V.G. Bogin, S.I. Vdovina, L.M. Feldman
BASIC CATEGORIES AND CONCEPTS
OF THE NEW HUMANITARIAN SCHOOL
First published in the journal Innovatsii v obrazovanii, No.6, 2006.
1. The scheme of thinking activity as a means of revealing defective and insufficient knowledge of students
If the teacher wants the child to acquire full-fledged rather than defective knowledge and wants to teach them how to understand and think, they need to know the way thinking and understanding are organized, how these processes work and how they are connected with knowledge.
The scheme of thinking activity is one of the most convenient means for understanding the essence of these processes. Furthermore, in many situations of education this scheme is an effective instrument of teaching children such things as thinking, reflectivity, and understanding. It is also a working means of revealing and correcting defective and insufficient knowledge.
First of all we will try to explain what we view as defective knowledge. As an example we will cite the following situation. A 5th grade student reads a fragment from Lev Tolstoy’s “A Captive of the Caucasus”: «…Âûøåë òàòàðèí â÷åðàøíèé ñ êðàñíîé áîðîäîé, â áåøìåòå øåëêîâîì, íà ðåìíå êèíæàë ñåðåáðÿíûé, â áàøìàêàõ íà áîñó íîãó. Íà ãîëîâå øàïêà âûñîêàÿ, áàðàíüÿ…» (“… Out went yesterday’s Tatar with a red beard, in a silk beshmet, with a silver dagger on the belt and in boots on bare feet. On his head he was wearing a high sheepskin shapka…” The word “beshmet” is supplied with the footnote: “Beshmet is an ethnic item of clothing of some nations in the Caucasus”. The authors of the textbook believe that after reading this footnote the child will know what a beshmet is. They are right to some extent: when asked about the denotation of this word a diligent child will say: “A beshmet is an ethnic item of clothing of some nations in the Caucasus”. In this way he will allegedly display the possession of the knowledge of what a beshmet is. However, this piece of knowledge will be a defective one, since a child who has acquired this “knowledge” cannot use it: they will not be able to tell a beshmet from any other item of clothing of Caucasus nations or any other ethnic clothes. Moreover, the footnotes supplying children with this sort of knowledge, along with not giving children actual knowledge and not teaching children to understand texts, also teach them out of it replacing the intention to understand by the intention to receive the ready-made “knowledge”. The point is that the context of Tolstoy’s story says that a beshmet can be nothing but an item of clothing: it can be neither a hat nor a piece of footwear nor an article of furniture, and it takes a child only to look attentively at the context to understand it. However, the presence of the footnote spares the child the necessity to do it, whereas contextual understanding is one of the most important components of understanding proper.
Unfortunately, authors of most of textbooks and teaching manuals replace the process of understanding by the process of memorizing something that has not been understood. Children tend to do this task successfully. And these “brilliant” results are disastrous for their further development, although this fact is not usually viewed as a disaster either by the teachers or by the learners. Schoolbooks are full of such examples of defective knowledge.
The better the student is, the more of such defective knowledge he acquires, thus having increasingly more chances to lose the ability to understand anything at all. Intruding of defective knowledge on children teaches them to memorize and reproduce texts without thinking and understanding them.
A lot of people bear this burden of defective knowledge throughout their lives without even suspecting it. For instance, everyone knows that “the sun rises in the East and sets in the West”. However, this knowledge is not much use somewhere off St. Petersburg around the white nights, when the sun rises and sets nearly in the same point. What if somebody wished to use this knowledge for orientation in a forest? Alas, in the woods of other regions of our land of many sufferings this knowledge will do no good either. Defective knowledge is different from the actual knowledge by impossibility of applying it in real life, however hard teaching methods experts might call to children to apply their knowledge.
Another example of the outcomes of defective knowledge is taken from real school life. A school graduate at an examination solves a task in physics, in which she needs to find the mass of an electron and her answer is two kilograms. However, this result does not embarrass her, she hands in the paper and composedly leaves the classroom. It is noteworthy that the girl was a good student, she was not mentally retarded, and when asked to give the definition of an electron she would say that it is “an elementary particle included in the atom”.
So what is the specificity of the defective knowledge and how does the schema of thinking activity help fight it?
First of all, the schema of thinking activity makes it possible to differentiate between the actual and defective knowledge.
First of all let us look at how the schema of thinking activity is laid out.
This schema divides all kinds of a person’s intellectual activity into three types: pure thinking (T), thought communication (T-C), and thinking action (tA). According to this schema, all activities of a person are divided into three principally different types, three sectors, which are termed as “fields” (in English translations of Georgy P. Shchedrovitsky’s works; the Russian term is “ïîÿñ” (“belt”) – translator’s note).
The lower field on the schema features practical senses-based activities of a person. For instance, the person sees something, feels something, touches something, makes something, etc.
The second field (in the middle of the schema) is expressed and reinforced primarily in verbal texts, e.g. when the person produces and perceives texts in their mother tongue or a foreign language, or uses some other form of communication, such as arithmetical, algebraic, chemical, etc. For instance, a person says about something aforementioned: “I see a kettle on the table.”
Thus, the kettle has two hypostases on the schema of thinking activity: as a certain object and as the word “kettle”. This division may sound banal, but a 5-6 year-old child (as well as a primordial human) cannot differentiate between the real kettle and the word ”kettle”. If you ask a five-year-old if it is possible to call the kettle a crocodile and then boil water in it, he will answer in the negative without a second thought.
The third, upper field features abstract things: models, schemata, tables, etc. Our kettle may be reflected in the upper field as an element of some structure, e.g. as a product in the manufacturing – consumption structure, or as a household facility in the structure of household.
Thus, the same thing may exist simultaneously in all the three fields of the schema of thinking activity. And it is noteworthy that this “same thing” exists as something different in each of the fields: as an object, as a word (a sign), and as an abstract notion.
A person uses all the three fields but in different ways.
If he “sees” objects, events, actions as “pictures” or “films” and/or operates in his consciousness with these “pictures”, then he is “operating” in the “lower field”. These “films” are mute and have no subtitles: they are filled with sounds, sensations, feelings, but they have no words, either oral or written.
If a person “sees” structures and models and operates them, he is in the upper field.
The medium field is the realm of communication, i.e. thought communication. When the person is in the medium field, he can express what he has in his upper and lower fields by means of signs, which exist in this field, and then convey all this as a piece of information to other people. What a person has in the upper and lower fields only exists for the person himself and no one knows about it. And the language (as well as all the other sorts of sign systems) always belongs to communities. Therefore, the medium field is a sort of “forum” for people’s communication.
models and structures
models and structures
The common language (sign) field for a group of people: the mother tongue, foreign languages and texts in these languages, and other sign systems describe what is stored in the zones that are closed for others (the upper field and the lower field).
If something exists for a person only in one field, this thing will be defective for them. If this thing exists in two fields, it will not be full-fledged either. This something becomes valid only if it comes to exist for the person in the three fields simultaneously.
Thus, in theory, there should be three “basic” types of “pure” defective thinking activity (which equals the number of the fields) and several types of insufficient thinking activity.
Let us start with “pure” defectiveness.
In real life we are most likely to come across defective thinking activity in the medium field and we can seldom face defective actions in the lower field. We cannot come across defective pure thinking. Even if it does exist, it is not reflected in the medium field (is not worded up) and has no counterparts in the field of real objects, and thus even those who have it cannot trace it.
The purely defective actions (the lower field) are not frequent but still can be traced. For example, a girl asks her mum to teach her how to knit, and the mother gladly agrees but then finds out that she cannot describe the actions with words, since it is “her fingers” that “remember” this action rather than she herself. As a result, the mother says: “I’ll knit and you sit and watch me doing it.” This is how medieval artisans taught their apprentices. Probably that is why the term of apprenticehood was so long: methods and principles of the actions were not summarized and structured (the upper field), nor were they expressed in signs (the medium field). Thus, the activity was concentrated only in the lower field.
The most frequent type of defective thinking activity is concentrated in the medium field. This concerns both teaching practice and the reality forming this practice. Let us cite a few examples.
A classical example is like that of the old joke about a child who solved a task in maths and got “two diggers and two thirds” as the solution. He got this solution as a result of nonsensical operations with figures in the medium field as the lower field was not employed – he did not “see” any diggers.
Actually, mathematics is rather indifferent to features of the real world: 16+14 always equals 30, regardless of whether we have been counting windows or birches behind them. 30 windows and 30 birches are the same things for mathematics as a rule. Therefore, if you do not take any “preventive measures”, mathematics will encourage the child to operate in the medium field only. It is also worth mentioning that the school program abounds in tasks like “do the sums” or “simplify the combination”. Such tasks lead to the fact that a child stops relating numbers to real objects, i.e. operating in the medium field only without referring to his lower field. As a result, a child can fail to solve even very easy tasks, like the following: “There was a bobbin of wire, first 15 meters were cut off from it, and then 13 meters were cut off. How long was the piece of wire cut off from the bobbin?” Most children tend to subtract 13 from 15, since the act of cutting off is associated with the process of subtraction for them. Referring to the thinking activity schema, we can see that the child operates in the medium field only and so his activity is defective. To solve this task the child should first “double” the actions described in the lower field, i.e. visualize the conditions of the task as a “film” and then match the question of the task with the right “snapshots”.
Let us touch on another example of defective knowledge. At the lesson of mathematics the teacher writes the following on the board:
(õ1 + õ2) 2 = 72
Then, using the usual formula of reduced multiplication, the teacher writes down the following:
õ12 +2 õ1õ2 + õ22= 49
The student looks at the board and does not understand how the left part of the first equation developed into the left part of the second one. The teacher supposes that the student does not know the formula of reduced multiplication and writes on the board: (à + b) 2 =, and asks the student to continue. The students immediately says: “A squared plus two AB plus B squared”. “And so?” says the teacher believing that the student has come to understand everything after that. But the child goes on staring at the blackboard being at a loss about why the teacher put this question to him and how his answer to this question could possibly help him overcome the difficulty connected with solving this equation.
Now we will describe this episode referring to the thinking activity schema. The child has memorized the following text (the medium field): “A plus B squared equals A squared plus two AB plus B squared” and now uses it as magic words helping him get the teacher’s favor, like a poem in a foreign language with a vague meaning that can be easily reproduced by the child both orally and in the written form. The letters A and B do not exist for the aforementioned child as separate signs standing for any numbers. This expression exists for this child as some integrity, for no one will change anything in an incantation or a poem.
As for X, the child perceives it as a sign referring to an unknown number that should be found by means of arithmetic operations.
Therefore, there is nothing strange about the fact that the child does not see anything in common between the formula and the expression written on the blackboard.
Another situation that we are going to discuss is an anecdote from a lesson of the Russian language. The teacher asked a seventh-grade student what conjugation is. Having made sure that she knew the definition, the teacher asked her to conjugate the word “ìåøîê” (a sack). The girl immediately produced the text: “ß ìåøîê, òû ìåøîê, îí ìåøîê…” (I a sack, you a sack, he a sack…). Mind you, the child is quite adequate; moreover, if you try to repeat this experiment with another seventh-grade student, you are likely to get the same results. Why does it happen? Because the child has two texts etched on his brain (in the middle field): 1) “Conjugation is changing of words by the person and the number” and 2) “I + word, you + word, he + word.” Since the teacher usually (or always) gives the child verbs as examples to conjugate, the student’s subsequent actions usually sound sensible. However, these two texts are not connected with one another in any way, since the first one is just their reaction to the question “What is conjugation?” and the second one is the reaction to the command to conjugate something. The child’s thinking does not go beyond the medium field: both of these texts exist in this field for the child and their existences are independent of each other. To make the child refrain from conjugating the noun it is necessary to get him to move from the middle field to the upper field. For this purpose the teacher should ask the child a few questions like these:
1. What is conjugation?
2. What are the significant details of this definition? (The child is supposed to point to the words “changing”, “person”, and “number”).
3. Can we change the word “ìåøîê” (a sack) by the person and the number?
4. Referring to the aforementioned, is it possible to conjugate the word “ìåøîê”?
This series of questions that are seldom asked in everyday life is the description of the actions that the child should perform having received the task to conjugate the word “ìåøîê”. All this procedure should not be unfolded as a complete verbal discourse in the middle field: there just should be a movement from “thinking” by means of words concentrated in the middle field to thinking by means of structures and schemas (the upper field). Moreover, the child will not be able to independently build this verbal chain unless they have the necessary structure in the upper level. They will have to memorize a huge number of algorithms without understanding when and where these algorithms should be applied.
Unfortunately, teachers do not always have sufficient capabilities to differentiate between defective knowledge from the full-fledged one. Therefore, the students quite often get away with reproducing defective knowledge in their answers. There are lots of examples illustrating this statement, and one of them is cited below.
In a history lesson a student answers the question about the difference between personal bondage and predial bondage saying: “Personal bondage is when someone has personal bonds, and predial bondage is when someone does not have personal bonds.” The teacher may well be satisfied with such an answer, although it is not clear what example from the lower field they have employed to illustrate the words “personal bondage” and if they have such an example at all (to all appearances, the child just learned a phrase from the textbook thus enclosing his thinking within the medium level.
Generally speaking, the teacher who asks their students questions that can be directly answered by phrases from the textbook can never be sure if their students’ knowledge is not defective. For instance, when a sixth-grade pupil is asked what a medieval parliament is and correctly answers that it is “the estate representation government body” (i.e. quotes the textbook), the teacher should draw a conclusion that the pupil is hardly likely to understand what a medieval parliament is, since in his upper level there are not enough elements of structures of the notions used for this definition. Moreover, for the child some words from this definition may be connected with absolutely different notions from his lower level, e.g. the word “estate” may be connected with an old-fashioned mansion in the countryside and “body” with the human body.
Sadly, we have to state that texts of many schoolbooks are organized in the way that makes it impossible for children to connect what is written there with their personal experience. Although many of them are rich in “examples from everyday life”, these examples do not usually encourage the child to link the text with their personal experience and sometimes even wean the child away from this habit.
For example, a textbook in physics (by Myakishev and Bukhovtsev, Ìoscow: Prosveshcheniye, 2000) says:
"However, the correct outer shape of a crystal is not the only and not the main consequence of the ordered structure of the crystal. The main point is the dependence of physical properties on the direction chosen inside the crystal. The most conspicuous is the difference in mechanical strength of crystals in different directions. For example, a piece of mica easily flakes in one direction into thin fragments, but it is much harder to tear it in the direction perpendicular to the direction of the flakes. A crystal of graphite also easily flakes in one direction. When you write in pencil, the process of flaking leaves traces on paper. This happens because graphite has a flaking lattice.” Then comes the description of the model of the lattice of graphite explaining this property:
“The layers are formed by a row of parallel flat nets consisting of atoms of carbon. The atoms are placed on the apexes of regular hexagons. The distance between the layers is relatively long: approximately twice as long as the length of a leg of the hexagon. Therefore, the links between them are less strong than the links inside them.”
Having read that graphite, like mica, “flakes in one direction,” an inquisitive pupil will take out the lead from a pencil and find out in surprise that this piece of graphite leaves a trace on paper in any direction. Thus, the personal experience in the lower field contradicts the text of the schoolbook.
After a few such attempts to connect the medium field of texts of schoolbooks with the lower field of personal experience, a diligent child will get convinced in the futility of this activity and stop doing it, since of the two choices, to disbelieve the textbook or to learn it by heart, the latter is the easiest.
Another example can be taken from the textbook in the Russian language. The standard definitions of parts of speech used practically in every schoolbook in Russian sound like this: “A noun is a part of speech answering the questions “Who?” and “What?” and referring to a thing (item)”; “an adjective is a part of speech answering the questions “What kind of?” or “Whose?” and referring to a feature of a thing;” “a verb is a part of speech answering the question “What to do?” and referring to an action.”
The categories “a thing (item)”, “an action”, and “a feature” are notions from the upper level. A child’s recepts of whiteness of snow and short-distance race (the lower field) are in no way related in his consciousness to the category of “a thing”. In all likelihood, whiteness is viewed as a feature, while a short-distance race is certainly an action. Thus, the text of the schoolbook contradicts the child’s experience.
This can be presented on the thinking activity schema in the following way.
Thus, the child connecting the medium field information from the textbook with his personal lower field experience will get into a hard position. If he follows the instructions of the textbook conscientiously, i.e. defines the parts of speech by these two criteria, neither race nor swimming, nor whiteness or redness will fit into the category of nouns; as a result, the range of nouns in the child’s consciousness will considerably shrink.
It will shrink even more if a fifth-grade student who likes to connect thinking activity fields (i.e. to construct full-fledged knowledge) relates the aforementioned definition of a noun with the definition of artisanship from a textbook in history: “production of various ITEMS”. The child will either have to imagine an artisan producing a forest, a river, an elephant and other such “items” (which is hardly likely unless the child is a client of a psychiatrist), or he will have to exclude all natural objects from the list of nouns.
However, the sources that are quite authoritative for the child, i.e. teachers, parents and authors of textbooks assert that all the above words are nouns. Therefore, the child confines himself within the defective knowledge based on the principle: “This cannot be understood, this should be remembered”. This knowledge is also connected with the defective knowledge model “a word” = “a word” (“swimming” is a noun, “redness” is a noun).
This way of presenting the material in schoolbooks does not only break the connection with the lower field but also does not encourage the child to get into the upper level to models, for a model can explain things only when it is linked with the real world. What is described in the text of schoolbooks DOES NOT TAKE PLACE in the real world. Why try to understand a model if it does not explain anything in the real world? That is, if the model explaining the structure of graphite does not explain the way the lead in the pencil works, what is the point of understanding this model? If a definition from a grammar book does not help us identify parts of speech, why should we understand this definition?
About insufficient thinking activity:
Along with the purely defective thinking activity there is also insufficient thinking activity.
In this case the human employs two fields of thinking activity. Now we will consider the most widespread types.
Type 1: The person’s thinking is confined within the lower type, but they are trying to explain the meaning of their actions with words. In this case, only the middle field is used, but not the upper field.
For example, a certain worker is performing some practical activity, and his thinking is concentrated in the lower field. However, this worker can describe what he is doing only in the medium field without involvement of the upper one. Thus, when asked the question “What are you doing?” this worker will say: “Can’t you see? Hammering nails!” This worker does not understand and cannot explain what system envelopes his activity as an element; similarly, he cannot explain the structure of activity his product will be included in. In other words, he does not understand and cannot explain where, how and why he is hammering the nails and what function they will perform afterwards. The result of such an activity may be like the one described by the Russian satirist Mikhail Zhvanetsky: ”The buttons on a suit are attached really strongly but to wrong places: the placement of the buttons has nothing to do with the location of the buttonholes. And the sleeve hinders the hand to perform one of its main functions: it cannot bend.”
The sufficient answer in this case would be the following: “I’m attaching floorboards to battens, for if I don’t do it, they will sag too much when you start to walk on them.” This text reflects a model from the upper field whose structure contains the following elements: the vibration amplitude, the concept of the lever with all of its components, and the function of the floor. The worker who “sees” his activity and its results in all the three fields can modify some components of his activity in changing circumstances, e.g. in case of non-standard floor-battens or nails, so that eventually the change of circumstances does not lead to a ruin of the whole job.
As an example of operating within the middle and lower fields without referring to the upper one we can cite an actual case. When the decision to manufacture KamAZ heavy-duty trucks was made in the USSR, no one thought of changing standards for roads in the country. This led to the ruin of roads throughout the country and “unforeseen” expenditures on their reparation.
Now we will describe an example of insufficient thinking activity from school practice. A student has mastered the algorithm of long division (he was trained at school so that he will never forget how to do it until his deathbed) and is given the task to orally divide 52 by 4. The knowledge of the long division is concentrated in the lower field, and further he acts within this field: he rolls up his eyes and visualizes this process as if he were performing it on paper and putting down intermediate results: “5 divided by 4 equals 1”, etc. Curiously enough, younger children sometimes even move their fingers along the lines as if they were writing down intermediate results.
Thus, the child acts simultaneously in two fields: he reproduces the familiar sequence of actions in the lower field and comments on his actions in the medium field. However, the upper field is not used for this activity: he does not understand the STRUCTURE of the object.
Strictly speaking, the above actions have nothing to do with mathematics, since the child does not operate with the numbers 52 and 4 but works with the FIGURES, and these figures do not have the function of signs of numbers but just serve as signs indicating the algorithm to be performed. It does not matter what numbers he is dealing with, since the algorithm of long division does not depend on any particular numbers.
But if the person acts in three fields of thinking activity, he will find it significant what kind of NUMBERS he deals with: if he divides 52 by 4 he will most likely view 52 as the sum of 40 and 12 and divide both these components by 4. If he deals with the numbers 164 and 4, he will view 164 as the sum of 160 and 4 or 100, 40 and 24, i.e. he “sees” the structure of the number by means of employing the upper field.
It is noteworthy that most children who have been thoroughly taught the defective mathematics and easily multiply and divide big numbers tend to be stupefied when asked what the APPROXIMATE product of 47 and 32 is. This child will easily give the exact result (but only after the magic procedure of long multiplication), but giving an APPROXIMATE result is beyond him. This happens because this child, as we have already mentioned, DOES NOT SEE a number behind these figures, i.e. the PLACE of this VALUE in the system of numbers, its DECIMAL STRUCTURE, the variety of splitting the same number into elements, the MEANING OF MULTIPLICATION, etc., since these concepts are all in the upper field, into which a child accustomed to insufficient thinking activity does not “peep”.
The second type of insufficient thinking activity formally resembles the previous one, but is absolutely different in its essence. The person is confined within the medium field and is trying to describe something involving the lower field without referring to the upper one. For example, many people in their speech easily use the words denoting items from the upper field (evaluation, knowledge, thought, idea, happiness, beauty, etc.). However, most of them, when asked to explain the meanings of such words as “evaluation” or “knowledge” or “beauty”, try to describe something involving only the lower field. For example, “evaluation is when a teacher gives you a grade,” “happiness is when you are understood,” “knowledge is when you can answer any question”, etc.
This sort of thinking is formally backed by the definitions of a special structure: “Knowledge (meaning, understanding, beauty, etc. is WHEN…” The person who defines the concepts above in this way displays the following: he “takes” some notion and “looks” down into the lower field trying to find the situations in which this word has been pronounced. Then he reproduces descriptions of these situations and presents them as definitions. In order to construct a full-fledged definition it is necessary to take a model from the upper level (or use an existent model), describe its essential features (the medium field), and then cite examples of functioning of the model (but not the word) in concrete real situations (the lower field). Let us interpret this by means of the thinking activity schema.
Suppose a person operating with the full-fledged thinking activity wants to define the concept “evaluation”.
1) First, he will recollect the whole variety of situations of evaluation (in the lower field): grading tests, assessing people’s appearances, clothes and manners, the quality of goods, the speed of a car, the distance between some objects, etc.
2) Next, he will distinguish the COMMON that is present in all these situations, i.e. a) the presence of some control gauge (etalon), b) an object of evaluation, c) the assessor, d) the procedure of comparing the object with the etalon, and e) the decision on how much the object differs from the etalon.
3) Then he constructs a model displaying the essence of evaluation (in the upper field).
4) Finally, he will verbally describe this model, e.g. EVALUATION IS THE ACTION IMPLYING THE OPERATION OF COMPARING THE OBJECT OF EVALUATION WITH THE ETALON (SUITABLE FOR THIS OBJECT) RESULTING IN A CONCLUSION ABOUT THE QUALITATIVE OR QUANTITATIVE RELATION BETWEEN THE OBJECT AND THE ETALON.
If necessary (for instance, while explaining it to people) he can illustrate this description of the model by examples from the lower field.
In the real school practice things tend to be pretty hard regarding involvement of the upper field in the child’s learning activities. At best, the student memorizes the verbal description of the model (in the medium field) and some particular examples (the lower field) without “seeing” and even trying to reconstruct in his consciousness this model in the upper field in the form of a schema.
This student can reproduce a definition from the textbook and give examples from the textbook or analogous ones illustrating this definition. For instance, if the definition of a noun is illustrated by the word “cat” the child will add “a dog” as his own example but will hardly add “friendship”, “length” or “darkness”. And he will be absolutely dumbfounded if you ask him if the word “on the roads” is a noun. In other words, the child cannot tell if some other real object (which is not mentioned in the textbook) suits the definition because in his upper field he does not have a model that is described by this definition, and the words forming even an absolutely correct definition tend to be polysemic, sometimes even metaphorical or causing multiple associations. For example, the word “side” is automatically associated with “one side out of four”.
Let us take one more example: a pupil of the third or fourth grade knows the definition of perimeter. At school he has only dealt with perimeters of rectangles. Facing any other figure (a triangle, a five-point star, etc.) this child will try to find out its length and breadth, add them to one another, and then multiply by two. Or, in some cases, will refuse to do this task saying that this figure does not have a perimeter.
The third type of insufficient thinking activity involves only the upper field and medium field without involving the lower one. For example, the text “slithy means looking like slithe” may well serve as an example of this kind of insufficient thinking activity. This type of “explanation” is especially popular with academicians and professors: that is why students have so much trouble understanding them.
For example, a pupil asks: “What’s a scaffold?” The teacher answers: “It’s a place for execution.” The teacher thus uses two fields: the medium and the upper ones, since he gives the definition of the word only in terms of pure thinking. Indeed, a scaffold is a specially constructed place for making public somebody’s violent deprivation of their life for the sake of intimidation of others. Having said this, the teacher will think that he has explained everything.
However, as a result of this explanation, you may well visualize Aesop climbing a rock or an American gangster sitting down on an electric chair, since the teacher did not refer to any image from the lower field in his explanation.
The child memorizes the text of the teacher’s explanation visualizing in the lower field what is closer to him. As a result, reading about a medieval knight who “mounted the scaffold” on the central square of the city (and remembering there was no electricity at that time and there are usually no rocks in a city center) the child finds himself in the situation of complete incomprehension and eventually ceases to visualize anything at all since it is impossible to fancy anything at all. This considerably harms learning, since a child remembers only those places in the text that have links with the lower field, while other parts of the text are not even noticed. Numerous surveys and experiments show that if the child is asked to read one page of a text and retell everything that he remembers, he will retell only those parts of the text that have “touched” his lower field. The child simply disregards other fragments and when asked if he has retold everything he will confidently answer in the affirmative. If he is shown the fragments of the text he has missed, he will look at them in surprise as if this were the first time he had ever seen them. If the child retells only those parts of a paragraph that he has understood at the lesson, he will get a fair or a poor grade, and so he is just forced to learn by heart the parts of the text he has failed to visualize. As a result, he gets a good or excellent grade at the lesson and draws the conclusion that in order to be successful it is necessary to “switch off” the lower field and briskly retell the texts in which he does not even try to understand anything (i.e. does not try at least to visualize what he has read about). Thus, the child refrains even from insufficient thinking activity and plunges down to the defective one.
The thinking activity schema does not only help reveal and classify the types of mistakes a child makes in the educational process, but also serves as an effective tool for correcting and preventing such mistakes. This issue will be more thoroughly considered in our next article.
 * The scheme of thinking activity was proposed by Georgy Petrovich Shchedrovitsky (1929-1995), the founder of the systemic thinking activity methodology, the leader of the Moscow Methodological Club, the initiator of organizational activity games that have become widespread both inside Russia and abroad.
 For those who care about what sort of knowledge about the sunset and sunrise should be viewed as full-fledged we can note that the sun rises in the East and sets in the West only twice a year: on the days of the equinoxes. On all other days the sunrise and sunset are shifted in our hemisphere towards the North in spring and towards the South in autumn. On the Polar Circle, on December 23 and June 22, the sun rises and sets right in the North in summer and right in the South in winter. It is also noteworthy that the words “rises” and “sets” are not quite suitable here: it only slightly moves down on June 22 and slightly moves up above the horizon on December 23.
 It is noteworthy that although mathematics has special love of the upper field (actually, mathematics is a science of describing structures and processes of the upper field by the mathematical language), the standard system of school tasks leads to a breech of the link between the medium and the upper fields, since a short explanation is usually followed by a long period of practicing algorithms whose meaning is gradually lost.
As for the teachers, they have the “object-number-letter” schema standing behind all mathematical algorithms, and therefore it seems to them that the child has this schema as well (“I have explained all this, haven’t I?”). But as for the child, it is much easier for him to memorize an algorithm than to understand its meaning, and so children tend to suffice with the simplest and most convenient way out: thoughtless reproduction. Besides, most methods of control of the knowledge acquired by the child are based on demonstration of the algorithms the child has mastered rather than explanation of why these algorithms are needed, what they are for, what meanings stand behind them, why we have to use this particular algorithm rather than other ones, and so on.
 The list of things that can embarrass a thinking child can be continued. For instance, the Russian words “Òàíèí (ñàðàôàí)“ (Tanya’s sarafan) and “Ïåòèí (áîòèíîê)” (Petya’s boot) are viewed as adjectives, but they do not refer to a feature; besides, they are spelt with a capital letter like proper nouns. As for the word “áåçäåëüíè÷àòü” (to idle), it will not be viewed as a verb because it does not refer to any action for a child.
 We do not include in this category the definitions like “knowledge is when you know something” or “beauty is something beautiful”, since they demonstrate defective rather than insufficient knowledge, since in such utterances both the definition and the word that is defined are verbal structures of the medium field.