'Trojan Horse" Teaching

Poddiakov, A.N. Lomonosov Moscow State University, Moscow, Russia

1. Introduction

“The ability to learn faster than your competitors may be only sustainable competitive advantage.” Arie de Geus

This statement, logically and emotionally linked with Bacon’s “Knowledge is power” becomes more and more popular. Yet understanding that knowledge is power in general and a base of economics nowadays can result in hiding knowledge and, occasionally, in disorientation, if the competition is strong. Similarly, the awareness of the crucial importance of teaching/learning may cause advanced strategic behavior. This behavior includes the counteraction to the competitors’ learning and the so-called “Trojan horse” teaching, in which a “teacher”, ostensibly helping his or her rival to learn something, really teaches useless or disadvantageous things (Poddiakov, 2001). This type of behavior may be an object of interdisciplinary research. It relates to theories of conflict, human capital, agency, knowledge management, strategic behavior and Machiavellianism, and to social and educational psychology. Let us consider some of the approaches.

On the one hand, G.S. Becker’s theory analyzes how human capital is increased by education and training (Becker, 1964). Aim-directed teaching is of great importance for education and training. The teaching is conducted under the leadership of educators, instructors, and other persons, who give learners recommendations, advice, methods, techniques of work, etc. On the other hand, in the theory of agency it has been shown that if an advisor (an agent) and a client have incongruent, conflicting goals, the agent can display self-serving behavior (an “agency problem”). “Physicians, nurses, clinical psychologists, teachers, lawyers, CPAs, financial advisors and other service-oriented professionals are supposed to use their specialized knowledge and skills solely in the best interests of the patients, students or clients who have placed themselves (and some of their resources) in professional hands in exchange for the professionals’ promises to act on their behalf” (Johnson, n.d.). Yet an advisor can deliberately to stimulate a client to make a decision, which is not good for the client, but good for the advisor (Bonaccio, and Dalal, 2006; Eisenhardt, 1989; Jonas, and Frey, 2003).

This moral hazard concerns informal situations as well. For example, J. Valsiner (Valsiner, 2000, p. 288) analyzes advice-givers’ behavior aimed to their own profit in intra-gender group competition. The concept of moral hazard in strategic advice-giving resonates with V.A. Lefebvre’s theory of conflict. “The opponent’s doctrine is imposed on the opponent by teaching him” (Lefebvre, 1977, p. 118). To win over a rival, it often suffices, and may even be preferable, to shape a certain image of a bridge-head in the rival. It works not only in armed conflicts, but also in economics, high technologies, sports, etc.

We have not found publications on the applicability of the concept of moral hazard (or of the approach to doctrines imposed on competitors) to the situations in which teachers consciously disorient their learners. Paradigms of teaching / learning, like “enlightening” activity generally, seem incompatible with considering the participants of this activity as possible rivals that can use the strategy of Trojan horse teaching. This gap should be bridged.

We suggest the following statements. Development of individuals, social groups and societies is under the influence of two opposite and interrelated types of social interactions: (a) support of, and (b) the counteraction and inhibition of learning, instruction, education and development, caused by different reasons, including economic ones. Learning and development, related to counteraction, are not isolated and exceptional but a fundamental psychological and educational phenomenon. A blow to the abilities to learn and acquire competence in new activities and domains is the most effective means if one wants to make a competitor inadequate in the technological and social world (Poddiakov, 2001). Trojan horse teaching is regular work aimed to decrease competitors’ human capital.

2. Reasons for the counteraction to other persons’ learning

Significant reasons for premeditated counteraction to learning, instruction and development are dishonest competition and rivalry between individuals, social groups, societies, etc.

On the whole, all the reasons for Trojan horse teaching can be divided into two types:

1. obtaining profit, satisfaction, etc., from the imperfect performance of the persons taught;
2. avoiding disadvantages, troubles, etc., which might be caused by too perfect performance of the persons.

The types can work in combination as well. As a result, there may be a variety of particular reasons for conducting Trojan horse teaching in various formal and informal situations. Some private instructors artificially drag out the process of instruction so as to be paid for a larger number of sessions. In financial pyramid schemes instructors train “recruits” to recruit and teach other “recruits” of the next generation – until the pyramid collapses. A person can conduct Trojan horse teaching to protect third-party interests, e.g., protégés, relatives, etc. Finally, a person can conduct Trojan horse teaching just for fun.

Below we will consider one type of economic reason for Trojan horse teaching related to competitive relations, first, between the teachers and, second, between the learners who are working or are going to work in the same area and are able to achieve approximately equal (or, at least comparable) competence. In these situations, moral hazard can be related to attempts at decreasing the rate of human capital growth of other people, and Trojan horse teaching is a means to achieve this aim. The most efficient Trojan horse teaching makes the retraining, which a learner needs to achieve the required level of competence, more energy-consuming than would be necessary without the disorientation. In such a case, one can say that Trojan horse teaching decreases, in its intellectual and psychological dimensions, the human capital of the person taught.

3. Examples of Trojan horse teaching and the counteraction to other people’s learning

Cases of hidden counteraction to other people’s learning and of the use of Trojan horse teaching can be found in various age, social and professional groups, and in various domains – from children’s plays to teaching military activities and high-competitive business. Some examples are described below.

Myths, tales, proverbs. Many situations of counteraction to other people’s learning are presented in the cultural form of preserving, narrating and transferring social experience as myths, fairy tales, proverbs, etc. They describe aims, means and results of counteraction to learning and the use of such situations to do damage to one’s learning. A classical example is the myth about Prometheus. Zeus prevented men from learning how to use fire. He cruelly punished Prometheus, who gave fire to men and taught them how to use it. Many tales contain situations in which a master, a magician, or a god prevents his underling from learning the secrets of his trade. Often, the characters teach each other to do things, which are dangerous or disadvantageous to them, for example in the tale in which Brer Rabbit teaches Brer Fox how a deceased person should appear. In Brer Rabbit’s words, the deceased must shout: “Ogo-go!” (according to the Russian translation of Harris’ tales). More examples can be found in literature and films.

The Russian language has many proverbs, not only about the necessity of learning (e.g., “Learning is light, and ignorance is darkness”), but also about the necessity of counteracting education and about potential danger of cognition, learning and teaching in some situations (e.g., “to teach on one’s misfortune”, “to teach something bad”, etc.).

Now let us address some real situations.

Relations between children. A kindergarten teacher shared with me what she observed when the children in her kindergarten played a board game. Elder preschoolers, who are part of a mixed age group in the kindergarten, teach younger preschoolers losing strategies of the game in which they want to win themselves. The teaching is accompanied by the elder children’s hidden smiles and an exchange of glances. It confirms that they understand what they do. The next year, the “ex-victims of the instruction”, who are now in the elder group, teach the same Trojan teaching strategy to the novices, and this situation is repeated.

Relations between young adult students. V.S. Ageev (1983) conducted the following provocative experiment. Being a university teacher, he organized competitive relations between two groups of his students. He declared that all students belonging to the group that shows the best results during a certain marking period would get good marks for his course without the final examination. By contrast, all students of the other group would have to take the examination. It was shown that the situation of competition caused the students to act against the winning group. The students tried to inhibit successful performances of the competitors and they gave to the teacher negative recommendations concerning the competitors.

Relations between specialists. A staff psychologist, who works in a commercial bank, may try to conceal the secrets of his job from a new psychologist who has been assigned to him for training during his probationary period, and may even disorient him in some situations of the job. During the skills upgrade training for specialists in the area of oil processing, a lecturer may purposely not give the audience the most effective methods of calculation he knows.

Interpersonal relations in everyday life. A friend of mine told me that she hid instructions for the use of a new telephone from her husband, so that she could be the sole user of the new telephone.

Relations between firms. The following is an example of how high quality instruction may be used to counteract to a rival’s development. Moscow Physical Institute of Nuclear Power was offered, by another firm, free training in the use of computer programs for nuclear reactors. A legal investigation disclosed that if the firm’s proposals were accepted, the firm could use the intellectual property law to veto any international transaction the Institute might engage in while using these programs. The Head of the Institute thinks that the teaching was intended to be a means of counteracting the competitor’s development, a hidden means to “enslave rivals” (Konovalova, and Konovalov, 1998). The more projects use the results of the training, the greater damage the training causes. If used consciously, it is real Trojan horse teaching.

Counter-terrorist struggle and e-teaching/learning technologies. Yael Shahar, a researcher of Institute for Counter-terrorism, said in her interview for magazine Computerra: “Internet must be dangerous for terrorists. It is very important for us to learn that what they teach one another. We see their Internet-discussions of various weapons and explosives. We can participate in these discussions (under presence of terrorists – A.P.), recommend some weapons and explosives, and next day see those who has lost fingers on their hands” (Levkovich-Masliuk, 2007).

Of course, such “Trojan horse” teaching is a Machiavellian technique. Yet who can condemn it, if terrorists try to kill as more people including children, as possible?

4. People’s beliefs about teaching with “evil intent”

Do people believe in teaching “with evil intent”?

An original survey concerning adults’ beliefs about counteraction to other people’s learning and teaching “with evil intent” was administered on a Russian sample (Poddiakov, 2004). On the basis of its results, in cooperation with Prof. Silvia von Kluge, from Eastern Michigan University, we translated the survey, which was then administered on American and Russian samples.

Method

The survey has the following introduction.

“We study interactions that a person can come across in the process of formal or informal learning and instruction, and how they think about these situations. We would appreciate it if you would answer these questions”.

The questions concerning Trojan horse teaching are the following:

1. In a Russian tale a fox teaches a wolf how to catch fish in an ice-hole, using the wolf ’s own tail. As a result, the wolf freezes to the ice and experiences other troubles. In your opinion: are there similar situations of “instruction with evil intent” in real life?
2. Do they happen in schools or universities?
3. Has anyone tried to conduct teaching or instruction with “evil intent” towards yourself?
4. Have you conducted teaching or instruction with “evil intent” towards anyone?
5. Has anyone tried to conduct teaching or instruction with “evil intent” towards yourself during the fight for school (university, etc.) grades and opportunities?
6. Have you conducted teaching or instruction with “evil intent” towards anybody during the fight for school (university, etc.) grades and opportunities?

Options of answering these questions are “no”, “rarely, “from time to time”, “often”, “very often”.

This version of the survey was administered to American undergraduate university students without regard to their major (i.e. non teachers) and to a sample of Russian participants, a portion of which where students and a portion of which were laypeople.

A very similar version of the survey has also been offered to school and university teachers. Changes in this version were the following. The 5th and 6th questions included words “during the fight for social status, estimates, financial profit, and other outcomes” instead of “during the fight for school (university, etc.) grades and opportunities”.

In all the versions answering is anonymous.

Participants

Samples of non-teachers included 279 North-American (171 females and 108 males of 18-51 years) and 361 Russian persons (216 females and 145 males of 16-58 years).

A sample of teachers included 32 teachers from Russian schools and universities (27 females and 5 males of 23-59 years).

Thus, the total sample has included 672 participants.

Results and discussion

Table 1 contains general results concerning beliefs about Trojan horse teaching.

One can see that the pattern of answers of the ordinary participants is very similar in the American and Russian samples. One should emphasize that the answers “rarely”, “often”, “very often”, etc., reflect a whole, cognitive and affective estimation of frequency of the phenomenon, personal sensitivity to it and level of representation of the phenomenon in consciousness. So these estimations are not necessarily objective: both underestimations and overestimations are possible because of some reasons.

Table 1. Participants’ answers about Trojan horse teaching.

Questions	Percentages of participants giving affirmative answers
	Non-teachers		Teachers
	American	Russian	Russian
1. In a Russian tale a fox teaches a wolf… Are there similar situations of “instruction with evil intent” in real life?	96	97	97
2. Do they happen in schools or universities?	94	86	84
3. Has anyone tried to conduct teaching or instruction with “evil intent” towards yourself?	55	37	34
4. Have you conducted teaching or instruction with “evil intent” towards anyone?	23	17	6
5. Has anyone tried to conduct teaching or instruction with “evil intent” towards yourself during the fight for..?	43	21	47
6. Have you conducted teaching or instruction with “evil intent” towards anybody during the fight for..?	15	12	9

For example, an interesting feature of the teachers’ answers is that the teachers, in contrast with the ordinary participants, more often gave affirmative answers to the questions with the specification “during the fight for...” (i.e., to the 5th and 6th questions) than to the previous more general questions without the specification (i.e., to the 3rd and 4th questions). Though this logical contradiction concerning logical class inclusion has also been observed in a small part of the ordinary participants, in the professional teachers it was a stronger trend. It may mean that for them this issue is more important.

This is in correspondence with Tversky’s and Kahneman’s results, concerning conjunction fallacy. For example, in their experiments most of participants thought that a character in the task given, Linda, resembled a feminist bank teller rather than a bank teller (Kahneman, 2003). Slovic’s affect heuristic (Kahneman, 2003) could work in the teachers’ answers as well. Anyhow, it is important for our study of teaching with “evil intent” that these paradoxical results have been shown by professional teachers.

To summarize, approximately 90% of all the participants believe that teaching with “evil intent” does exist in real life and takes place in schools and universities. Approximately half of the participants think that such teaching has been directed towards themselves. Approximately 10-20% of the participants have conducted teaching with “evil intent” towards someone. These results highlight the problem of Trojan horse teaching and show its importance. It is a topic worthy of attention and systematic research. Beliefs about Trojan horse teaching can be a part of implicit theories of education and of teaching / learning.

5. Teachers’ aims and strategies of making decisions

In areas of strong competition, persons may be motivated to give to others or to teach others the least significant material, to conceal the most valuable strategies and to impede their own discovery of strategies for as long as possible. Yet the “teachers’” task is ambivalent because, at one and the same time, some level of learning must be achieved (or at least the person should believe this) and the true goals must not be revealed.

Taking into account these difficulties of investigation of Trojan horse teaching strategies and the conditions related to their secrecy, we have designed and conducted laboratory experiments with participation of adults and children.

5.1. Play as “the Devil’s advocate”:

An experiment with adults’ participation

To study strategies of teaching with “evil intent”, Polina Vykolovahad designed and conducted the following experiment under our supervision.

Method. A participant was asked to help to reveal dishonest strategies of competition, playing the role of “Devil’s advocate”. After the participant’s agreement, s/he was taught to use a certain mathematical formula to predict meanings of an abstract mathematical variable, using some data patterns. (A real analogue of this task might be prediction of exchange rates based on different data, but the formula used was not related to any real financial calculations and transactions.)

After having learned the formula and achieved sufficient mastery, the participant became an “expert” in this area and s/he was told to design a plan of teaching an imagined student, who would be going to compete with the expert-teacher in preciseness of predictions.

The participant was given 48 cards with pieces of information about the formula for selection and sequential presentation of 20 of them to this virtual learner-rival. There is no any false information on the cards. Each card contained true but incomplete information about some part of the formula and the operations with it. Different combinations of 20 cards presented information of different degrees of completeness and clearness about the formula.

Participants: 16 Russian students aged 18 to 25 years.

Results.The participants’ teaching strategies included: decrease of essential information for the learner and increase of non-essential information; selection of information which looked unclear and was most difficult to understand; sudden changes of the order of presentation of information to distort the naturally required logic (“jumps” in the content taught); and hiding “the evil intent”. In other words, playing the role of “Devil’s advocate”, the participants successfully demonstrated abilities to conduct an “upside-down” teaching aimed to make effective learning as difficult as possible for a potential competitor.

5.2. To teach or not to teach? Children’s decisions about “bad and good guys”

Two experiments with participation of preschool children have been conducted (Poddiakov, 2006a). The aim was to find out what the preschoolers’ think about help and counteraction of other people’s exploration and learning, and how they make decisions.

Study 1.

Method. A child was shown how to construct and use a simple exploratory tool (named “a treasure seeker”) to find “gold coins” (plastic yellow circles) in a board game, which required intuitive understanding of geometric probability. The tool could be efficient or not depending on the method of combination of two simple details. After playing the game, the child was shown a picture of three cruel and repugnant hyenas from the popular cartoon “Lion King” and was told that they had resolved themselves to find gold coins in order to buy bane and poison the young lion Simba’s father. The child was then told to construct a treasure seeker for the hyenas.

Then the child was shown a picture of the main positive personages of the cartoon, that is Simba and his friend Nala, who wanted to find the coins in order to buy medicine for the father, who was in trouble. The child was told to construct a treasure seeker for Simba and Nala.

Participants: 25 Russian children aged 5 years and 28 children aged 6 years.

Results. 22 children aged 5 years (88%) and 26 children aged 6 years (93%) constructed an inefficient search tool for hyenas, but an efficient search tool for lions. The children’s verbal comments clearly showed their understanding of both situations and their aims, which were of counteraction (“I’ll construct in such way that they [the hyenas] will find nothing!”), and of help (“The larger seeker for them [for the lions], in order that there will be more coins”).

Thus, the experiment showed that preschoolers can intentionally construct simple tools, appropriate for helping or counteracting others’ efforts in exploration and getting profit.

Study 2.

Method. A child was told the following story about the characters of the cartoon, “Lion King”. Three hyenas (i.e., bad characters) wanted to hunt defenseless nestlings and their mothers while their fathers were absent. Young brave lion Simba (i.e., a good character) decided to prevent it.

The child was instructed to choose from a variety of skills for these personages (e.g., to teach them to turn into other animals, to speak other animals’ language, to climb trees, to smoke, etc.). At first, the child was asked 5 questions about teaching the negative characters, and then 5 questions about teaching the positive characters.

Participants:36 children aged 5 years and 29 children aged 6 years, who did not participate in the previous experiment with the treasure seeker.

Results and discussion. On average, the children aged 5 and 6 years gave, respectively, 94% and 95% of the answers, which could help to save the nestlings. They gave opposite answers about teaching the positive and negative characters. That is, the children “helped” the positive character to learn something good, but “prevented” him from learning something bad, wrong or unnecessary. By contrast, the children “prevented” the negative characters from learning something that could help them to reach their bad aims. Also, the children “helped” the negative characters to learn something wrong, disadvantageous or even bad for them (e.g., to smoke).

Thus, the preschoolers had definite and similar beliefs about different social situations of teaching and learning, which require either help or counteraction to other people’s learning.

As a whole, the analysis of real-life cases and the results of all the studies described above show that the metaphoric rule “to give a rod, not a fish”, often announced in the process of economic education as a principle, can be understood and applied in different ways, depending on the person’s understanding of morality, on her or his attitude to another person, and on the character of their relationship and whether it involves either competition or cooperation. The “rods” given can be of different quality, and this is a problem of moral hazard in education and teaching.

At the same time, the experiments with making decisions about the “hyenas” show that moral hazard can be connected not with educators’ and teachers’ immoral behavior, but with the immoral behavior expected of the persons wishing to be taught. It is evident that people, who are going to become robbers, must not be taught to shoot–if we have information about their intents.

5.3. Teaching to see Trojan horse teaching

A (honest) teacher can pursue the special aim of teaching students to see situations of Trojan horse teaching, whether potential or real. Different ways are possible. One of them is a provocative imitation of Trojan horse teaching with consequent discussion (Poddiakov, 2006b).

Method.A teacher in a technological university, training specialists in upgrading their skills, deliberately made a hidden change in a computer program for the design of oil industry equipment in order to decrease its efficacy, but presented the program to the students as efficient. Yet the defect had been designed in such a way that it could be revealed through experimenting with the program and comparing it with the information from the recommended literature. (Naturally, a real rival would not do such things in a premeditated way.) The learners were not told about the defect. Their activity was recorded for one week.

Participants:38 specialists aged 23 to 45 years.

Results. Twenty seven students (71%) did not explore the program by comparing its work with the data from the literature. Eleven students (28%) did so and found the contradictions. Four of them (11%) revealed the hidden reason for the contradictions through independent cross-testing of the program with the data from the literature.

After a week, the teacher revealed the hidden defect and organized a discussion of the problems of competition in the area in which students were going to work. In particular, he underlined that independent exploratory activity during learning could protect one against dishonest actions from competitors (even if the learners did not know about the actions).

The discussion caused considerable interest among the students.

6. Trojan horse teaching and artificial intelligence

Learning ability of artificial intelligence (AI) systems is considered a most important feature by most researchers (Russel, and Norvig, 2003; Shavlik, and Diettrich, 1990). Respectively, great efforts are directed to make learning abilities of the AI systems higher and higher – in particular, by use of competitive environment stimulating learning. Yet, paradoxically, the following possibilities are ignored. If lots of people believe that learning ability is the most important feature with parameters, which can be increased by a technical way, some of the people can premeditatedly try to design such devices and environmental conditions that decrease the parameters, and influence on this most important feature (the learning ability) in a negative way.

Respectively, possible directions of development of AI systems can be design of systems that are able to:

1. counteract other systems’ learning, decrease their learning abilities and general “intellectual level”, teach them “with evil intent” (e.g., by designing and presenting patterns of irrelevant examples, etc.), and make them take decisions which contradict the aims of owners and/or users of the systems taught (it can be more profitable than halt or termination of the systems);
2. learn and increase level of their leaning abilities and general “intellectual level” in conditions of counteraction to their own learning and attempts of their Trojan horse teaching (Poddiakov, 2001).

First of all, these kinds of activities will be developed in artificial intellectual systems for military purposes. Some examples show possible starting points of such struggle. From time to time countries with dangerous regimes try to buy high-performance computers of top secrecy from abroad illegally (e.g., via third countries), but really get “Trojan horses”– computers premeditatedly sabotaged in such a way that, for example, a radar tracking system or a pipeline controlled by the stolen computers works non-effectively and is able to cause damage (Olson, 2006). One can expect that in the future sabotage can be aimed at computers’ learning ability as a crucial characteristic. As a result, a computer of high learning ability will loose this feature to the extent desirable by the sabotaging party; an advanced computer used for design of learning intelligent agents will generate agents with learning abilities of low levels, etc.

Similar strategies and devices can be used in high-competitive business, in which use of various kinds of Trojan horses (or so called “kisses of death”) given, for example, to competing firms is traditional (Dussauge, Garrette, and Mitchell, 2000; Hennart, Roehl, and Zietlow, 1999).

An interesting area relatively available for observation can be design of new software and hardware for spam and anti-spam, virus and antivirus struggle, agents of which become more and more advanced learning systems able to counteract other systems’ learning and learn in conditions of counteraction. In complex dynamical environments, advanced self-organizing intelligent systems can independently “discover” opportunities of stimulation of partners’ learning, counteraction to development of competitors’ learning, and of learning in conditions of the counteraction.

It is important to emphasize here that one should distinguish between: (a) control of learning process, and (b) control of learning ability. One may try to control other humans’, animals’ or agents’ learning process as acquirement of some knowledge, competencies, skills without changes of their learning abilities. Many kinds of non-human animals teach their young, but there are not any facts that the animals purposefully control learning ability of the next generation (though perhaps can influence the ability in involuntary way). Purposeful design and realization of projects and programs for increase of learning abilities (“learning to learn”) is a prerogative of humans and perhaps of artificial systems created by them.

From theoretical and practical points of view, an important direction of future researches can be design of competitive environments, in which struggle for higher levels of learning abilities is presented in explicit way as a key parameter of the environments. The aim is to find such competitive environments, which stimulate development of agents’ learning and provide with an opportunity to generate and select the agents with optimal learning abilities.

7. Counteraction and development

Negative results of counteraction to learning, education and development are evident, and many of them are described above. It should be emphasized, however, that the effects of counteraction on development are ambivalent. Of course, counteraction can decrease the efficiency of the learner’s activity because this is its main goal. But it can also have a positive influence on development. O.K. Tikhomirov (2002) has analyzed the increase of creative activity as a result of conflict. V.A. Lefebvre (1977) has shown that some strategies of behavior are much more effective under the condition of counteraction than without it. M.G. Yaroshevsky (1995) has formulated a concept of an opponent circle of a scientist. He has shown that various types of conflicts with the opponents can be important sources of the scientist’s creative activity. Cognitive and interpersonal conflicts can equally have positive effects on learning, education and development (Perret-Clermont, 1986).

Developmental trajectories in the process of help and counteraction tend to change the direction of development in different ways (Poddiakov, 2003). Help and support tend to change the direction of development in a predictable way, a way desired by the helping party (an educator, a teacher, etc.). Counteraction most often changes the direction of development in an unpredictable way. Let us consider it in detail.

Help and support provided in effective education change the course of development in a way desired by the educator. Otherwise the aims of education will not be reached (if the main aim is not the stimulation of spontaneity and self-development). Counteraction to learning and development also tries to keep the activity of the counteracting subject in a definite channel, but the aim of the subject is to break out of this channel. Situations of counteraction, rivalry and struggle lead to potentially endless variety, complexity and simplification of new situations and decisions because the aim of each side is to find ways to deceive its competitor (Lefebvre, 1977; Lotman, 1992). Formally, the logic of resistance in social relations includes formalisms with recursive functions (Bauer, 1995). A recursive function can result in a great variety of trajectories and final effects, even in conditions of very small (including infinitesimal) differences in variables in very similar initial situations. Thus, the instability, dynamics and variety of situations that arise in Trojan horse teaching and counteraction to teaching/learning means that break of the “channel” built by one of the parties can happen in any area and can develop in an unpredictable way.

Acknowledgements

I am most grateful to Professor Silvia von Kluge from Eastern Michigan University for her kind help with the English version of the survey, with collecting data on the American sample, and discussions of the issues presented in the article. I also wish to thank Assistant Professor Irina Kalutskaya from Higher School of Economics for her help with collecting data on the American sample, Assistant Professor Sergey Buriagin from Tomsk State Teachers’ University, graduate students Svetlana Mamiof and Christina Kharitonova from Natalia Nesterova’s University, and Olga Gremiakova from Higher School of Economics for their help with collecting data on the Russian sample.

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