Experience of Mediated Learning
Deming and Feuerstein
Bloom and Feuerstein
Vygotsky and Feuerstein

An Impact of Feuerstein's Theory in Education and Psychology

Edited by
A. Kozulin, The International Center for the Enhancement of Learning Potential, 47 Narkis Street, PO Box 7755, Jerusalem 91077, Israel,
Y. Rand, School of Education, Bar-Ilan University, Ramat-Gan, Israel

Description
In this volume the authors examine the impact of Feuerstein's theory of Mediated Learning Experience (MLE) on our understanding of the learning, instruction and cognitive modifiability of children, adolescents and young adults. The book begins with a historical essay charting the origins of the theory in Feuerstein's work with holocaust survivors and immigrant children, to the current international acceptance and application of his ideas.

The authors discuss key issues such as: the relationship between Feuerstein's theory and the changing agenda of psychological research; developments in the fields of learning potential assessment and their contribution to a more culturally equitable evaluation procedure; the influence of MLE theory on the enhancement of the learning potential of students.
The discussion concludes with a consideration of the more problematic aspects of Feuerstein's work and an examination of alternative assessment methods.

Audience
For educational researchers, educational psychologists and graduate students specialising in school psychology, psychological assessment, special education and cognitive science
Contents
Preface

Part 1.
Propelling the change, preserving continuity: a portrait of Reuven Feuerstein (R. Burgess).
Science, pedagogy and ethics in Feuerstein's theory and applications (C. Hadji).
Mediating environments: creating conditions for intellectual growth (A. Costa).
Feuerstein's unique contribution to educational and school psychology (R. Burden).
Group and individual differences in intelligence: what can and should we do about them? (R. Sternberg).
'To be, to have and to do': an integration and expansion of existing concepts (Y. Rand, A. Tannenbaum).
Reflective teaching and its relation to modes of existence in practical teaching experience (R. Reichenberg, Y. Rand).
Questioning as a form of mediation (S. Feuerstein).

Part 2
Dynamic cognitive assessment and the instrumental enrichment program (R.S. Feuerstein).
Theme and some variations on the concepts of mediated learning experience and dynamic assessment (C. Lidz).
Learning test concepts and dynamic assessment (J. Guthke. J. F. Beckmann).
Culture-fair assessment and the process of mental attention (J. Pascual-Leone et al.)

Part 3.
Developmental perspectives of mediated learning experience theory (D. Tzuriel).
A mediational approach to early intervention (P. Klein).
The diversity of instrumental enrichment applications (A. Kozulin).
Cognitive education and reading disability (J.P. Das et al.).
Cognitive-developmental therapy: an overview (C. Haywood).
Mediated learning experience and the counselling process (L Falik).
Selected bibliography of Reuven Feuerstein.
References.
Index.

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Improving the Quality of Education According to the Teachings of Deming and Feuerstein

Myron Tribus
Quality Counselor and
Co-Director of
The Western Center for
Cognitive Development and Learning

Introduction
While there have been many contributors to the theories of management and of education, two names stand out for both the boldness of their departures from past thinking and the comprehensiveness of their approaches. Dr. W. Edwards Deming (1900-1993) and Dr. Reuven Feuerstein (1921- ) have each pioneered new ways to think and to act, the one in management and the other in education. Together they provide a new way to approach teaching and learning.

Some educators may not see the connection between management and education. That is because the teachings of Deming and Feuerstein involve a drastic change in paradigm. One of the inescapable features of a paradigm shift is that in the beginning, those who are learning of the new paradigm interpret it in terms of the paradigm they are to leave. This difficulty is inevitable. My purpose in writing is to make the transitions at the personal level and organizational levels easier.

Dr. Feuerstein has concentrated his attention on how children learn. He builds on the work of Piaget, but goes much further. For about a half century he has developed his system for the improvement of learning and is guiding its adoption in many countries around the world. If teachers adopt the Feuerstein approach, they will change in dramatic ways the way schools operate. As a result, the way schools are managed will also change.
W. Edwards Deming, in over a half century of teaching and lecturing, has influenced managerial practices all over the world. His book, "Out of the Crisis" has been translated into many languages. The Deming Prize in Japan is given to companies which show excellence in the application of his ideas. Companies in Japan and elsewhere now compete for this prestigious prize. If the work of Feuerstein is to succeed, it is essential that educators also understand the work of Deming. What goes on in the classroom is constrained by what goes on in administration; and vice-versa.
By sampling educational and managerial practices in several countries, I have concluded that the ideas of W. Edwards Deming and Reuven Feuerstein are still unknown to most administrators and teachers. What these pioneers have to teach us is of the utmost importance. The growth of world populations, the depletion of natural resources, the degradation of the environment, the demands for a higher standard of living by an increasing number of people, the spread of information by satellites, the creation of a world wide economic system (in which money travels at the speed of light) and the proliferation of weapons of mass destruction… these forces have produced an era of rapid change. The depth and complexity of this era of change have been described by Drucker 1 in an insightful and thought provoking essay, "The Age of Social Transformation." Drucker argues that we are in the midst of the most extreme societal changes in recorded history. These changes now challenge our abilities to manage our institutions and to learn, collectively. We need to learn how to adapt to new and ever changing conditions.

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The Taxonomy of Cognitive Objectives and the Theory of Structural Cognitive Modifiability

Howard Rotterdam

In the 1950’s, an American Psychologist, Benjamin Bloom, headed a task force for the American Psychological Association to create a taxonomy of objectives for assessors. Bloom and his colleagues eventually developed three taxonomies: Cognitive, Affective, and Psychomotor. The most famous of these endeavors was the cognitive officially entitled the Taxonomy of Objectives in the Cognitive Domain. It is usually simply called Bloom’s Taxonomy. Also in the 1950’s a young cognitive psychologist, who studied in Geneva with Piaget, was working in Israel developing his theory of structural cognitive modifiability. His name was Reuven Feuerstein. This short paper proposes to investigate the work of both of these eminent psychologists, to examine Bloom’s taxonomy and Feuerstein’s cognitive modifiability and to discuss the commonalties between the two.

Briefly the work of Professor Bloom can be stated as assessment in the cognitive domain and has six components:

• Knowledge
• Comprehension
• Application
• Analysis
• Synthesis
• Evaluation

The essence of Professor Feuerstein’s theory is that
"Intelligence is not fixed. It is modifiable."

The Taxonomy of Cognitive Objectives
Bloom places knowledge at the first level of cognition. Knowledge can be characterized as awareness of specifics and of the ways and means of dealing with specifics. Essentially, the knowledge level focuses on memory or recall. While this is the lowest level of cognition, it is not a level to be ignored. Recall can be related to terms or facts or of procedures. It can be a simple definition or a lengthy poem, a remembrance of the steps in finding the area of a rectangle or the steps to a surgical procedure. This first level of the taxonomy provides a floor upon which the other levels depend and can build. The student recalls or recognizes information, ideas, and/or principles in the approximate form in which they were learned.
Examples:

List in order the presidents who have held office since FDR.
When did Columbus discover America?
Who were the three bears?

The next level of cognition is comprehension. Comprehension is understanding. Has the knowledge been internalized or understood? Often at this level, we will ask students to explain a concept in their own words. We ask them to translate, interpret, or extrapolate. Reading can be defined as a knowledge task – decode the words, read them orally – or a comprehension task – extrapolate some piece of information from the passage. The student translates, comprehends, or interprets information based on prior learning.

Examples:
Using class notes, make a chart of the U.S. presidents since FDR and list the major accomplishments of each.
Tell why Columbus wanted to sail to America?
Why did Goldilocks go into the bears’ house?

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Alex Kozulin

The comparative analysis of Vygotskian and MLE paradigms in teacher training inevitably involves a broader discussion of the learning process including the parameters of teacher, learning material, and student.

A modern trend in the theories of instruction and learning, to which both the Vygotskian and the Feuersteinian approaches belong, places emphasis on the constructive activity of the student, the cognitive-developmental appropriateness of material, and the involvement of the teacher in the design and implementation of classroom activities above and beyond a mere provision of information. Thus, before focusing on the preparation of teachers for their specific roles, it is imperative to offer a brief outline of Vygotskian and Feuersteinian notions of the learner and learning material.

For Vygotsky (1978; Vygotsky and Luria, 1993), a child is first and foremost a member of a particular socio-cultural group who appropriates learning tools characteristic of the group. Education in a broader sense is the process by which a novice acquires an individualized version of his or her group's culture. One aspect of this acquisition process that is particularly emphasized by Vygotsky is the role played by psychological tools. Psychological tools are those symbolic mediators (signs, symbols, formulae, texts, graphic organizers) that allow the individual to organize, restructure and control his or her “natural” functions of perception, attention, memory, communication, and problem solving. Appropriation, internalization and the use of psychological tools constitute the basis of human learning as distinct from that of animals. The notion of psychological tools provides a link between the social level of the transmission of culture and the individual level of learning and development. For example, such a tool as literacy on the one hand provides a means for transmitting cultural texts while on the other contributes to structural changes in individual cognitive processes (Olson, 1993).

The learning material represents the accumulated experience of mankind that is condensed and transformed for the need of transmitting it to the novice. Formal school-based education can be distinguished from informal practical education because the former presents knowledge in the form of “scientific” concepts while the latter operates with everyday notions (Vygotsky, 1986). Conceptual learning is by necessity a disciplinary one because it reflects a specific cultural-historical practice of formulating physical, biological, historical, linguistic and other concepts.

According to Vygotsky, educational process leads the child’s cognitive development, but does not coincide with it. Higher cognitive functions depend on education for their development. At the same time, it would be erroneous to claim that development just follows learning as a shadow. Vygotsky argued that it is impossible to find the universal formula of the relationship between a study of a given subject and the child's development: “Each school subject has its own specific relation to the course of child development, a relation that varies as the child goes from one stage to another” (Vygotsky, 1978, p.91).

The student appears in Vygotsky’s theory as an active learner whose mind is never a “tabula rasa”. Even before formal education starts the child already has spontaneous notions of quantity, causality, time, space, and others. These notions should be taken into account when the child is introduced to formal mathematical, historical, or literary learning. Because of this emphasis on the spontaneous notions held by the child, Vygotsky’s theory is often associated with the “constructivist” approach (Newman, Griffin, and Cole, 1989). It is important, however, to remember that Vygotsky never claimed that the student's construction of knowledge can be accomplished spontaneously or independently. The process of concept formation in the student occurs in the constant interaction between the student's spontaneous notions and systematic concepts introduced by teachers.

A somewhat similar interaction takes place between the student's maturational processes, and new opportunities created by learning. The maturational processes, including sensory-motor, hormonal, and affective processes do not cease to exist once formal learning starts, but enter into complex relationships with higher cognitive functions dependent on learning. The ontogenetic process is neither uniform nor monotonous, but full of crises that puncture the student’s development.

Feuerstein’s (1980; 1990) notion of a learner is anchored to the phenomenon of mediated learning experience as distinct from the experience of direct learning. According to Feuerstein, the child is exposed to two types of learning situations. The situation of direct learning includes an unmediated interaction between learning material and the child’s mind. If the child’s mind is ready to accept this material it will benefit from it. If, however, the child does not know how to accept the material, cannot identify its meaning, or does not know how to respond, the second type of learning, the mediated one, becomes crucially important. “The mediated learning experience can be defined as a quality of interaction between child and environment which depends on the activity of an initiated and intentioned adult who interposes him/herself between the child and the world. In the process of such mediation the adult selects and frames stimuli for the child, creates artificial schedules and sequences of stimuli, removes certain stimuli and makes the other stimuli more conspicuous... Mediated learning experiences are a very important condition for the development of the very unique human conditions of modifiability, or the capacity to benefit from exposure to stimuli in a more generalized way than is usually the case” (Feuerstein, 1991, p.26).

Not every interaction between the child, the adult and the learning material qualifies as a mediated learning interaction. Feuerstein (1990) provides a detailed list of universal and contextual criteria of mediated learning experience. At the center of Feuerstein’s learning theory lies the problem of what happens when the type or amount of mediation is inappropriate for the child's needs. The condition caused by the lack of MLE is characterized as that of reduced cognitive modifiability. Thus, the role of learning materials is formulated in the context of this overall task of enhancing the student’s cognitive modifiability through MLE producing interactions.

The goal of enhancing the student’s cognitive modifiability dictates the content-free nature of learning materials developed by Feuerstein et al (1980). These materials, which together constitute the Instrumental Enrichment (IE) cognitive intervention program are deliberately detached from specific content subjects. Feuerstein et al (1994) argued that the acquisition of the most basic cognitive functions and strategies - that are the process of learning how to learn - do not require specific content materials: “When one deals with elementary cognitive functions that have not been established, for whatever reason, in the individual cognitive operations, then the issue of specificity is much less important” (p.32). In addition, Feuerstein presented a number of specific reasons for the content-free nature of the IE program. The first is the resistance of the student who perceives content material as “information only” and is reluctant to engage in a broader study of cognitive principles embedded into this material. The second reason is the teacher’s resistance to spending time allocated to teaching specific material or operations on instruction in more general thinking skills. The third reason is that the content material has its own logic - mathematical, geographic, literary, etc. - that does not necessarily coincide with the logic of acquisition of basic cognitive functions. Finally, there is the factor of failure previously experienced by the student in his or her confrontation with specific content material. As we will see later, the issue of content-free versus content-based nature of instruction constitutes one of the important points distinguishing Vygotskian and MLE paradigms.

The Vygotskian paradigm of teacher training is based on two presuppositions. The first is the presupposition regarding the relationship between instruction and development; the second is the notion of the Zone of Proximal Development (ZPD) as a “space” within which the instruction takes place. Vygotsky (1978) rejected a popular belief, associated with Piagetian theory, that instruction should follow the child’s cognitive development. He claimed that, to the contrary, instruction and learning constitute an important factor, “a motor” of child development. Thus, from the Vygotskian point of view, learning and development are just two aspects of one and the same process of "developing education". As a result, instead of conceiving instruction as a mere provision of information and rules to be processed by already existent psychological functions, Vygotsky suggested that instruction and learning are responsible for the development of higher psychological functions which are absent in the “natural” cognitive endowment of the child. Teacher training should therefore be not only subject-oriented but also development-oriented. The educator should be aware of the current cognitive status of the child, and of those cognitive changes that can and should be produced with the help of instructional process.

To make education truly “developing”, instruction should be carried on in what Vygotsky (1978; 1986) defined as the Zone of Proximal Development (ZPD). The ZPD constitutes an “area” within which the child’s functions are in a state of development. Functions and concepts situated “below” ZPD have already been formed and the child can use them independently. “Above” ZPD, there are no relevant functions that can be developed through instruction at a given moment in the child’s development. “Within” the ZPD functions exist in their nascent state. They cannot be displayed by the child him or herself, because they have not yet been formed, but if the child receives help from the adult or from the more competent peer these functions can be displayed as an outcome of such a cooperative action. One of the primary roles of the teacher, assisted by psychologists, is to identify the ZPD of each student and to attune the instruction in such a way that the student’s learning takes place within this zone. Simultaneously, the teacher works on extending the “upper” limit of the child’s ZPD.

The notion of ZPD constitutes an important aspect of interface between Vygotskian theory and the concept of learning potential or propensity proposed by Feuerstein et al (1979; 1991). Actually, a number of psychologists who use learning potential assessment procedures formulated by Feuerstein conceptualize them in terms of ZPD (Lidz 1987; 1995). In both cases, the notion of cognitive assessment is firmly anchored to the goal of educational intervention and change in child’s performance.

ZPD oriented instruction has two major forms. One of them is aimed at using and developing functions situated “within” the ZPD with an ultimate goal of turning them into functions fully mastered by the students themselves. The second type of instruction is aimed at constructing or extending ZPD in those students whose ZPD is not “deep” enough. This second task includes teaching students the strategies of meta-cognition and cooperative learning, e.g. teaching them how to receive assistance from the teacher in the course of problem-solving.

The other way in which ZPD was conceptualized by Vygotsky (1986) is as a “space” within which the everyday, empirical notions of the child meet systematic, theoretical concepts supplied by the teacher. In terms of teacher training, this poses two challenges. One of them is to prepare teachers themselves for the use of theoretical rather than everyday concepts, and to be able to distinguish between them. Vygotskians (Davydov, 1990; Lompscher, 1984; Karpov and Bransford, 1995) made a thorough analysis of a number of school subjects and demonstrated that in many cases, the notions used by teachers and curriculum developers do not differ from spontaneous generalizations acquired in everyday life. As a result, students enrich their everyday knowledge but do not acquire the structure of thinking necessary for “scientific” reasoning. The term “scientific” is used here in a broader sense to include not only math and natural sciences, but also social and language sciences. The absence of proper scientific reasoning becomes particularly obvious when students start confronting “real” scientific disciplines in high school and find themselves unprepared for their conceptual structure.

According to the Vygotskian model, theoretical instruction should start in the primary school. For example, instead of teaching children how to count objects in the hope that in this way they will acquire the notion of number, Vygotskians propose starting with forming the notion of number as a universal relation or multiple derived from the activity of measuring one value with the help of another selected as a standard. The child is taught, for example, that the length of a couch can be expressed as “one broom” or “six toy crocodiles”. It was shown that the notion of number as universal and unrelated to counting concrete objects greatly facilitates further learning of math concepts including that of fractions and negative numbers (Davydov and Tzvetkovich, 1991).

The second challenge for teacher training brought about by Vygotskian theory is to construct age-appropriate activities for teaching theoretical concepts. Vygotskians made an important distinction between learning in a generic sense and a specially designed learning activity (Kozulin 1995). While learning in a generic sense can become a part of many human activities, such as play, practical activity, interpersonal interaction, etc., learning in a generic sense is not a goal of any of these activities. What distinguishes learning as a special kind of activity is its focus on the changes produced in the learner him or herself. At the risk of sounding tautological, the goal of learning activity is to make the individual a competent learner.

Learning activity includes four major components: learning tasks, operations, control, and self-evaluation. It is important to understand that a learning task does not coincide with concrete reading or writing exercises, or mathematical problems. The learning task always reflects the general principle of the formation and transformation of the subject of learning. Thus, the learning task becomes a model for solving all tasks of this type. Operations involved in learning activities always follow some paradigmatic example which is either presented by the teacher or discovered by the child him or herself. The acquisition of operations includes the phase of the formation of some preliminary image of such an operation and an attempt to carry it out. The development of the control function is closely linked to the acquisition of operations, because control includes the comparison of operations with its paradigmatic example. The paradigmatic example has some universal support elements which ensure the possibility of control irrespective of the concrete variation of material. The last component of the learning activity is the student's self-evaluation. The student is oriented toward evaluation of success in mastering the general principle applicable to all problems of this type rather than specific tasks.

Instruction based on the principles of learning activity is not only age-appropriate in respect to the complexity of the learning materials, but also in terms of student-student and student-teacher interactions. For example, in the middle school a special model of cooperative learning is used that reflects special interpersonal needs of adolescents at this age (Rubtsov, 1991).

It was shown (Davydov 1988; Karpov 1995) that students who were exposed to a curriculum based on principles of learning activity acquire a much greater facility in solving non-trivial problems, problems that require data restructuring, and problems that involve far-transfer of the principle. This means that instruction based on the principles of learning activity forms in students those meta-cognitive skills and strategies which are the goal of various cognitive education programs (Fischer, 1990). The distinctive feature of the learning activity paradigm is that it is content-based and that it requires the activity to be age-appropriate.

The paradigm of learning activity constitutes another point interfacing between Vygotskian and Feuersteinian systems. Many features of learning activity appear in the MLE system as the criteria of “transcendence” and “mediation of meaning”. A significant number of IE tasks and mediational principles of teaching them have the same cognitive goals as learning activity. The material of IE tasks closely corresponds to what Vygotsky designates as symbolic mediators (see Kozulin, 1998). At the same time, while IE aims at developing general cognitive strategies which are later “bridged” to concrete subjects, the learning activity constructs these strategies as an integral element of the acquisition of a given subject.

One may also notice that Vygotskian programs aimed at pre-school children have a greater resemblance to IE. Venger and Gorbov (1993) observed: “Learning activity presupposes the development of theoretical thinking, the basis for which is a system of scientific concepts. For six year old children, however, logical-conceptual forms of cognition are not nearly as typical as visual-imaginative ones. Accordingly, at this age it is not yet a learning activity as such that should be developed, but rather its prerequisites. The most adequate foundation for the subsequent mastering of the system of scientific concepts are generalized schematic notions which visually reflect the essential links and relationships of the concepts to be mastered” (p.3). There is a certain logic in this because one of the goals of IE is to form in older children those functions that more advantaged children acquired at an earlier age. Thus, IE in its compensatory function is similar to Vygotskian pre-school and first grade programs in their development generating capacity.

The teacher appears in MLE theory and practice first of all as a mediator. Because of this, the general task of teacher training is seen as preparing the teacher for this mediational role. In a more restricted sense, one can also speak of teacher training in IE as a subject in itself. The teacher as a mediator is armed with the criteria of MLE, with the cognitive map, with the list of deficient cognitive functions, and with the belief in the human cognitive modifiability (Feuerstein, 1990). Some of the problems that confront other teachers become even more insistent for the MLE-trained teacher. For example, a heterogeneous class always requires a special effort from the teacher, but for a teacher who becomes sensitized to the MLE criteria, the task of working with such a class becomes particularly challenging. How can each interaction be infused with intentionality when the class has a number of distinct subgroups of students? How can meaning be mediated when the level of acquisition of meaning is different? How can the feeling of competence be conveyed to a weak student when other students are so obviously superior in their performance? All teachers should be aware of these problems, but in more formalistic education devoid of mediational components, the teacher can “hide” behind standard procedures of the dispensation of information and rules. Thus, the first outcome of MLE-based teacher training is the heightened awareness on the part of the teacher of the interactional requirements of instruction.

Both MLE and IE focus on the formation of the cognitive prerequisites of learning in students. The process of acquisition of learning material requires certain cognitive prerequisites beyond that of the basic functions of perception, memory, and attention. The student is supposed to be able to detect the problem in the pool of raw data, to select the relevant parameters, to form hypotheses and check them, and so on. The inadequate school performance of the student can easily stem from underdevelopment of these prerequisites rather than poor acquisition of specific rules or operations. Thus, the second outcome of MLE-based teacher training is providing teachers with intellectual and operational tools for identification of those cognitive prerequisites that are lacking in students. IE serves as an operational tool that allows teachers to develop these previously lacking prerequisites in a systematic way.

Though there is an obvious affinity between the Vygotskian notion of learning activity and the process of the formation of cognitive prerequisites discussed above, there is also a certain difference between the goals of MLE-based learning and learning according to the Vygotskian paradigm. According to Feuerstein et al (1980), the acquisition of MLE does not directly depend on either content of learning or modality of interaction: “Using the example of instruction in a preliterate society, it is clear that mediation may take a nonverbal form. The mediator illustrates his actions to an interested observer with only limited verbal, and even less semantic, interaction occurring. In our experience, the changes that occur as a result of nonverbal mediation transcend both the content and the means by which the content is transmitted” (p.23). For this reason, the experience of mediated learning is considered equally beneficial for everyday and classroom thinking. Vygotsky (1978) and his followers (Cole and Scribner, 1974; Scribner 1997), on the contrary, place considerable emphasis on changes occurring in the child’s reasoning under the influence of the acquisition of higher order symbolic tools, first of all literacy and writing. For them, there is a principal distinction between interactions carried out non-verbally, orally, and with the help of written symbolization. Writing externalizes thought, takes it out of its concrete context, and makes it available for conscious analysis. Literacy skills require analytic approach. They are acquired consciously and deliberately, thus shifting cognitive functions from the natural responsive mode to the cultural deliberate mode. One may legitimately pose the question of whether the same type of “transcendence” or mediation of meaning can be achieved with and without the experience of literacy. Studies of MLE interactions in different socio-economic and socio-cultural groups (Tzuriel, 1997) indicate that there is a marked prevalence of “transcendence” in the interaction between more educated parents and their children. One may guess that this is a direct result of the literate orientation of these parents.

Beyond the acquisition of written symbolic systems lies a vast area of the acquisition of conceptual systems belonging to different content subjects. While there is no doubt that some basic cognitive prerequisites, e.g. the ability to compare, are necessary for learning any of these subjects, it is equally clear that comparisons in history, physics, and biology all require their own cognitive apparatus. This apparatus does not coincide with that of knowledge or content understood as mere information. It is rather directly related to the conceptual structure of a given subject, the acquisition of which depends on the theoretical mode of learning proposed by Vygotskians.

This brings us to the last interface between the MLE and Vygotskian theories. IE as a tool for the development of basic cognitive prerequisites interfaces with the conceptual structure of learning subjects, and a proper borderline should be found at which the general functions promoted by IE become absorbed and subjugated by this higher order conceptual structure. Vygotsky (1978) indicated that “natural” cognitive functions do not disappear with the emergence of higher order literacy-based functions, but become incorporated and transformed within the new cognitive systems. One may say that, in a similar way, basic cognitive prerequisites become absorbed within the new conceptual systems. Thus, the last outcome for teacher training can be formulated as the necessity for a teacher to distinguish between the general cognitive prerequisites and those higher order cognitive systems which alone can support conceptual learning.