(1) Communication. According to Vygotsky, communication is a process that mediates psychological development. However, Vygotsky did not present communication as a mediated process; instead, he offered a sociological understanding of communication as a process of the development of signs. Indeed, Galperin addresses a controversial issue in Vygotsky's approach, which does not focus on examining the process of communication but emphasises the process of generalisation. Hence, Vygotsky's understanding of the development of humans as a unity of communication and generalisation remains unfinished. In Lecture 4, Galperin discusses the double role of communication as a verbal action and as a message about the performed action:

When you remove the material support, the action will not be immediately transferred to the mental plane. First, it is transferred to the plane of externalised social speech…. This speech is aloud, not only in its form, but more importantly in its function as speech directed to another person. It is important that this is both a verbal action a nd a message about the performed action. (Lecture 4)

(2) Intellect as mediation of psychological development. Galperin criticises Vygotsky's understanding that psychological development and mediation depend on a matured intellect. Therefore, the initial phases of ontogenesis, in which the intellect is not dominant, cannot be examined either theoretically or empirically. Neither can they be explained by the cultural and historical development of humans, but only by human natural development. This understanding indicates that Vygotsky's approach was intellectual, which he acknowledged in his critical reflections in the early 1930s. Vygotsky made a considerable effort to overcome intellectualism in his theory by introducing the unity of affect and intellect although these ideas were not fully developed in his works. In Lecture 5, Galperin responds to Vygotsky's position:

For a long time, it was considered that the development of conceptual understanding is only possible with 11- and 12-year-old students. Such an understanding resulted in the idea that learning concepts before the ages of 11 and 12 was not recommended and even forbidden. It was considered that children develop so-called quasi- and pseudo- concepts, as they are unable to develop their true understanding of the target concept. Therefore, teachers must introduce incomplete concepts or the "simplified" version of a concept. (Lecture 5)

However, Vygotsky's understanding of the human ability to think through speech, which became central in his theory in the 1930s, was identified as a specifically human characteristic: moreover, this ability had practical and methodological implications. A person who is able to think conceptually and independently using language to mediate his thoughts, express emotions, and control motives was considered to reflect a target in human development. When the significance of speech mediation came to the fore (see the law of sociogenesis in the Pedology of the Adolescent), Vygotsky's understanding of psychological development also changed. In the 1930s, he argued that speech affects human consciousness as a whole and not its individual components (Vygotsky, 1997, p. 137). He indicated that human consciousness did not depend on the matured intellect, but the sequential replacement of one dominating psychological function starting with a diffuse affect determined the process of the development of humans. Vygotsky concluded that non-intellectual mediation occurs before the intellect matures and becomes the leading psychological function in the psychological system of an adult. Vygotsky's position might serve as a reply to Galperin's critique.

reflected in his works, such as Studies on the History of Behaviour (Vygotsky & Luria, 1993). In his candidate dissertation, Galperin (1936) elaborated the significance of the development of sign meaning in children.

(5) Theoretical and practical limitations of the concept "ideal form". The most detailed elaboration of the concept of the ideal form was offered by Vygotsky in Foundations of Pedology (1934):

The child speaks in one-word phrases, but his mother talks to him in language, which is already grammatically and syntactically formed and which has a large vocabulary, even though it is being toned down for the child's benefit. All the same, she speaks using the fully perfected form of speech. Let us agree to call this developed form, which is supposed to make its appearance at the end of the child's development, the final or ideal form … ideal in the sense that it acts as a model for that which should be achieved at the end of the developmental period…. The greatest characteristic feature of child development is that is achieved under particular conditions of interaction with the environment, where this ideal and final form … is not only already there in the environment and from the very start in contact with the child, but actually interacts and exerts a real influence on the primary form, on the first steps of the child's development. (Van der Veer & Valsiner, 1994, pp. 348–349)

Vygotsky's statement about the interaction of ideal and real forms is controversial, considering his unacceptance of dualism. We might suggest that if Vygotsky had lived longer, he would have clarified his concept of the ideal form. However, in 1934, this concept was relatively new in psychology, and it carried an important function in the development of peak psychology (Vygotsky, 1997, p. 137), which implemented the idea of a reverse method, as suggested by Marx, which offered to take the best abilities that could be developed in learners as a reference point for the target development. Galperin suggested that the limitations of Vygotsky's ideal form could be overcome by examining not the individual's subjective understanding of the world but how the world influences the individual:

[I]f you study the formation of actions in its final form and trace the unfolding all the way from the material to the ideal form, then you might develop an understanding of how an exquisite psychological phenomenon such as an individual thought is formed.

This is very important because it opens up a new direction for the study of mental processes. (Lecture 4)

(6) Galperin's idea that it is impossible to develop a theory of consciousness per se is an important methodological point that Vygotsky made in his late works. Consciousness is essentially a boundary phenomenon, and if it exists in the form of speech in which a person expresses his or her relationships with the world, then such relationships should be examined not only as generalisation and communication but also as the unity of affect and intellect. However, even in Thinking and Speech, Vygotsky did not elaborate this matter, and Galperin rightfully points that out that a learner is presented as a "theorising subject" who develops consciousness but does not communicate and does not interact with the world:

[I]f we assume that any psychological process is purely subjective, then it becomes impossible to investigate the process. (Lecture 4)

(7) The next argument put forward by Galperin is that the system of cultural-historical psychology is not closed from above by motives. Without including the reasons to why Vygotsky did not manage to develop the theory of affect and the steps that he pursued in that direction, we would like to mention his fruitful dialogue with Kurt Lewin. The approaches of Vygotsky and Lewin were complementary, and they were central in the development of theories of affect and intellect. By applying the foundations of dynamic psychology, Vygotsky, in collaboration with his research group, modified Lewin's experimental methodologies to apply them in clinical practice. In one of the studies published after his death, which considered the analysis of dynamic meaningful systems in Peak's disease (Samukhin et al., 1934), Vygotsky attempted to trace how individual features of character affected the trajectory of the pathological process in different patients. The findings indicated that as their consciousness deteriorated, the patients showed decreases not only in the level of generalisation, the dynamic nature of the inter-psychological system, and deterioration in the field of significance but also reduction in freedom. A similar tendency was observed concerning the affect system; the patients demonstrated increased simplicity, structural and dynamic degradation, distortion of personal boundaries, and changed interactions with the world. All these symptoms could not be justified by the diagnosis but by the personalities of the patients. The suggestion about the unity of structural-dynamic aspects and the types of activities that employed them, which were introduced in that study, strongly affected the ideas of Lewin. In addition, such results were described in the cultural-historical approach to explain the structural similarity between the cross-sectional research of the action, affect, and thought and the activity approach. However, Vygotsky was not completely satisfied with this solution, and the final lines of the speech introduce the central idea in Galperin's critical reflections: the need to shift from cross-sectional to causal investigations:

[O]ur first conclusion concerns the method of psychological research. We do not dismiss the method of self-observation; we use it and accept it. Self-observation can describe a mental phenomenon. However, this is only a description of the phenomenon and nothing else! What lies behind this phenomenon? We can only discover this when we are creating the phenomenon and shaping it in a controlled process. (Lecture 4)

This direction, which was identified by both Vygotsky and Galperin, is important in contemporary psychological research, in which cross-sectional, correlational, and often sociological investigations prevail. Instead, attention should be given to design based research aimed to examine the target phenomenon by constructing it instead of observing.

In summary, the critical reflections Galperin outlines in his speech resonate with the ideas that Vygotsky developed in 1933 and 1934, which reflect a dialogue in time between these outstanding scholars. However, Galperin went further by outlining the directions of the development of Vygotsky's theory: (i) to consider the study on human consciousness an approach to developing the study of human personality. The key to this approach is to further examine meaningful activities, particularly the process of the development of actions and motives; (ii) to examine "the natural origin of signs" during practical social activities in which humans and material objects interact to create a stable, viable, and necessary structure; (iii) to transfer methodologically from the cross-sectional examination of activities to study the causality of the activities in which humans engage. In another study (Engeness & Lund, 2018), we found that Galperin's contribution to cultural-historical theory was as follows: (i) specifying the unique character of the development of human consciousness emerging in social activities and cultural, tool-mediated practices; (ii) identifying the role and the function of tools as imbued with relevant social experience and mediating learning activity; (iii) conceptualising the nature and functions of human psychological processes as specific forms of activity and by outlining its structure and identifying the subject of psychology in studying the ontogenesis of object- oriented activity. It is difficult to disagree with the similarity between the steps outlined in the speech and Galperin's scientific legacy.

#### Concluding Remarks

Surprisingly, many similarities may be observed in the ideas put forward by Galperin and the directions identified by Vygotsky in his works from 1932–1934 (Zavershneva & Van der Veer, 2018). Galperin's speech exemplifies his subtle and profound understanding of Vygotsky's theory. A similar understanding has not been achieved by any of Vygotsky's followers. The speech is a unique historical document that makes a considerable theoretical contribution by presenting a concise and consistent summary of the theory of consciousness outlined by Vygotsky at the end of 1932. We believe that Galperin's speech is of particular significance for contemporary research in light of the predominant trend to oversimplify, fragment and distort Vygotsky's ideas. The speech may be considered the missing piece of a jig-saw puzzle that bridges cultural-historical and activity theories. The divisions between these theories have not been overcome in the unified version of cultural-historical activity theory (CHAT) (Nussbaumer, 2012).

Galperin did not work closely with Vygotsky. He entered the field of psychology in 1932, in the move of the Moscow group to Kharkov. However, Galperin assumed the task of providing a thorough analysis of Vygotsky's system in his speech in 1935. By identifying the central concepts in Vygotsky's legacy, Galperin reveals the connections and the interplay among these concepts to create a system that was not finally developed by Vygotsky. Even though in his later works, Vygotsky indicated that the ontological foundations of his theory were aimed to conceptualise human development as the gradual development of consciousness and human freedom, this emphasis was not pursued by any of Vygotsky's followers except Galperin. Paradoxically, Galperin was not a student of Vygotsky, and very few overviews of Vygotsky's legacy have presented Galperin as his follower (Arievitch, 2003; Haenen, 1996).

To conclude, first, Galperin's speech not only represents a valuable overview of Vygotsky's system and outlines his critical reflections, but also provides thorough analytical considerations of the approaches pursued by Vygotsky. Galperin offers clear descriptions of the ideas that are central in Vygotsky's legacy, many of which remained vague and underdeveloped in the works of the latter.

Second, Galperin's speech not only offers critical reflections but also demonstrates a subtle and profound understanding of Vygotsky's original ideas and outlines ways to enrich and extend these ideas to further develop the cultural-historical approach. Several of these ideas are elaborated in Galperin's lectures included in this book and which offer valuable examples of productive critical reflections. They are a rare illustration of the high standard to which researchers should strive to achieve. In his speech, Galperin is not harshly critical, nor does he attempt to attribute his own ideas to Vygotsky or make any additions that could interfere or distort Vygotsky's ideas.

Third, one of Galperin's most significant contributions was to explain internalisation as the transformation of a learning activity from the external (social) to the (individual) internal plane. This transformation was described by the measure of its acquisition by the learners engaged in the activity. It was conceptualised in outlining the dialectically developing forms of this transformation: (i) motivation, (ii) orientation, (iii) materialised action, (iv) communicated thinking, (v) dialogical thinking and (vi) acting mentally (Engeness & Edwards, 2017). These phases might be considered as Galperin's re-evaluation of Vygotsky's law of the parallelogram, which he mentioned in his speech and which was not fully developed by Vygotsky.

Finally, Galperin offers the following elegant conclusion:

The main contribution of Vygotsky is the idea of the meaningfulness and freedom of human consciousness. If we would like to accept the contribution of Vygotsky and develop it further, we have to find the need that would ensure implementing his theory.

Galperin's study of orientation, particularly the third type of orientation (Engeness, 2020; Engeness & Lund, 2018), extends Vygotsky's ideas and shows how the freedom and meaningfulness of human consciousness can be achieved in education. Galperin emphasises that the third type of orientation reveals the essence of learning, promotes abstract thinking and offers a unified approach to learning by creating links between the sciences and the approaches to studying them. By applying the third type of orientation, learners master the essence of learning through studying a phenomenon, which carries a new function not as a studied object, but as a tool for studying the essence of the learning and how to go about it. In so doing, learners develop their understanding about the nature of learning across contexts and subject areas, thus enhancing their agentic capacity as independent and conscientious learners. This approach is incredibly useful now in the age of fast-developing technology and advances in knowledge, "fake" news, and unstructured streams of information. Galperin argued for the need to make a transfer from studying human consciousness to studying real individuals and their relationships with the surrounding world. His scientific legacy is an extraordinary example of this pursuit, in which Galperin transferred the legacy of Vygotsky from the ideal plane to the real world.

#### Funding

This study was supported by the Russian Science Foundation Grant No 20-18-00028.

> Irina Engeness Faculty of Education Østfold University College Halden, Norway<EMAIL_ADDRESS>
Ekaterina Zavershneva https://orcid.org/0000-0002-5423-6225 Faculty of Social Sciences Department of Psychology National Research University Higher School of Economics Moscow, Russia

#### References

## Contents

## **Chapter 1 The Development of Mental Actions and the Orienting Basis of Actions**

#### **Outline of Lecture 1**

This lecture introduces the Study of the Development of Human Mental Activity. Galperin argues that to plan an action, it is necessary to create an *image of an action*. Any human action (both real and ideal) has a binary structure comprised of *orienting* and *executive* parts. Therefore, planning an action should include the creation of both its orienting and the executive parts. The *orienting part* comprises two subsystems, *motivational* and *operating*, the latter of which consists of four components: (i) constructing an image of the present situation; (ii) revealing the potential of the individual components of the present situation to the learners; (iii) planning the future action; (iv) facilitating the action in the course of its execution. These four components are not only complex but also different. However, they are similar in the presence of *images* of one kind or another: an image of the present situation, an image of the plan of action, or an image of the action that is being executed. In summary, there are two types of images: *images of the surrounding reality* and *images of ideal actions*. These two types of images constitute the two main components of human orienting activity.

Galperin proceeds to discuss the formation of ideal actions. He bases his logic on Marx's premise that the ideal is the material transferred to the human mind and is transformed in it (*the first premise*). Therefore, ideal actions are nothing more than real, substantive, and external actions with material objects. However, ideal actions do not appear by themselves; they have to be created, and it is important to find or create a material action from which an ideal action could be derived (*the second premise*). *The third premise* is that not all actions can be transferred to the ideal or mental plane; motor skills are an example. However, some actions can be transferred completely to the mental plane, such as mathematical calculations. Galperin explains the difference between the ideal and mental plane as follows: *the mental plane* belongs to the person reflecting the surrounding reality, and *the ideal plane* might comprise a person's reflections and perceptions. Based on the difference between the mental plane and the ideal plane, Galperin proceeds by investigating the actions that can be completely transferred to the mental plane of a person. He argues that the development of actions that can be transferred to the mental plane is of primary significance in overcoming the present situation in pedagogy, where teachers educate learners by simply explaining target concepts. By following such an approach, the entire process of learning remains "behind the wall" and invisible to learners. Instead, Galperin argues that the process of *learning should be deployed and revealed to learners* by identifying the following two steps:

In *the first subsystem* of the conditions necessary to design an action, its final product or outcome should be identified according to its desired characteristics, such as the size, the speed of execution, and so on. In addition, the elements (units) of this product, the order in which they should be constructed, and the operations necessary to create each unit should be specified. What then follows is the reference to the *tools* that learners can use: natural or artificial, material or materialised. Finally, an *operational scheme of thinking* should be constructed to indicate how to perform the action. Galperin describes how an operational scheme of thinking can be constructed by referring to a case study in which learners were taught to analyse Russian Orthodox churches. In summary, the first subsystem facilitates the construction of a new action. *The second subsystem* facilitates the acquisition of the desired properties of the action. Galperin's detailed elaboration of the second subsystem to achieve the desired properties of the action are the topic of lecture 2.

#### **Lecture 1**

Today we begin the study of the formation of mental functions. As long as the mobility of animals creates unique and non-repetitive situations it is impossible to manage an action without creating an image of this action. As you know, any action of an animal or a human consists of two main parts: orienting and executive. These two aspects are important because normally when we are talking about an action we have in mind its executive part only. Of course an action cannot exist without its executive part. What can exist without an executive part—is only a plan of actions, a scheme of the future. However, we usually have in mind only the executive part of an action and forget about the fact that every performance critically depends on the orientation of a person or a learner while performing this action, we simply forget about the orienting part. In fact, we should regard orienting as an aspect of managing the action. As you will see later, some important aspects of the formation of individual actions, the success of their application and generally their significance in the life of an individual depends on the quality of the orienting part of the action. It is the orienting part and not an action itself that constitutes the focus of psychology and therefore, in what follows we will consider the focus of psychology as the orienting part of an action.

In examining orienting, one can distinguish several systems, but above all there are two large systems—a motivational system and an operating system. The operating system comprises the elements of the action. We are not going to introduce the motivational system now, not because it is not worth doing so, but because it will be presented later. Now we will focus on the operating system as elements in the orientation of the action. In the operating system we can distinguish at least *four main components*.

*The first component*—is constructing an image of the present situation, describing the location of the things we will need to act with. It may not necessarily be a totally new situation, but a situation that needs to be clarified or, at least, confirmed that it is the same situation learners have been exposed to before. We should either confirm this, or add something, or describe in detail a totally new situation. So, the first component is building or updating the image of the present situation.

*The second component* of the operating aspect of orientation is clarification of the potential of the individual components of the present situation for the interests of the acting subject—a learner. This clarification is the primary purpose, because there are other functions of these components: as a tool to perform an action or create additional conditions for the action. However, it is important to identify the potential of the individual components for the primary, the actual, need of the learner. Alexei Leontiev describes this need in the lofty term of 'a personal meaning'. Of course, this is correct in relation to a person, although it is not always so lofty. In general, we are talking about the significance of the individual components for the needs of the learner.

*The third component* is planning future actions. Animals do not create plans, but they identify the way to reach the desired objective, or, the opposite, the way to retreat from the objective if it is dangerous or undesirable.

Finally, *the fourth component* is very complicated: it is the further orientation of the action during its execution. We call it: facilitation of the action in the course of its execution. This facilitation comprises two major parts: (a) actual control over the process of execution of the action; and (b) correction of the observed deviations.

As you can imagine, each of these four major components of the scheme<sup>1</sup> that comprises the orienting part of an action and especially the last component, can grow

<sup>1</sup>Galperin gives more details on thescheme later in the lecture.

into a large independent field of study. For example, the construction of the image of the present situation, in fact, can become a form of a cognitive activity and so present a separate scientific area of study with all its ramifications.

However, I would like to warn about the following: the fact that the process of the development of cognition can grow into an independent area of study, does not mean that at the beginning of ontogenesis, we can say that a baby is able to conduct a very small cognitive activity on a reduced scale. A cognitive activity, being a particular type of human activity, is qualitatively different from the type of activity a baby can perform. The orienting activity of a baby is closely related to and is marked by its immediate practical implementation. So, the difference between the cognition of a baby and an adult is qualitative rather than always easily measurable.

Similarly, an understanding of the potential of the elements in the present situation for current needs happens differently with small children and with adults. In an adult, this understanding may present ethical problems with their ramifications. The potential of the objectives in a situation is not always clear in relation to someone's actual needs. Therefore, clarification of the potential of the elements in the present situation for the current needs of the learner can be seen at the very beginning of all human actions.

Each of these four components can turn into an independent area, with its particular significance. However, even being in a simple form and inseparable from each other, these four components are always present in orientation—in humans and in animals. Another thing is that for an animal, it is natural that objects possess useful potentials which an animal is already aware of. This is because an animal lives in the world of instinctive relations and a significant feature presents itself immediately as an unconditioned stimulus that evokes positive or negative attitudes to it. Hence, each of these complex four components can be identified in any orienting activity.

These four components are not only complex, but they are different too. To begin with, we would like to start with some simple ideas: the two main components in the managing aspects of orientation. These are always images of one kind or another (either it is an image of the present situation, or an image of the action plan, or an image of an action that is being executed that merges at some point with its plan, or an image that has a kind of scattered potential—something matters, but something does not matter, etc.). So these are images, different, but images. In addition, there are always actions that are performed in terms of these images. Well, let us say we make a visual estimation of the distance from ourselves to an objective. This is an action in terms of images, because we deal with perception, we do not do anything with hands; if we move our eyes, which is only of secondary importance, this does not represent the way we estimate the distance, because sometimes we do it even without moving our eyes at all. Hence, we perform an action: estimating the distance in the visible field, but without performing material actions. This is an ideal action of which there are many, including those that are performed in mind. There are many other activities that are carried out by us on the ideal plane either in terms of perception, or mentally, but, anyway, these are ideal actions. They differ in purposes, but they are all defined as ideal actions.

So, we have two main components of any orienting activity—these are images that represent the reality around us (images as such, with their potential, as a plan or as a real ongoing process), and then, the actions that we perform in terms of these images which are ideal too. Therefore, our task today is narrowed to the two main elements of orientation: images and ideal actions in terms of images. Having identified the two main components, the question is: which of them do we start with?

Any ideal action takes place in terms of images and therefore, it presupposes the existence of these images. On the other hand, images themselves are the products of the actions, and the actions that are not only ideal, but above all in their original form—real actions with objects, which are later presented for us as images. So, images themselves are the products of the actions with objects represented in images. Strictly speaking, these are two inseparable elements, but we would like to start with the one that we could use as a clue in our study of these complex phenomena. That is why we choose the development of ideal actions as a starting point of our investigation and, as you see, images are needed, in fact, to enable us to perform these actions; while images themselves are the products of actions (material and ideal).

So we start with the formation of ideal actions. In this endeavour, we cannot begin as if we were the first humans on earth, because there are certain premises we need to start with. *The first premise* of the formation of an ideal field in general, and specifically the formation of an ideal action, is the famous statement by Marx in his foreword to the second edition of the first volume of "Capital". Marx contrasts his method to the method of Hegel, saying that for Hegel ideal is a demiurge, the initial motor of the entire universe, and for him, for Marx (his exact words), "*the ideal is nothing else but the material transferred to the human head and transformed in it*". Let us consider this statement as a starting point.

Based on this premise we can consider ideal actions, which we produce in the field of perception, in terms of speech, or mind, as derived from external subjective, material actions, which are then transferred into a human head. During this transferring and further functioning in the human mind these actions undergo regular changes, becoming what we discover later as ideal actions.

These ideal actions are nothing more than real, substantive, external actions in their origin, content and primary function. But for us it is very important (and here comes the second premise), that these material actions should be also created. We say that ideal actions derive from material actions, which do not appear by themselves in their final form, but have to be created. Hence, *the second premise,* is to find or create a material action, which an ideal action could be derived from. This is a very difficult task, because usually we get so separated from the material in our mental activity, that we cannot find its roots, its origin. This is a particular challenge. Every time we would like to investigate the formation of an action, we need to find an appropriate material action, create this action in this form, and then transfer it to the human head, and transform it into an ideal action.

*The third premise* is that not all actions can be transferred to the ideal or mental plane. Well, let's say, such actions as you are busy with now, writing. Your writing remains on the paper: if you do not write, there will not be any notes. So, writing, in its executive part, is an external action. It has its orienting part which is found with children who are learning to write and then gets reduced and transfers to the internal plane. The same happens, for example, when you learn a foreign language. In order to construct a proper phrase or a sentence, you have to get a detailed orientation to the relevant parts of grammar, phonetics, lexicology, and then, when you master this language, it seems that you just speak it. So, the speech as an external (oral or written) action remains external, while its orienting part undergoes changes, is transferred to the internal plane and is transformed there. Not every action can be transferred to the mental plane. There is a very wide range of what are traditionally called motor skills, which remain in the external field, in the field of material objects, while their orienting part transfers to the internal plane. On the other hand, there are actions that can be entirely transferred to the mental plane and they can be performed on both the external and internal planes. Imagine that you are studying maths. You can perform mathematical calculations in writing, externally, and you can learn to execute them in your head. When you perform calculations mentally, the whole action is transferred to the internal plane. For research purposes, for instance, it is very advantageous to select the forms of activities that can be completely transferred to the internal, mental plane. I would like to emphasise that this is not just an ideal plane, but a mental plane, because not every ideal plane is internal and mental. For example, the field of perception. Perception is a psychological concept, however it is different from imagination, although it belongs to the ideal plane. This plane has one very important feature that has been identified in psychology: the subject himself separates this ideal plane from the plane of external things.

There are very many phenomena that are considered to be on the internal plane, but psychologically, strictly speaking, they refer to the external plane: for example, hallucinations. A hallucinating person believes that what he hears, sees or feels really exists. The same false sense of reality of what is perceived differentiates hallucinations from illusions. Therefore, a psychological plane—is an external plane! Hallucinations might be an indicator of poor health, but psychologically these perceptions refer to an external plane. Importantly, it is not what someone sees or hears, but that someone has mixed reality and the internal plane. There are some very beautiful (in the psychiatric sense "beautiful") hallucinations described by a famous Russian psychiatrist Kandinsky and, thus, called "Kandinsky hallucinations". They are very bright, and projected to the outside world, but one is absolutely sure that these are hallucinations, not reality. This means that a person's confidence in objectivity does not correspond to the vividness of the images. One might see a very vivid picture and be sure that this is one's imagination. Alternatively, psychiatric patients may listen carefully to some voices, which they cannot make out, but they are completely sure that these are real voices and someone is whispering something to them, usually something unpleasant. What is important is that the patient is convinced about the existence of these voices. He might not make out words, but the person has no doubts that these voices are real.

What I have just described constitutes the difference between the mental plane that belongs to an individual and the ideal plane that might comprise a person's reflections and perceptions.

Based on this difference between the mental and ideal plane, we will start investigating the actions that can be completely transferred to the internal, mental plane. But here we need to establish a few preliminary conditions; otherwise we can easily slip into the situation in which psychology and pedagogy have found themselves. We cannot, if we are researchers, (if we are teachers and we have no time for research, this is another matter) behave in the same way as people who educate others with regard to creating mental actions. We cannot just explain something. Imagine that we explain an arithmetic rule of addition or the identification of sounds in a word to a child. These are basic things that are taught in school. How is this usually done?  Sometimes a teacher shows how this should be done. Then the most capable child is asked to repeat what has been explained and he does so. Then the teacher assigns homework to practise undertaking the action. When the children are back in school, they are tested to ascertain if they have mastered this action. So, the whole process of learning takes place, in fact, beyond any control and it happens as if by itself. We just evaluate skills demonstrated by students by awarding grades. One student is performing well, another very well, the third is mediocre, and very many perform, in fact, poorly. If students still cannot perform the action, we repeat the instructions, ask students to practise more, but if someone still cannot do it, we say, removing all the responsibility from us that he "lacks some cells in his head" and we blame the child.

We are not going to discuss how this happens in detail. What is important is that the whole process of learning remains "behind a wall" and is not visible for us. In this case there is nothing to study and nothing to research. Of course, this approach can be used in educational practice, if practitioners cannot offer anything better they cannot be blamed for that. However, if we would like to study this learning process, we must reveal it, but how? To start with, we cannot limit ourselves to observing only what actually happens, it may then seem that the learning process gets started and then proceeds as if by itself and we evaluate only the final outcome. I do not believe this is the right way to go about things, but how can we manage and control the whole process of learning?

*Firstly,* we must accurately identify the qualities of the future learning process. For example, if we would like to teach a child how to break down words into sounds, it is necessary to identify the requirements this skill has to meet: should a child be able to break down words in fast speech, a speech of another person, whether he should do it out loud or learn to perform it silently, and so on. When we design for an action, and above all if this action is going to be assessed, we should identify the qualities of this future action, which will be used later for the assessment. What is more important is that an action always leads to some result or an outcome which should be achieved under certain conditions. If you would like to examine how students learn in a planned activity, you need to describe in detail the conditions and the way the activity should be carried out and identify its expected outcome. Hence, you should describe in detail the qualities of the action you are designing for.

*Secondly,* you have to select the system of conditions to ensure the desired properties of the designed action. This does not mean you should only highlight what is present already. Very often these conditions must be created and likewise, you should also identify potential pitfalls in the designed action. This is, actually, just the opposite of what an ordinary teacher normally does. Usually a teacher explains the task, emphasises why it is important, and shows how to complete or solve the task. Then he asks students to learn everything that needs to be learnt by solving other tasks; however, how the students learn remains out of the sight of the teacher. The teacher just assesses the final outcome. I would like to suggest another approach: not to delegate our duties to students, but to find a system of conditions under which students *cannot help mastering the action and, in doing so, learn how to complete/solve other tasks*. Above all, the action needs to possess the desired properties that have been identified previously and hence, we have to employ a rigid system of conditions under which students will definitely master the action with its predetermined properties.

Yesterday, I read a study. The author reported that using a system of certain conditions, even children with learning difficulties can learn things which they would never be able to learn under usual teaching. A task should be broken down into such small units of the kind, that we would never use for ordinary children, because such small steps represent something very painful and disturbing, as any division hinders and delays learning. So, what is negative for an ordinary child, can be beneficial for a child with learning difficulties. It turns out that if you break down an action into smaller chunks, then even a child with disabilities can master this action. However, there is another very interesting aspect of this matter, but I will tell you about it later. Hence, it is important that we do not just set a task for a learner by saying: I have explained everything to you and now you have to solve it yourself; but instead we select a set or a system of certain conditions that would assist the child in solving this task.

This system of conditions is labelled the phases of mental development and ensures that the action being designed for will possess the predetermined qualities. This is a very narrow label, however. This system of conditions includes three large, though interrelated and intertwined, subsystems: the first—is a subsystem of conditions necessary to design an action; the second—is a subsystem of conditions necessary for the acquisition of this action and its desired qualities; and the third—is a subsystem, so-to-say, "transferring" the action from the external plane into the human mind.

Let us explore each of these subsystems. The first—is a subsystem of the conditions necessary to design a particular action. When identifying these conditions, we have to recognise that every action is characterised by what it produces—its product or outcome. All actions have an outcome; even those that seemingly do not have one. For example, gymnastic movements, what product or outcome do they have? The outcome is a particular form of an action, which is desired to be achieved and which, as you know, can be achieved only with great effort, because it is one thing—just to perform a movement, and another—to perform the movement with its predefined qualities. Of course, you are aware that this requires considerable effort and those who engage in sports or gymnastics know how difficult it is to perform floor exercises.

So, every action has its own outcome and is characterised by this particular outcome. An identification of the final outcome with its distinctive characteristics is the first point to be considered when designing for an action. For example, if you would like to design a writing activity, then you will need to teach explicitly how to write fast and clearly. Well, perhaps most of the students in this room do write more or less fast, but whether they write clearly—this is very doubtful.

As I have already said, the starting point in the design of an activity is identification of its final product with its desired characteristics. Usually these characteristics are: the size, the speed of execution, etc. The second point is that we identify the units of this product in the order they need to be constructed, in other words we specify the parts of this product in the order of their execution. This order may not match the sequence in which these units appear in the final product or outcome, however, you need to specify those that make up the final product in the order of their execution, and each unit should have its specific characteristics. When you have identified the characteristics of all the units to be created, then, in the third step you specify the operations necessary to create each unit, which sometimes may require several operations, and you specify them: (i) in the order of their performance and (ii) the desired qualities of these operations in terms of speed, sequence, size, etc. (We will talk about this in detail later.)

Hence, it is necessary to introduce the order of all the operations that constitute each unit. Of course, this should include the initial material you are working with or the starting point. After all, an action will lead to the final product, which comes from the existing initial material. The characteristics of the initial material of an action are also important and they are included in the same description.

What then follows is the reference to the tools learners can use. Almost all human actions are performed with various tools. These tools can be natural in origin, for example, their own bodies, or they may be artificial. Even when writing, you use a pen, which has to meet certain requirements (often we are unhappy with the quality of pens), paper, which also has to be of certain quality, etc. Hence, there are tools that we use, but there are also other tools. For example, when we study a foreign language, we have to learn to pronounce its sounds correctly with the help of another natural tool—the larynx. We force our poor larynx to speak the way it has not been used to from childhood—in a foreign language, based on other principles of intonation. You know this is one of the most difficult tasks—to learn the proper intonation, the phonetics of a foreign language; however, this is absolutely necessary. In the descriptions of how to perform physical exercises it is pointed out clearly how to teach our limbs to move, not the way we move them in everyday life: for instance, sometimes how some people walk looks awful. In the military, soldiers are taught different types of marching or steps, and not only in the military, but in ballet schools too. If you at some point meet a person who can walk properly: you will envy this person and will also try to walk, not anyhow, but in a way that means that you would be looked at and admired. Hence, everything needs to be learnt, and we must teach our own body movements to meet these specific requirements.

Tools can be of all sorts. If you take the production of material things, then these tools are machines, cutting, assisting, measuring instruments—all these instruments should be linked into a single, interconnected system.

There is another very important point, which I introduced only in a general, very descriptive way and now I would like to present it as a separate part of the system. A learner, and we consider a learner any person who is learning, if he is an academic—he is still a learner, if he is to learn something, he has to be presented with the overview of the whole activity. Previously, we said that the fourth component item of the scheme, which we label the scheme of the orienting basis of an action, is the representation of the scheme of action as a whole. Consequently, a person has to follow this scheme when he begins to perform a new action. Now we can clearly specify this last component as *an operational scheme of thinking*. This is a very important point, which shows the difference between a machine and human approach to an action: a machine does not need this operational scheme of thinking, everything else can be supplied to the machine, but not this scheme. This is a general scheme of action. If the system of instructions is very difficult or when students have to act without any visible cues, then we need to offer the learner the general operational scheme of thinking in addition to a list of the order of operations to be performed.

Let me give you an example of one very beautiful operational scheme of thinking. The students in the 3rd–4th grades were taught to analyse the monuments of ancient Russian architecture (mostly churches). Generally, Orthodox Churches are complex buildings: they have a lot of different elements, they are characterised by different parameters, and there are different schools: Moscow, Vladimir, Novgorod, Kiev, etc. These schools have their own well-defined features. In addition, within each school, churches of different types were built: some of them—strictly monumental, others solemn, and others—festive. There were churches, so-called, for home use, which were more intimate, etc. So, the students were to learn to distinguish which church belonged to which school according to clearly defined criteria. One of these criteria used in the analysis, was the structure of the churches. This structure was analysed, starting from the foundation (Fig. 1).

Then the main box (Fig. 2).

Then the roof (Fig. 3).

Then the drum (Fig. 4).

Then comes the head that finishes everything (Figs. 5 and 6).

**Fig. 1** The foundation of the church building

**Fig. 2** The main box of the church building

Then the doors (Fig. 7).

Then the windows (Fig. 8).

Then other auxiliary buildings (Fig. 9).

In addition, each of these elements has a number of specific items. For example, the foundation: which materials it was built from and according to which plan, etc. Each of these elements contains 6–7 such items. For instance, the main box could be cubic, rectangular, hexagonal, or octagonal. All this requires a detailed analysis. It turned out that when the children were given a card with the scheme, this card appeared to be very complicated (Table 1).

The children could use this scheme by moving from one item to the next one, analysing and drawing conclusions about the type of construction. However, it was

**Fig. 6** The structure of the church building

**Fig. 8** The windows of the church building

**Fig. 9** Other auxiliary buildings

very difficult to transfer such a complex scheme to a mental plane. As soon this scheme was taken away from the children, they appeared to be helpless. Meanwhile to teach—means to develop the capacity with learners to analyse independently, on their own, rather than using this card. In order to do so, children should be given an operative scheme which surprises them because of its emptiness; but also because of its usefulness (Fig. 10).

The analysis proceeds from the foundation of the church to the box from the box to the roof, from the roof to the drum from the drum to the head, and then it turns to the door, then to the windows, and then to other buildings. So, in addition to a huge list, another scheme is needed. But what does it actually add? After all, it is empty. This scheme provides the general division of the object into its elements and

**Fig. 10** The operative scheme of thinking

also the procedure for the analysis, which guides the analysis of the object. This is a very interesting thing. You see, this is exactly what a machine does not need because it follows the uploaded scheme or programme and produces an answer. A machine does not need this special operative scheme. Schemes of this general nature are operative and have special relation to the way we learn. Earlier we used to think if you have some knowledge—good, if you do not—bad. It may happen that you have knowledge, but may not be able to operate with it, if you do not have an operational scheme which forms a so-called meta-understanding of how knowledge is created within a particular subject.

This is what the last point of the scheme of the orienting basis of an action should be (we call it a scheme because the action has not happened yet and when the action happens, then the scheme will turn into the orienting basis of the action). In addition to this scheme, there should be an operational scheme of thinking regarding what a person should do. If the scheme of the operating basis of the action is relatively simple, if the movement from one item to another is enough to perform the action, then we do not need to identify an operational scheme as a separate item, but psychologically this operational scheme is still being identified by learners. However, if the scheme of the orienting basis is complex, then the operational scheme has to be introduced separately.

What also seems important is that the division of the action into individual steps should take into account how well the learner is prepared for these steps: if a learner is well-prepared, then the steps will be larger; and if a learner is less prepared, the steps should be smaller, fragmented. There is, of course, a limit for this fragmentation; because if learning is divided into very small chunks then it is always necessary to make sure that the preliminary knowledge and skills have been mastered by students. The prerequisite for mastering new knowledge is very important for a student who, for example, is not able to learn even the simplest component of the new knowledge on his own. Therefore, it is important to distinguish between the general division of the desired action and the student's individual and psychological needs. Equally, it is necessary to distinguish between the units of the action and the individual steps of a student in this scheme. A learner starts with the steps he can do himself and then the steps should increase, although the general structure of the action remains the same. After a while the learner is able to proceed in bigger steps, which is one of the most important tasks—to increase the size of the steps of the action while it is being performed. In the end, the action turns into one continuous stream, into one single step. Sometimes it happens that individual actions merge and form steps that exceed the size of these individual actions. Objectively, they are a chain of actions, but for a learner they are merged into one continuous stream. This should be pointed out very clearly, because one thing is what you need to master, and another thing is that while mastering it you modify the way you perform the action, and, accordingly the way this action appears to you—as integral or divided.

There is one very characteristic signal that indicates whether the scheme of the orienting basis of an action is complete. After all, you can create this scheme based on your own premises, but a student, following the outline of your scheme may not always perform the action. Who is to blame in this case? You! If a learner has all the necessary prerequisites and if you have created the complete scheme, then the indicator of this is a paradoxical situation that, following the outline of this scheme, a student who has been unable to perform the action without the scheme, can perform it correctly from the first attempt and repeat this performance correctly every time afterwards. A learner is not able to perform the action without the scheme that you have created, but using it, he performs the action step-by-step. When the scheme has been constructed properly, then the student will inevitably achieve the desired result. This circumstance is somewhat paradoxical at first glance, but it is absolutely clear that a learner, who was previously unable to perform the action, by following the scheme of orientation, now performs the action correctly from the first attempt and every time afterwards. If this is the case, the learner's performance indicates you that you have created a plan of action correctly. However, if a learner follows your plan (if he gets distracted, this should not be taken into account), performs one step after another and does not reach the desired result, this might indicate that the scheme is incomplete and you have missed something. Then look for these missing parts! This has always been very important to us and that is why we have spent over 20 years investigating possible scenarios, since it is not an easy thing to construct the scheme of the orienting basis of an action.

Therefore, the scheme of the orienting basis of an action is presented as a sequence of steps. It is often called an algorithm, but this is not an algorithm in its proper sense, not a mathematical algorithm. It is an algorithmic prescription, and it differs from the mathematical algorithm that a machine follows without any understanding. It is quite the opposite. You always make a prescription in such a way that it would be understood by a learner. This can be a very small prescription, for example for the child with learning difficulties that I told you about previously, but it should be oriented towards the child's understanding because, even within a very short operation, the child should be able to manage his action on his own. An action does not happen by itself, it has to be managed. So, contrary to what is required for the computer, we, from the very beginning, rely on the learner's understanding of the element or a step of the action that is being performed. In addition, there are also the characteristics of the product, the characteristics of its components and the characteristics of the existing material. A machine does not need any information about these features, but a person does. This operational scheme is always needed for a person, although it is not always presented as an individual resource, but psychologically it accompanies any action. A person will always identify it himself, or the scheme can be supplied to the learner, which will certainly make managing the task and the action in general easier. This is *the first subsystem*—the subsystem that facilitates the construction or formation of a new action.

*The second subsystem*—is a subsystem that facilitates the acquisition of the desired properties of the action. We have come to the point when a learner is able to perform a new action, using the scheme of the orienting basis, but how do we ensure that the action acquires the properties we would like it to have? And actually, what properties do we want this action to have? This is in the next lecture.

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## **Chapter 2 The Phases of the Development of Mental Actions**

#### **Outline of Lecture 2**

The focus of lecture 2 is the *executive part* of the action, which comprises *three subsystems*: (i) the conditions for constructing the action (*a scheme of the orienting basis* of the action); (ii) the acquisition of the desired properties of the action; and (iii) the transfer of the original external action to the mental plane of the learner and the transformation of the action into a new psychological process. Galperin elaborates in detail the first and the second subsystems of the executive part of the action.

Galperin points out that to create *a scheme of the orienting basis* of the action, the action should be visualised, and *the outcome of the action* with its particular characteristics should be identified. The desired outcome of the action should be divided into the elements (units) presented in the order of their execution or performance. The properties of each individual unit and its intermediate outcomes should be specified. In the process of the development of the action, these units eventually become combined into a single step, and the action is performed in a single, continuous, and indivisible process. Galperin emphasises the *properties of the initial materials* and the tools of the action, which can be divided into primary tools, auxiliary tools, and control tools. The control of the action can be performed against previously identified, critically important indicators of the action—the criteria of control.

Galperin describes the *operational scheme of thinking* as a complete generalised scheme of action and shows how such a scheme may be created to solve problems in physics, for example. Drawing on Piaget's experiments, Galperin discusses how to facilitate a general change from children pre-scientific, naïve, and egocentric thinking to scientific thinking by identifying the generalised essence of the target phenomenon and its characteristic features.

In the *second subsystem of conditions*, the desired properties of the actions should be identified. These properties are as follows: (i) *rationality*—the learner focuses on identifying the action's objective and significant relationships; (ii) *generalisation*—the learner is able to identify the significant conditions among the variety of conditions in which he or she operates; (iii) *consciousness* of the action—the learner's ability to give a verbal report of the action; (iv) *criticality*—the comparison or verification of the selected criteria for an assessment of the action in relation to reality; (v) *measure of the mastery of the action*—whether the action can be performed by the learner using the initial material resources or whether it can be performed verbally in symbolic form, or mentally and how quickly it can be performed.

Galperin then turns his attention to the *primary properties* of any action: (1) The nature of the object with which the action is performed. These objects can be material, materialised, or verbal. The differences between the objects with which the action is performed can be described as levels of the action: the starting level is material, the intermediate level is verbal, and finally, the mental level. Galperin summarises that these main levels of action can be considered gateways through which the action can be developed from the material level to the level of speech and then to the level of acting mentally. (2) In designing an action, each unit should be carefully developed. In some cases, several units of the action can be skipped, and the action is always performed with a certain degree of completeness: it can be deployed to a lesser or greater degree or deployed differently in its different units, but the original completeness of the units is a mandatory property of the action. (3) The measure of the differentiation of the action is characterised by (i) separating the essential from the non-essential and ii) resistance to what is inessential and may interfere in the action. (4) The timely parameters of the action are tempo and rhythm. (5) The power characteristics of the action are the size and the distribution of the effort of the learner engaged in the action. Finally, Galperin poses a question about how to develop the desired properties of the action. The detailed answer to this question is the topic of lecture 3.

#### **Lecture 2**

I will start with a quick overview of what I was talking about in my previous lecture. I said that we would begin the study of the formation of mental actions with the development of ideal actions because it is the ideal actions that form the basis of all mental processes. I also said that in this endeavour, we would take Marx's statement as a starting point that the ideal is nothing other than the material, "transferred" into the human mind, and transformed there. In this lecture, we are going to trace this process.

To start with, we need to find out how actions are first formed as external actions with objects, and then transferred to the ideal plane. As a result of this transfer, external actions undergo changes, which make them totally unrecognisable and they begin to look like mental processes.

We will examine the formation of an action by starting with some pre-defined indicators. Such an approach will allow us to establish a causal relationship between the properties of the action and the conditions that lead to the formation of these properties. The whole of school practice, and life in a broader sense demand that some actions should be performed not physically, but ideally. For instance, when you cross the road, you estimate the distance and the speed of vehicles and evaluate whether you are able to move faster than the approaching vehicles and cross the road safely. In doing so, you perform an ideal action in the field of perceptions, and very often life teaches us how to perform these ideal actions in the surrounding environment. If we do not set ourselves the task of creating an (ideal) action with certain properties, but instead go about it in the usual way, (for example, first the action is explained, then it has to be learnt, and then it is checked or tested), then different people under different circumstances, perform this action in totally different ways and correspondingly get different results. This way of working makes it very difficult to understand why and how the results achieved by learners are so different.

To avoid such a situation, we need to define in advance the properties we would like an ideal action to have. We should also choose the system of conditions that will ensure the formation of these desired properties. This system of conditions is divided into three subsystems. I'll name them first, and then we will look at each of them in detail.

*The first subsystem* contains the conditions necessary to construct a specific action or create a scheme of the orienting basis of the action.

*The second subsystem* ensures the acquisition of the desired properties of the action. The same action can be performed with different indicators that may serve as a measure for evaluation of the action: e.g. speed, the degree of dependency on certain conditions, etc.

*The third subsystem* transfers the original external action with objects to the ideal plane of the subject and transforms this action into a new psychological process.

In my previous lecture, when talking about the first subsystem, I said that it comprised the conditions the subject should take into account when creating a totally new action and learning how to perform this new action. First of all, you should specify a so-called "model" of the action. To achieve this, we have to visualise the future action—how it should be performed. An action, as you remember, is characterised primarily by what it produces—its outcome.1 Therefore, you should also specify the outcome to be achieved with its particular characteristics and the action that creates this outcome. Such an approach represents a clear idea of what needs to be achieved (outcome) and how this can be achieved (process—action). However, since any process happens in time and the desired outcome cannot be achieved immediately, then the outcome should be divided into elements, which are presented in the order of their execution. This may not be the order in which these elements appear in the final outcome, but this is the sequence in which the elements, that constitute the final outcome, should be produced. So, we divide the desired outcome into elements in the order in which they have to be created and correspondingly we divide the action into individual units in the order of their performance. We should specify in advance the properties of each of these individual units of an action and their intermediate outcomes. I have previously emphasised that we should distinguish between a unit of an action and a step that a learner is able to perform which can, in fact, differ

<sup>1</sup>An outcome can be also understood as a learning outcome.

from the unit of the action (in this case the unit should be divided into steps that are manageable for the learner). What usually happens in the process of the formation of an action is that these units eventually become combined into one single step and the action is performed as a single, continuous, indivisible process. It is therefore important for us to separate the objective units of an action from the ability of a learner to perform these units (either in smaller steps, or in the steps of the size of the actual unit, or perhaps in larger steps).

The next point to be taken into account is the properties of the initial material that the action "deals with". Such material is always present, even when it is not visible and, as I have already told you, it is present even in the movements of free gymnastics: it is the ability of a person to perform the physical movements, their muscles and how well they can use them. So, the level of a person's physical development when learning these free movements is the initial material he is going to work with. In this case, it may seem that no initial material exists in the external field; however, in other cases such initial material can be recognised. In physical labour the initial material is the "raw" material we begin to work with. In mental work the initial material is the numerous sources we collect in order to do the work, for example, examining a problem and drawing a conclusion. So, there is always some type of initial material.

It is also very important to organise the initial material beforehand and not, as often happens, move immediately into the action without forethought. Organising the initial material ahead of acting is a very big task. Firstly, we need to verify whether the initial material is sufficient and suitable for the main purpose of the action. However, even if the initial material turns out to be suitable, it is still necessary to organise it in such a way that it can be used by learners in the corresponding individual units of the future action.

Then there are the tools of an action. Here we must clarify something I have been confused about myself for a long time. You see, tools can be used in the executive and in the orienting parts of an action and these tools are different. The tools of the executive part are quite obvious—these are tools used in an action as an external objective process. I will elaborate in detail on the tools of the orienting part a bit later.

Tools can be divided into groups: primary tools, auxiliary tools and control tools. This is a very important point, because you know how hard it is for a person undertaking intellectual labour to be in the position of controlling what he has done. Sometimes, it is necessary "to leave" the product for a while and to distance oneself from it. This distancing may involve a long wait time, which is not always possible. Therefore, it is very important to have some objective tools of control, especially in intellectual, mental forms of activity, where control has to be particularly precise and sensitive. Nevertheless, generally speaking, this type of control is not different from control in any other types of activity.

Control, although it may seem to be quite straightforward, should also be organised. Organisation of control comprises the identification of some of the points of control, because you cannot control absolutely everything. You can control an action as a process, and its outcome, in relation to some of the critically important indicators, which together with the means of control may serve as criteria of control. These criteria can be of any nature, but they should be objective. We also have to describe how these criteria will be used. So control, as you can see—is quite a complicated matter.

What follows after control (and this also should be planned in advance in the scheme of the orienting basis of an action) is the correction that may be necessary if some deviations (in the outcome or the process) have been identified.

Finally, in my previous lecture, I made a point about presenting a complete generalised scheme of an action. However, you may wonder what is "a complete generalised scheme of an action"? I have always considered this complete generalised scheme important as it highlights the difference between a human and a machine. A significant part of work (if it is very complex) could and should be transferred to a machine. However, there is something that cannot be transferred to a machine and this is the point we are discussing. A machine does not need to have an overview of an action as a whole. It operates according to some selected indicators: it reads the indicator and performs the operation. A machine does not require anything else because it, actually, cannot think. That is why, as you know, a mathematical algorithm that contains instructions or prescriptions can be performed without understanding, but when we deal with a human, a learner, this is another matter. In addition to ensuring that each instruction can be understood by the learner, we have to create an understanding of the complete generalised orienting scheme of the action as a whole.

Therefore, the last point in the scheme of the orienting basis of an action is, strictly speaking, a complete generalised scheme, presenting an action as a whole, or, as we have come to call it in recent years, an *operational scheme of thinking*. This scheme may be of various types: it can be, for example, quite specific, as it was in the analysis of the structure of church buildings mentioned in the previous lecture. However, back in I960, L.F. Obukhova used a similar scheme for solving problems in a physics course in secondary schools, such as the problems of the pressure of solid objects, and indicated that this scheme could be applied to a whole range of tasks. We did not recognise the significance of the operational scheme of thinking at the time; we thought it was only an auxiliary tool of low importance. It turned out that this scheme was of very high importance for human actions.

Imagine, for example, a carriage with four wheels (Fig. 1). It is loaded with boxes; each of which has a certain weight. Your task is to calculate the pressure exerted by

**Fig. 1** A Carriage with four wheels and loaded with boxes

these boxes together with the carriage and the wheels on the rails. You know the bearing surface area of each wheel on the rails. What do we have to do? Firstly, we have to calculate the weight of all the bodies that exert pressure, and secondly, we need to calculate all the bearing areas. Then we divide the total weight by the total area.

It turned out (this is also interesting), that if you present a finished diagram to learners that depicts this problem, it does not provide any help: a child needs to see how you draw these lines, how you highlight and add all the parts that make the total weight, and the areas of support of each wheel. It is a very peculiar thing that a wide variety of problems can be solved in a similar way, with a very complex arrangement of the bodies in relation to their bearing area. Imagine the scales (Fig. 2).

Here the weight of the cups is combined with the weight of the yoke and the bearing area is, in fact, the pointing part of the beam. As you can imagine, various combinations can be very difficult. It is very important that in these different combinations the scheme becomes very similar: there is the mass of the bodies, which exerts pressure, which means there is a pressing force P, and the total mass exerts its pressure on the area S (Fig. 3).

This is, in fact, a scheme that can be used for solving any problem about the pressure of solid objects. But this—its final form, and the original form—are the lines that connect all the bodies, exerting the pressure and all the bearing points where the pressure is exerted. So, this is a generalised operational scheme of thinking, the scheme that can be applied for a range of problems.

Together with L. F. Obukhova we analysed the differences that occur in children's thinking in the transition from a happy preschool age to an early school age, when the school "drill" starts. It turns out that a child's thinking undergoes very significant changes. In its happy preschool age, a child believes that the things are the way he2 sees them. This is the age when a child does not want to know anything about measuring, adjusting, etc.  In addition, a child usually thinks that

<sup>2</sup>Child (noun) is masculine in Russian.

**Fig. 3** A pressing force P exerts its pressure on the area S

all the properties of a thing are equivalent to the very thing itself. In philosophical terms, this means: a thing has its essence, and because the essence is singular - it makes a single entity with the thing which is expressed by its different properties. Moreover, all of these properties are equivalent expressions of this single entity. Therefore, a child can easily make judgements about some of the properties of a thing from the perspective of other properties. Well, with a skilful experimenter a child always misses the mark.

There are the wonderful experiments of Piaget used by L. F. Obukhova, in which a child is presented with two bottles filled with coloured water (Fig. 4).

The child is asked if there is more water in one of the bottles. When both bottles are next to each other, he says that the amount of water is the same in both bottles.  Then, we add a drop of water, and he says: "Now it's the same." We have to compromise, and we agree that now the amount of water is the same. After that we immediately turn one bottle upside down (Fig. 5).

The water fills the narrow part and it seems that there is more water in one of the bottles. And when the child is asked: "Well, now where is more water?" He replies without hesitation: "Here" (pointing to the upside down bottle). We say to him: "How did it happen? We did not do anything". He replies: "You turned it upside down, so there was more water". It is difficult to prove that the child is wrong as he does not even want to measure. He just sees more water in the upside down bottle and that is all.

When a child becomes older he begins to recognise all sorts of difficulties in life, then he begins to evaluate things not on the basis of how they seem, but on the basis of how they really are, which means by measuring: a fundamentally different position

in terms of an objective method. Importantly in this transition, from pre-scientific to the first proper scientific thinking in children, what happens is not so much a shift in knowledge, but a shift in a generalised operational scheme of thinking.

An interesting point is that you can teach a child how to measure, and he will measure and will get results, but these results will have no impact on the child's thinking at all. Let's say you showed a child how to measure, and when the bottles were next to each other, he measured the amount of water in the bottles with the help of, for example, a cup and found that there were four cups of water in each bottle (the child could also see that the amount of water in the bottles was the same). However, when you turned one bottle upside down, there came the contradiction. We asked the child: "Well, now how many cups are in this bottle?" He replied: "Now there are seven cups."—"Why seven if we didn't add more water?"—"You turned it upside down, so it became seven instead of four". You have taught arithmetic and measuring, but still his understanding of the situation is subjected to his perception of things. Since the child sees that there is more water, then there are not four cups of water, but seven. You have taught him how to measure using technical tools but his understanding of the phenomenon remained the same. Therefore, it is important not only to teach some knowledge, but to facilitate a general change in the ways of thinking, from pre-scientific, naïve, egocentric thinking to scientific thinking itself.

In scientific thinking too there are a number of schemes, which include, for example, a shift from the naively egocentric position to the objective position of identifying the essence of a phenomenon by using pre-defined criteria. It is important to remember that these operational schemes of thinking may be of different types: they can be applicable for particular cases, or may cover an area of knowledge (as regional schemes). They may relate to the sciences as a whole, or to knowledge about specific physical phenomena. Even younger children, when they make the transition to initial scientific thinking, start evaluating things on the basis of measurements, from the perspective of an objective position. However, when young learners are presented with a problem from an area of, for instance, moral categories (again there are fascinating experiments by Piaget), they again demonstrate their original naivety. One example describes the situation when a boy, who was at home alone, without permission opened a cupboard to get some jam and dropped a cup, which unfortunately smashed. And another boy, in contrast, while helping his mother to put the clean dishes into a cupboard dropped three cups, which also smashed. The question is: "Which boy carried out the bigger offence?" The child usually answers: "The boy who smashed three cups." However, from the moral perspective the response should be the opposite. The first boy disobeyed and consciously committed a moral offence. And the second boy did it accidentally. This is not a moral offence, but, so to speak, a physical one; but the child judges only by the amount of damage, the physical damage. As you see, in the area of morality the learner is still lacking the true criteria, he still thinks very naively, but at the same time the same learner can demonstrate some elements of scientific thinking when dealing with physical phenomena.

Operational schemes of a philosophical type are also worth mentioning. You know that there are great scientists who have very peculiar views in areas that are not relevant to their field of competence. Let me give you an example of a big physiologist, the professor of Leningrad University, who died recently. He was a very clever scientist and had made a number of important discoveries in the physiology of nerve conductivity; but he was always interested in psychology. He, in fact, tried to transfer schemes suitable for the analysis of neural processes to a completely different area—the field of psychology. So he organised the Laboratory of Parapsychology at Leningrad University to study psychological phenomena. However, the direct transfer of schemes applied in one field to another field does not always work. Schemes of scientific thinking, applied for real material objects, are not suitable for the explanation of social or psychological phenomena. The scheme of thinking and analysis used, for instance, in the study of the struggle for survival in the animal world cannot be transferred and used for the analysis of human social relations. Why is it not suitable for the analysis of human social relations? This is mainly because of the nature of the laws applied in these sciences, which are completely different. Correspondingly, I believe that the schemes suitable in one area cannot be transferred to another area. This is a very important point, but we are not going to dwell on it for long. The important thing is that the operational scheme of thinking is always present, even in the smallest activities, either collective or individual. A person must be given not only a system of rigid instructions about what to do, but the whole perspective, the overview of the action. The operational scheme of thinking constitutes the last and a very important item of the orienting basis for an action.

This last point ends, as far as we know at the moment, the first subsystem of conditions necessary for the construction of an action that is new for the learner, who simply cannot perform the action without these conditions.

You now may be wondering how a person, using the first subsystem of conditions, can construct an action and perform it with the pre-determined and desired properties? In an attempt to answer this question, we need to turn to *the second subsystem of conditions*. We need first to consider what properties we actually want the action to have. To start with, I believe that we need to identify the maximum amount of properties and find the conditions to achieve these properties and later, if we would like to, we can easily reduce the amount of desired properties. I am sure you understand, we cannot work the other way round. If we do not know all the circumstances and conditions of the acquisition of the action and its desired properties, we cannot be sure that the action will acquire the desired properties, for example, if the conditions are randomly selected.

But what are these properties? First, I will list all the properties, and then I will explain the meaning of each of them. First of all, we would like the action to be performed *rationally*. Next the action would need to be able to be *generalised* to a certain extent and applicable to *a range of circumstances* in which the action can be performed successfully. It is also desirable that the action is *performed consciously (with awareness)*. The action also needs *to be critical* (we will talk about this later). And finally, we need *a certain degree of mastery of the action*. This includes, for example, free and fast execution, performance with the minimum of attention employing automatism, etc.

These are the main properties that we would like an action to have. Since we need to teach these properties, we have to define how we understand them, otherwise risky naïve ideas may quickly arise. It can happen that we think we understand something, and then it turns out that this is not what we mean or what others understand. Let us therefore define each of the properties of the action in detail.

*Rationality of the action* means that the subject (the learner) focuses on identifying the action's objective and significant relationships. There are many relationships between phenomena and the circumstances that constitute an action. Consequently, the learner should be able to identify those, among all possible relationships, which are essential to perform the action.

Now the second property is usually called *generalisation*. This is also a very important aspect, because an action does not always occur under similar conditions. It can be performed under conditions that vary and sometimes are actually quite disruptive. Therefore, the idea of generalised action means that the acting subject (the learner) is able to identify the significant conditions for the particular action among the variety of conditions in which he operates. This is very important because some actions can be performed under very few conditions. Therefore, a learner has to demonstrate stability, a degree of insensitivity to any interference, and be able to identify the significant conditions needed to perform the action.

*Consciousness of the action*. We are not going to talk about what *consciousness* is in general, because there are ten thousand opinions on this point. Let us just agree about what we call *consciousness* of an action—it is a person's ability to give a verbal report of the action.

*Criticality* is a comparison or verification of the defined criteria for an assessment of the action in relation to reality. This is not just an application of the selected criteria to the action; it is an assessment of these criteria. Let us say I select some characteristics for the assessment of the action. Criticality means that I understand the reasons for selecting these characteristics as criteria. I need to understand whether these characteristics are the only characteristics available, or whether they are the most decisive and, in a broader sense, whether they correspond to reality, or whether I have imagined them myself and therefore decided that they were the most important criteria. Therefore, criticality of the action comprises the critical assessment of the criteria selected to assess the action.

Finally, *the measure of the mastery of the action*. This is an extremely important aspect. It is characterised, above all, by whether the action can only be performed by the learner using the initial material resources, or whether it can also be performed verbally, or in a symbolic form, or whether it can be performed mentally and how fast it can be performed, etc.

Clearly, when we plan these properties, we want the measure of mastery to be of maximum value. We want the learner to be able to perform the action at the maximum speed, consciously, and able to give an account of the action in many different ways: with material resources, without material resources, in writing, verbally or mentally, etc. Accordingly, we ask ourselves: how can these properties of the action be ensured? In order to answer this question, first of all, we have to analyse the constituent components of these properties and what initial material we need to transform to obtain these properties. We need to consider the desirable properties as derivative, secondary ones. These are the properties we want to form, but they may not be actually present in every case. Therefore, we should consider the initial existing properties of the action and form the desired properties from these initial ones by using some techniques.

We have listed all the final desired properties, but what are the primary properties of any action? These primary properties are as follows. *First*, I would say, it is *the nature of the objects with which the action is performed*. These objects can be either material, or verbal: represented in words or derivatives of words (e.g. all sorts of symbols). Ultimately, there might be actions with representations containing visual images of objects, or representations of various concepts. The differences between the objects with which the action is performed can be described as levels of the action, bearing in mind the following. The starting level—is material and is followed by the intermediate level. The intermediate level is a very special one, present only in humans: the level of speech, because speech has material basis. Marx used to say that the "curse of matter" gravitates onto speech. Language and speech in general always have a material basis, however meaning is ideal. And finally, we come to the next level—the mental level (in the sense that I told you earlier). These main levels are like gateways through which we raise the action from the material level to the level of speech and to the level of acting mentally. That's why we call them levels. These levels begin in the material world and through speech lead to the mental plane.

We have explored the first property of an action—the nature of the material, verbal and ideal objects with which we perform the action—which necessarily happens at the levels mentioned above, that is why this property is so important.

Now*the second property*, which is also always mandatory—is the initial completeness of the units of the action. Sometimes we can perform an action by skipping some of the intermediate units or by skipping all of the units, as it happens, for example, in mathematics when doing calculations with formulae. However, what is a formula? You have the initial conditions/components, the operational sign and the final result. By using the formula, we omit the whole action and we perform calculations according to this formula. This is an example of a maximum reduced action. An action is always performed with a certain degree of completeness: it can be deployed to a greater or lesser degree, deployed differently in its different units, but the original completeness of these units is a mandatory primary property of an action.

Now, *the third property*—is a measure of differentiation, separating the essential from the non-essential. This is useful both for the ability to generalise and for the development of the ability, mentioned above, to resist interferences. Just keep in mind two main aspects: (1) the separation of the essential from the non-essential; and (2) a resistance to what is obviously inessential, yet nevertheless, may interfere in the action.

*The fourth property*—are timely parameters of the action: the tempo and the rhythm. These, as you know, are not the same things, because you may have a certain rhythm at a different tempo.

And finally, *the fifth property*—is the power characteristics of an action, the size and the distribution of effort of the subject (e.g. the learner) engaged in the action.

No action, including mental, can exist without some indicators for each of the five main primary properties. These five properties may have different values at different levels of action (material, verbal or mental), however, greater or lesser differentiation, the varying tempo, rhythm and effort—are always present in any action, and mental actions are no exception.

Consequently, since these five properties may have different values, we can call them the parameters of the action.

We should also note that we consider an action to be both an objective and a subjective process. As an objective process, it can perhaps have only the properties of time and power, as a person has to learn to perform an action with a certain tempo, rhythm and with a predetermined speed. Other properties discussed above are the properties of an action of a human subject.

The next question is—how to form the desired properties from these basic parameters, the initial properties we have identified in the action? We will explore this in the next lecture.

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## **Chapter 3 The Conditions for the Development of the Properties of the Action. The Phases of the Development of the Action**

#### **Outline of Lecture 3**

The focus of this lecture is on the measures needed to achieve the desired properties of the action. For example, consciousness of the action is achieved by the learner orienting his or her action to the identification of the important relationships between the features of the target problem. To achieve the consciousness of the action, the teacher must fully deploy the action so that the learner is able to trace what happens within each unit of the action and how the transition from one unit to the next unit occurs. Galperin argues that if a learner can trace this process, then the action acquires the meaning of a generic and not merely a subjective process. The second measure in the formation of consciousness of the action is separating the essential from the inessential aspects of the action, which can be achieved by the systematic variation of the problems offered to the learners. Finally, the third measure concerns the presentation of the action as an external process. The action is new and unknown to the learner, so it cannot be assumed that he or she will know how to perform it. Therefore, the action should be explained and demonstrated as an external objective process.

Galperin describes how other desired properties of the action can be achieved (i.e., the generalisation, rationality, criticality, and the measure of the mastery of the action). Galperin defines generalisation as identifying the key features and separating essential features from inessential. To achieve the generalisation of the action, particular attention is given to the significance of introducing a general scheme to learners, which should be actively used to solve systematically selected problems. By employing this scheme, learners identify the key features of the target concepts and the essential relationships between them. However, the main idea is that the scheme should not be memorised but understood by learners. Generalisation happens in the process of applying this scheme to a wide range of problems. The general representation of a concept cannot be conveyed to a learner; in other words, it cannot be "transferred" from one head to another. By applying a generalised scheme to different learning materials, the generalised meaning that corresponds to the scheme begins to stand out, and the learners start to make sense of the target concept. In the process of applying this scheme to specific problems, learners identify the key features of the concept and the relationships between them. Therefore, the process of generalisation includes two intertwined elements: the general scheme and the systematically selected material.

Three main groups of learning materials can be used to study the target concept: (i) Discipline-specific tasks; (ii) Logical tasks that differ according to their logical characteristics and contain the following: (a) all the features necessary to solve the task, (b) all necessary and some unnecessary features, (c) not all necessary features, and (d) not all necessary and some obtrusive features; (iii) Psychological tasks that differ according to the ratio of visually represented and conceptual features; that is, tasks in which the visual and conceptual features either coincide or differ. Galperin suggests offering learners different tasks based on the principles of contrast and psychological surprise to keep learners in a state of high intellectual alertness. Such principles imply the random presentation of different materials to learners.

The next property of the action—rationality/awareness—is defined as the ability to present a verbal report of the action. To achieve this property, learners complete the action through talking. As an assessment of the conformity of the defined criteria to the objective reality, criticality can be achieved by evaluating the selected criteria in terms of their compliance with reality, which then should be evaluated by these criteria. The degree of the mastery of the action can be achieved by eventually merging the small individual units of the action into bigger units and subsequently into one continuous process. Establishing the rhythm of the action is an important indicator of the mastery of the action: when the rhythm is fully established, then the speed of the action can be increased.

Finally, Galperin turns to the third subsystem: the transformation of the action into mental action. He emphasises that in mastering a new action, it assumes a higher, mental form. The transformation of the action to the mental plane of the learner happens through six consecutive phases or forms of activity:

Galperin describes the formation of the motivational basis of the action (1) as a guiding aspect of the action, which defines the significance of both (i) the action as a process and (ii) its outcome for the learner. Three types of motivation are discussed: (i) external motivation in which a learning process acts as a tool for earning a reputation of being a good learner; (ii) "sporty" or competitive motivation. By achieving desirable results, a learner develops self-confidence and is eager to achieve more and better results. A learner is eager to achieve these results; however, the process of learning does not interest him; (iii) inner motivation as an unselfish and insatiable passion for learning. Galperin argues that such motivation can be developed with learners. How learning emerges in each of the other phases (2–6) is presented in detail in lecture 4.

#### **Lecture 3**

In the previous lecture, we talked about the primary properties of the action, or the parameters of the action. From these primary properties we would now like to turn to the secondary properties, which are of greater interest to us. In this lecture I will describe how the secondary properties are formed from a particular combination of the primary ones.

The first of the secondary properties is *consciousnessof the action*. However, how do we understand consciousness of the action? As I told you earlier (it appears very clearly in experiments with animals), consciousness of the action is characterised by the subject<sup>1</sup> orienting his action to the identification of the important relationships between the features of the problem that needs to be solved. It is important to emphasise that attention is directed to the identification of the necessary relationships between the features present in a specific task, because the features of one problem can include certain crucial relationships; while the features of another problem with the same objectives can have crucial relationships that may differ significantly.

For example, we have a problem. The features of this problem are related in some way to each other, and some of these relationships are crucial for solving this problem. We have to identify these crucial relationships and present them as a basis for the orientation of the actor. We can do so by applying a combination of the following measures. First, we have to deploy the action fully so that all its constituent individual units are completed. We cannot skip a single unit, as a learner will not be able to compensate for this unit himself and this will naturally create a gap in the sequence of the units. If this were to happen the action would not present itself as something performed consciously because the learner would not be able to understand why, after a gap, there follows another unit of the action. So, the *first measure* is to fully deploy the action. The term "a fully deployed action" is relative, because what is the sufficient deployment of an action will vary for different learners. Therefore, we should identify the required degree of deployment of a new action for a particular group of learners. To deploy an action means that the learner should be able to trace what happens within each unit, and how the transition from one unit to the next one occurs. If a learner is able to trace this process, then the action acquires the meaning of an objectively necessary process.

<sup>1</sup>A subject can be also understood as a learner. Subject (noun) is masculine in Russian.

However, that is not all. Any material2 has many aspects that may be irrelevant for a particular action. Therefore, the *second measure* for the formation of the consciousness of the action is the purification of the action from minor and insignificant aspects. In our conventional language, this is called differentiation, separating the essential from the inessential. How this is achieved, I will explain in detail later, but for now I shall mention that this can be done by a systemic variation in the problems offered to learners that can be solved by performing a particular action.

The speed at which a learner is able to trace the sequence of the transformations that happen to the initial material during this action is extremely important. Finally, *the third measure* that is always assumed, but which needs to be made explicit, is that the action in its successive units should be presented as an external objective process, not on the mental plane. We are dealing with a new action unknown to the learner, and we need to present this action as fully deployed as possible. This is absolutely necessary because the units of the action and their corresponding transitions are unknown to the learner. We cannot simply assume that the learner will get an idea of how to perform this action himself; we have to unravel the action and demonstrate it as an external objective process.

Now you see how many measures we have to pursue in order to help form the consciousness of the action with learners. This means that we have to create such an image of an action that would empower a learner to perform the action according to its key features and their objective relationships.

The second property is a *generalised action*. Generalisation can be understood in different ways. In our case, we are referring to generalisation in the sense of identifying the key features and separating the necessary relationships between these features from those that are inessential. As you will remember, this also constitutes the consciousness of the action and is achieved in two ways.

We used to believe that a new action, or more generally a new phenomenon, which is introduced to the learner, has to be demonstrated by a clear and simple example. It turns out, that this is not the best way to go about it, because a concrete example, simple and clear for the teacher may not be so simple and clear for the learner. The significant relationships are connected with the specific content of a particular example. Even if the example is simple (for the teacher), it is nevertheless associated with the specific content. Practice shows (I will tell you more about this later) that no matter how much you emphasise that this is a just an example and that the learners have to identify some general relationships, still this particular example gets unconsciously fixed and is remembered by students. Therefore, later on we have to get rid of the specific content of the example that we used in our explanation.

A better way is not to use a specific example (even if the example is very simple), but instead offer a (general) scheme. This scheme can be applied to all the cases where a particular rule can be used, or in all the cases of the target phenomenon. In this sense, the scheme is general; however in itself it is a specific schematic representation of some relationships. The main idea is that this schematic representation should not be simply memorised but should be understood by learners. I have already

<sup>2</sup>Material in the meaning "learning material".

mentioned that a traditional approach to teaching and learning with its reliance on prior memorising of knowledge for its subsequent application is very unfortunate. A better way is creating a scheme (which can be, for instance, in a form of a table) and then applying this scheme for solving systematically selected problems. Generalisation happens, in fact, in the process of application of such a scheme to a wide range of problems.

The view that emerged from our assumptions, that it is possible to give a (general) representation of a concept at the beginning of learning is, in fact, wrong. This (general) representation cannot be supplied to a learner. It cannot be "transferred" from one head to another, because initially you can show, at best, an abstract scheme without any specific content. Although originally this scheme was something quite specific and concrete, it appears to the learner as a schematic drawing, and nothing else. Only when you apply this scheme to varied material, does the generalised meaning that corresponds with the scheme begin to stand out from the material, and only then do learners start to make sense of this (general) representation. In the process of the application of this scheme to specific problems the learners identify the key features and the essential relationships between them.

Therefore, the process of generalisation comprises two intertwined elements: the first is the (general) scheme, and the second is systematically selected material.

However, how do we select this material? There are three main groups of learning material that are used for studying a specific rule or a concept.

The *first group* is specific for each subject. These are discipline specific types of material. I remember one of the studies: it was about teaching children to find the subject in sentences. It is important that the subject in the Russian language can be expressed with different parts of speech, including a verb in its infinitive form. Of course, these differences create certain difficulties which must be overcome.

So, the first group—are the discipline specific types of material. I would like to emphasise that these are different types, not just variations within one type, because, for example, a big book of problems, with many different tasks, in fact, contains only very few types of tasks. Therefore, there are types of tasks, and there are different tasks that belong to the same type. For example, a numeral can be a subject in a sentence, as in the saying: "Seven do not wait for one." Here "seven"—is a subject. Well, you may also say: "Five do not wait for one" This is a variation: seven—is not five, but this variation is of the same type. You can create many other similar variations. However, we should remember that only a difference in types has its differentiating value. So, *the first group is different types of discipline specific material*.

*The second group are the materials that are different according to their logical characteristics*. Each concept, including the concept of an action is characterised by a set of its essential features.<sup>3</sup> You may have material,<sup>4</sup> which contains only the necessary features or you may have material which contains all those that are necessary and, in addition, some unnecessary features. This is important because you need to identify not only all the present features, but the features that are crucial

<sup>3</sup>In a mathematical problem, the features are the conditions of the problem.

<sup>4</sup>Learning material, e.g. in the form of tasks.

for this action. Another possibility may be when not all the necessary features are to be found in the material. Strictly speaking, this means that the concept cannot be recognised because some of the features are missing; consequently, the target phenomenon fails to address the concept. Finally, the fourth type of material is when not all the necessary features are to be found in the problem and there are many unnecessary, obtrusive features. This means the learners are not supplied with all the necessary features, and they are also given many unnecessary and obtrusive features and they are required to make sense of all this information.

In sum, we have four logical types that contain:

A great variety of specific material should be selected for each of these four logical types.

Finally, *the third group are psychological types of material*. Psychological types differ according to the ratio of visually represented and conceptual features of the material. On the one hand, a task can contain a combination of these two, when visual features and conceptual features coincide (the easiest and the most enjoyable case). For example, there are tasks in which visual and conceptual features differ. You may have a situation where a feature is present in the visual representation, but conceptually it is not there. For example, when we were teaching children the concept of a perpendicular, the learners were given a picture and were told that the marked angle was 90° (Fig. 3.1).

The difference was only in one degree that could not be noticed with a naked eye and it seemed that the angle was right, but in fact, it was not right, but sharp. There was a discrepancy between the visual and conceptual features.

**Fig. 3.1** The learners were informed that the marked angle was 90°

**Fig. 3.2** A figure of a "circle"

We may also have the opposite situation. Let us say we draw a figure and say that it is a circle (Fig. 3.2).

We can see that this is not a circle, but the task says that this is a circle. Correspondingly, in a circle all the radii are equal. Working with the figure learners have to come to an understanding that if they were told, that this was a circle, then all its radii were equal.

In sum, you have to select three types of material that belong to a psychological type:

To sum up, there are three big groups of material that should be selected and offered to learners: (i) Discipline specific; (ii) Logical; and (iii) Psychological.

Each of these groups requires a selection of particular material in a sufficient amount: we need to fill each of these groups with its own specific content.

Since we have such a large number of different groups or types of material, traditionally there arises a problem of organising this material in terms of the order in which these groups or types should be introduced to learners. A common approach in traditional teaching and learning is to go from simple to difficult, but, as we know, traditional education does not provide a learner with reliable tools for solving problems. Traditional teaching relies heavily on the learner's individual guess at what to do and how to approach learning. Well, the result of such an approach is well known. In our approach, we provide a learner with a reliable tool—the scheme of the orienting basis of the action and different groups or types of materials. Since we provide this reliable tool, then the requirement of a gradual movement from simple to complicated becomes redundant because all the tasks can be solved with the help of the complete scheme of the orienting basis of an action. In this case, we are facing different requirements: not to move from simple to complicated, but another psychological approach previously identified by Pavlov should be followed. This is an approach based on the principle of contrast, psychological surprise to keep the learner in a state of high intellectual liveliness and intellectually alert.

To begin with, you offer a learner a problem at a low level of difficulty; you may even offer a simple task, which is suddenly followed by one of the most difficult tasks so that the learner does not relax and start thinking that everything can be solved so easily. Then offer a task, for example, with an incomplete set of features so that the learner cannot think that everything is ready for him and he needs only to perform the action. He needs to evaluate whether all necessary features are there. If not all the features are present in the task, a learner has to say that the problem cannot be solved, because such-and-such features are not found.

Therefore, the main principle of the sequence of problems offered to learners is the random presentation of different types of material and maintaining of a high level of tension in the orienting activity of the learner. Since we do not use prememorising and recognise that learning happens in the course of the action, in the process of solving problems, we need to have a great number of various problems in our repertoire.

Of course, you cannot rely on yourself being able to figure out quickly everything you need during teaching. It is necessary to arrange the order of the material in advance. We do it this way: we simply enumerate the tasks in the order they will be offered to the students. First, we select a large number of tasks. It is much better to have "leftovers" afterwards then to find ourselves in a situation when we do not have enough tasks. We write numbers on these tasks in advance in the order we will offer them to the students, so that there is no need to worry about that later. Then the tasks are presented according to the assigned numbers. The order of the tasks has to be thought through carefully and checked in advance whether it works well.

If we combine two conditions: give the complete orienting scheme of the action and immediately proceed to solving of the selected problems using this scheme, in doing so, we ensure the desired degree of generalisation. This implies that we cannot say, as it usually happens in traditional education, that a student is capable of doing something, but to a very limited extent. This just cannot happen and if this happens, it is our fault because we have not provided something for the learner.

We identify the levels of generalisation to be applied to the rule, and select the problems that would be directed towards the formation of this level of generalisation with learners. In this case, a student cannot help generalising. We force him to complete this action in its fullest, and the learning outcomes do not come as a surprise. These outcomes have been anticipated.

Now the next property is *rationality, awareness*. These are terms that have an infinite number of interpretations. That is why we are not going to deal with all these interpretations, but simply agree on a particular interpretation of this notion, which is a right of any researcher. The only thing is that the researcher has to let us know which interpretation: "I understand this notion in such—and—such way". You can disagree with me and say that perhaps another word should be used, but if I explain, what I mean by rationality, none can contradict me.

We understand rationality/awareness as an ability to present a verbal report of the action. The question now is how to ensure this property. It is very important that at the beginning of the action, a person explains what he is doing and why he is doing it. We will listen to what he is saying, and correct him if he is saying something wrong, even in the case of him performing everything correctly. This actually happens very often and we cannot allow such inconsistency. What is important is that students should not learn the most economic and perfect wording by memorising ready-made phrases and formulations. This should not happen, because a speech stereotype can be formed without any relation to what a learner is actually doing. Speech should be an active reflection of an objective process. In order to teach this active reflection, a learner should use a large variety of his own words and even when speaking with his own words, but rather monotonously, he should be told—"You know, dear, I have already heard you speaking that way. Try to speak, with more engagement, not so monotonously, not so boringly". It is curious to note that this process resembles other more subtle processes in other situations.

Apparently, Stanislavsky when rehearsing a new play, demanded that the actors read the play and, in particular, their parts in advance. At the rehearsal, Stanislavsky would not allow the actors to speak with the words written in the script. The actors had to play their parts using their own words. Only after they had played a certain part using their own words, he gradually transferred them to the words of the author of the play. Otherwise, the fixed words of the play would have turned into a speech stereotype that you can learn to enunciate, without thinking. This would have resulted in the actor mouthing some words but acting something different. It is necessary that speech itself actively reflects the situation. When this has been achieved, only then one can use other words. At this point you come to the specific speech formula and this process should accompany material action.

You see, at first, it is necessary to speak with your own wide vocabulary and when the speech formula has been "played around with", you can move on to the standard definition. In this way, we ensure the rationality of the action.

Now *criticality*. This is a difficult property. I have already told you that criticality is the assessment of the conformity of the defined criteria to the objective reality. Very often, we do not notice that certain features predefine some of the criteria that they are based on, and if we doubt these criteria then these features will be invalid. Recently I discussed a published book with its author, who believes that not everything is ideal in the human mind, that some part of mental activity should not be called ideal. I asked him: "Excuse me, but what are your criteria of ideal? What do you call ideal?" He said that ideal is, in fact, everything that comes from ideas. Well, since animals do not have any ideas, this means that the entire mind of an animal is not ideal. I told him: "Well, in this sense, it is banal, isn't it? We have known for a long time that animals do not have concepts. Does this mean that an animal's mind is something which is not ideal? Ideal should be understood in another sense".

This means that a person takes a criterion that he does not have a name for, that is only implicit, and then on the basis of this criterion he presents a risky statement such as mind is not ideal. I asked him: "Well, what is it then? Material?" To which he replied: "No, not material, but it is of itself". It is neither ideal, nor material, but something of a third nature. The main point, as it turned out, is that he had taken the concept of an idea in a human sense as the criterion of ideal. This is a narrow and simply a wrong criterion.

It is important to notice that very often we do not analyse the criteria we proceed from. They appear to us as something natural. This is always the case when we take the perspective of a criterion; you see things from this perspective. Therefore, understanding criteria is very important as in many cases criteria are adopted intuitively. Above all, the criteria should be evaluated in terms of their compliance with reality, which, in turn, should be evaluated by these criteria. Thus, ensuring criticality is a very difficult and demanding task, but it should be done by selecting the criteria, which are often being used intuitively and unconsciously, recognising that sometimes such an approach to selecting criteria is unjustified.

The next property is*the degree of mastery*. This is a particularly important property and I am going to explain why. After all, we believe (I will talk about it later) that the mastering of the action is not just memorising it in the form in which it is being explained and performed. There is a continuous change in the form of the action itself. You cannot move to the next higher form, until you recognise that the previous one has not been developed sufficiently. However, we cannot linger on these transitional forms for too long either, because every development means mastering the action in this particular form, which is only transitional, not yet the final one.

We conducted a study with children at the end of their first year of school and explored the difference between the underachieving students (those who usually get a grade two5) and those who are usually awarded a three; the difference between the grade three students and the grade four students, etc. We found out that underachieving students differ from achieving pupils not in the way they think. Underachieving students do not think poorly, sometimes they think very well, but they do their thinking in early and highly uneconomical forms.

Imagine that a child has a delay in counting, which means that he can only count objects and things. He uses his fingers for counting, which is extremely convenient, as with Russian counters that have tens, and the child can clearly distinguish fives on both hands. Therefore, fingers can be used for counting and this child is holding his hands somewhere under the desk and is counting with an incredible speed, bending his fingers. We were holding his hand and still were feeling the movement of his fingers, but we could not distinguish anything because he was moving them so fast when counting. His counting was absolutely correct; he did not make a single mistake. However, if we squeezed his hand so hard that it was difficult to move his fingers, he stopped counting with his fingers, and began to count using other methods: he counted spots on the blackboard, on the desk, on the walls, etc. He could perform any calculations, but only with objects. When he was given a task with numbers greater than ten, he would count his fingers several times and give the correct answer, but the teacher said, "He thinks so poorly and slowly". In fact, he thinks quickly, he thinks

<sup>5</sup>On the scale one (poorest)-five (best)—the grading system in the USSR.

with a speed of light, but just counted slowly because he was using his fingers. This is the delay in the earliest and first necessary forms of the action. If he remains in these forms for too long, they become the reason for his delay. The trouble is that this gap is not immediately clear to the teacher. Poor little boy, he is struggling to keep up with the others. How can he possibly do it? Only by automating his way of counting as much as possible. He reaches almost perfect virtuosity in performing these activities, but in doing so, he gets more and more "stuck" in this hopeless way of solving problems.

There is a danger of the opposite: intermediate forms of action should not be completely mastered. They need to be brought to a certain degree of mastery no more and no less. Otherwise you will not be able to transfer to the next forms of action. What indicates the mastery of the intermediate forms of action? Initially, an action appears to the child as a series of separate, independent links which are performed in such a way that the child always first inspects the closest link, which he has to perform. Once this link has been inspected—the child begins to complete it, and then he proceeds to the next link, stops again, performs an orientation to the next part of his work, and then completes it too.

In such a way an action is first being divided into independent links, separated by the periods of orientation. Then these links begin to merge into bigger units: instead of two small links, there appears one unit. Hence, the formation of bigger units happens. The mechanism of how smaller links merge—is a very important aspect of theoretical significance. I will tell you more about it later. In the meantime, it is important for us to understand that the original small links merge into bigger units or steps. This does not happen immediately all the way through, but, naturally, first in the easiest links. Later these bigger units also merge, until the action starts to flow as a continuous process without any pauses at individual units.

This is the first phase of mastering the action. Then the following happens: before this phase, the action cannot be performed either with the required rhythm or at the required speed. When, for the first time, the action begins to flow as a continuous process, then its rhythm can be identified, however it is still slower than the final version of it.

Establishing the rhythm of the action is a very important indicator of the mastery of the action. When the rhythm is fully established, then the speed of the action can be increased.