for, but also hypotheses are tested against the data and, where necessary, inferences are made imaginatively using outside ideas and data. (Examine whether a formal model (1.4—3A and 3B) is provided as an interpretation).</td></tr></tbody></table> </ephtml> </p> <p></p> <p> <ephtml> <table frame="hsides" rules="groups"><colgroup><col content-type="1" width="20%" /><col content-type="2" width="20%" /><col content-type="3" width="20%" /><col content-type="4" width="20%" /><col content-type="5" width="20%" /></colgroup><thead><tr><th colspan="5" align="left">Taxonomy 2: The development of different "schemas" required for the understanding of the sciences</th></tr><tr><th align="left">Type of problem</th><th align="left">2A early concrete</th><th align="left">2B mature concrete</th><th align="left">3A early formal</th><th align="left">3B mature formal</th></tr></thead><tbody><tr><td align="left">2.1 Conservation</td><td /><td /><td /><td /></tr><tr><td align="left">2.2 Proportionality</td><td /><td /><td /><td /></tr><tr><td align="left">2.3 Equilibria of systems</td><td /><td /><td /><td /></tr><tr><td align="left">2.4 Mathematical operations</td><td /><td /><td /><td /></tr><tr><td align="left">2.5 Control of variables</td><td /><td /><td /><td /></tr><tr><td align="left">2.6 Exclusion of variables</td><td /><td /><td /><td /></tr><tr><td align="left">2.7 Probabilistic thinking</td><td /><td /><td /><td /></tr><tr><td align="left">2.8 Correlational reasoning</td><td /><td /><td /><td /></tr><tr><td align="left">2.9 Measurement skills</td><td /><td /><td /><td /></tr></tbody></table> </ephtml> </p> <p>User would first look at Taxonomy 1 and see if one or two of the rows fit the context of the problem. Then he looks to see which of the different levels in the columns comes closest. Then he looks at Taxonomy 2 to see which type of scientific problem is involved, and again which level of thinking comes closest—he may have to look at one of the mathematical rows as well. Then uses all the evidence to arrive at an assessment of the cognitive level that is involved. Just one row of the table is given as an example of the detail of the whole.</p> <ref id="AN0160064500-24"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref6" type="bt">1</bibl> <bibtext> Concepts in Secondary Mathematics and Science (1974-1979). Research program funded by the SSRC.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref13" type="bt">2</bibl> <bibtext> see Dickens, 1854, Hard Times. Mayhew, 1851, London Labour and the London Poor.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref21" type="bt">3</bibl> <bibtext> In those days the keyboards used by the students would be connected up to a massive Dexion framework containing the circuits consisting of valves, condensers etc. being memory stores, etc. carrying information about students' choices. Later Pask went on to a distinguished career in cybernetics developing conversation theory.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref25" type="bt">4</bibl> <bibtext> Although the selection criteria for Special School are the bottom 5% in English and Maths, on the Piagetian battery the children lay between the 35th and 65th %le of the CSMS survey.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref30" type="bt">5</bibl> <bibtext> CASE. Cognitive Acceleration in Science Education (1984-87) Project funded by the SSRC.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref2" type="bt">6</bibl> <bibtext> Cognitive Acceleration in Mathematics Education I (1993-1995) project funded by the Leverhulme Foundation. Cognitive Acceleration in Mathematics Education II (1995-1997) project funded jointly by the Economic and Social Research Council and the Esmée Fairbairn Trust.</bibtext> </blist> <blist> <bibl id="bib7" idref="ref11" type="bt">7</bibl> <bibtext> GAIM project. Brown, M. 1989, Graded Assessment and Learning Hierarchies in Mathematics—an alternative view. 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  Data: A Modest Proposal: Towards a Theory and Practice of Teaching Using Vygotsky's N + 1 Principle in Dialogic Learning
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  Data: Journal Articles<br />Reports - Evaluative
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  Data: 1945-8959<br />1810-7621
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  Data: This article addresses the problem of "education for all," and offers a research proposal that replaces procedural learning by a learning practice whereby all are engaged. Although educational research since 1990 of dialogical learning (DL) and collaborative learning (CL) have shown that it is possible to promote the learning practices that they focus on, little evidence is available on long-term effects of school achievement. Teachers also face pressure from both the UK and USA governments having produced policy documents favouring procedural teaching. An exception is CASE, Cognitive Acceleration through Science Education (1984 onwards), and a 2-year course for 12-14 year-olds. This functioned by collaborative learning placed in highly structured theory-based science lessons based on Piagetian models of difficulty. Students consistently performed higher in National exams in science, maths and English at 16 (Shayer, 1999b). It is argued that a better way of changing teaching practice would be to place it in teachers' initial training. By assisting trainee science teachers, in designing their science curriculum lessons--assisted by DL and CL literature--to extract and use the same theory-base that had been used by CA staff for constructing CASE lessons, they would possess a valid theory and practice of teaching.
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  Data: 2023
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        PageCount: 21
        StartPage: 135
    Subjects:
      – SubjectFull: Learning Theories
        Type: general
      – SubjectFull: Sociocultural Patterns
        Type: general
      – SubjectFull: Science Instruction
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      – SubjectFull: Dialogs (Language)
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      – SubjectFull: Science Curriculum
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      – SubjectFull: Curriculum Development
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      – SubjectFull: Achievement Tests
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      – SubjectFull: Cooperative Learning
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      – SubjectFull: Preservice Teachers
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      – SubjectFull: United Kingdom (England)
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