2014. vol. 11. No. 3

The Psychology Journal of Higher School of Economics continues the tradition of special issues on a specific topic. In this issue we offer to the reader a block of articles on Psychology and Mathematics. This topic has not yet appeared as an independent theme in our special issues, though it has been addressed in some issues in different topics as well as in various articles 1. Development is the major topic of the four articles on psychology and mathematics, presented in this special issue: development at different levels, with different subjects of activity (behavior), in various areas that aroused interest of mathematical psychologists. The first two articles are presented in Russian, the other two — in English. It reflects the new editorial policy of the journal that seeks to create the best conditions for cooperation of domestic and foreign researchers. T.Savchenko and G.Golovina discuss the historical development of mathematical psychology and its role in the humanities. The paper formulates the subject and object of mathematical psychology, it described the classification of its historically arising and current models. It also gives a generalized and realistic description of the status of mathematical psychology in the system of the Russian psychological education and analyzes the achievements and difficulties of mathematical psychology at the present stage. A.Vinogradov shows the main directions of socio-cognitive theory of personality over the past decades and discusses the reasons why it is not as successful in competing with the theory of personality traits as it might be. He justifies the idea that social and cognitive theory needs to develop its own system of statistical methods, the research design and psychometrics. He offers own original approaches to the problem both at the level of a common methodology and of specific decisions concerning charting studies. It is important to draw attention to a common problem, different aspects of which are addressed by T.Savchenko, G.Golovina and A.Vinogradov, that is the need to improve the explanatory and predictive power of mathematical models of behavior in different situations. In terms of the outstanding philosopher, mathematician and mathematical psychologist, V.Lefebvre, who is referred to in another context by T.Savchenko and G.Golovina, psycho-diagnostics is the study of a system comparable to the researcher for excellence. This position makes one of the challenges for mathematical psychology. Among other things, it leads to the following assumption: even the best psychologists, armed with the best developments will be faced with the fact that the subject under study does not fit the model created by another subject, and turns out to be richer. Working with both the average and maximum values, “extreme examples” is one of the most important sources of development of methods of mathematical psychology. As one of the directions of the development A.Vinogradov sees the individually oriented psychometrics which provides tools to describe the quality of statistical models at the individual level, as well as the development of the psychological theory of situations with an adequate conceptual apparatus. Two other articles in the issue are devoted to the study of psychology of understanding mathematics itself and the attitude to it. The article by T.Havenson and E.Oryel continues the meaningful but brief analysis of the problems with the mathematical education of students in humanities, which ends the article of N.Savchenko and G.Golovina. T.Havenson and E.Oryel consider the relationship between understanding (or not understanding) statistics by sociology students, the attitude to it and persoanl characteristics of these students, their academic motivation and perseverance. Presenting this study we should mention the use of the statistics attitude questionnaire adapted for Russian students (SATS-36) with six subscales that enabled (using also other tools) to obtain important data about the attitude towards mathematics and its understanding by various groups of future professionals in humanities. A.Krichevets, A.Schwartz and D.Chumachenko represent the study of eye movements dynamics in solving mathematical problems on Cartesian coordinates by people differing in knowledge and understanding of mathematics (school students, first-year students of non-mathematical specialties and mathematical faculties graduates). It is shown that the logic of the perceptual actions change observed with the increasing mathematical competence, reflects the logic of the historical formation of the Cartesian plane as a visual model in mathematics. This study is one of the most important evidence of possibilities of the interaction of general methodology of cultural and historical approach, highly competent researchers in the study domain (in this case in mathematics and its history) and the art of specific experiments using the most modern equipment and methods of mathematical processing data. Of course, the four articles presented cannot cover all the problems of interaction between psychology and mathematics. It means that the journal will continue to systematically refer to this topic. Enjoy the reading!

(Footnote 1) Here we should mention the article by A.Belyanin Mathematical Psychology as a Branch of Economics (Psychology. Journal of Higher School of Economics. 2004. # 3), which goes far beyond the actual economics and mathematical psychology into a broader value-philosophical and methodological context.)

The article raises the question of the role of mathematics in the social sciences, describes the stages and steps of mathematization of psychological knowledge. The paper describes the mathematization of psychology in the narrow (use of formal mathematical language to describe mental phenomena and processes) and broad sense (adoption of natural science tradition of logical rigor and scientific thinking). The object, subject and method of mathematical psychology are introduced. The main method of mathematical psychology is modelling. The article presents a classification of mathematical models by mathematical apparatus: stochastic, deterministic and synergetic models. A brief description of the significant models of psychic reality, emphasizing models developed in Russia, is provided. The paper describes the current state of mathematical psychology and argues that it is characterized by not only using new mathematical principles, models, and methods, but also new understanding of existing approaches. At the moment, the analysis of the dynamics of mental processes, individual differences, the structure of the personality and interpersonal interaction becomes very important, so most probably, the synergetic approach, soft computing, quality integration and asymptotic mathematics should be considered as the most promising techniques for the modelling of mental systems, the interaction dynamics, the learning process and self-learning systems. There is a need in new approaches to psychological measurement, modelling of behavioural macro-dynamics as a result of micro-dynamic processes in the human psyche and modelling of natural systems (management, psychotherapy).To achieve this, psychologists would require a deeper mathematical understanding. Mathematical courses should be based on competence approach and take into account the demands of practice. Natural-scientific training of social sciences students should take into account the present state of mathematical psychology. Mathematical disciplines should help students to think outside the box, understand the logic of irrational behaviour, find creative solutions and not be limited by the formal use of mathematical methods as part of data processing.

The article reviews the mainapproaches to social-cognitive assessment of behavioral structures (behavioral or personality signatures) in order to outline possible development perspectives. It is articulated that social-cognitive theory could successfully compete with contemporary trait theory of personality only if it develops its own assessment theory as well as a system of statistical methods, research design and psychometrics. Based on the review of a number of studies employing external observation, self-report, preference analysis techniques, Q-sort and S-R inventories a general scheme of data collection and data analysis is suggested. The proposed scheme overcomes essential disadvantages of measurement tools currently used in social-cognitive personality research, particularly excessive complexity and low informativeness of the results. It is based on the use of experimental design methods for the formation of stimulus situations, combining self-report and external observation data, repeated measurements and in-depth interviews, as well as the application of a range of modern statistical methods to describe and explain the intra-individual variability in behaviour (conjoint analysis, cluster analysis, multi-level modelling, etc.). Based on this analysis, a system of indicators to describe the quality of statistical models at the level of the individual is proposed – individual indices of reliability, stability, internal consistency and validity. The scheme and system of indices proposed could be used for individual social-cognitive based assessment, as well as in research to explain the intraindividual variability in behaviour. It is concluded that the psychology of personality is currently developing an integrated system of idiographic analysis methods and that individual psychometrics should become its essential component. Further progress in this area involves the ability to integrate information about the active ingredients of the situation from various sources on the basis of the psychological theory of situations.

This paper describes the results of examining the relationship between attitudes towards statistics and academic motivation and perseverance in sociology students. Often, in everyday understanding, social sciences are identified with the humanities and therefore are considered as not requiring specific mathematical training. Such attitudes in social sciences students can lead to a decrease in their learning effectiveness and result in academic issues that could even lead to their expulsion. To measure attitudes towards statistics we used SATS-34, which covers a wide range of attitudes to both the academic subject and to statistics in general. The results showed that, based on the combination of various aspects of the attitude, the students can be divided into three types: those interested in mastering statistics, those who are nominally interested, and those who are uninterested in the subject. The groups differ in the level of perseverance and the prevailing academic motivation. In addition, significant differences between groups were found in the expected and actual grades in the course. The article concludes that attitudes towards statistics are related to both psychological characteristics of students and to the level of course mastery. The differences between the groups were significant notwithstanding the hard and regular monitoring and the high importance of the course in the curriculum, i.e. the hardness of control does not negate the contribution of psychological factors in the learning effectiveness. We assume that the differences between the groups would have been even more pronounced in a more relaxed learning environment.

In this paper we explore the perceptual actions that allow one to perceive pictures as representing mathematical concepts. The research is based on the cultural–historical approach. Following V.V. Davydov’s ideas on theoretical and, particularly, mathematical thinking, we consider a mathematical concept as being based on a historically determined method of action. Using the eye-tracking system we analyzed the difference between school students, university students, and expert mathematicians in their perception of special pictures (so called ‘external visual representations of the theoretical concept’) when performing a set of tasks, namely choosing a point with given coordinates from a set of points. A standard expert-novice research analysis of dwell time in relevant and irrelevant areas of interest was used. We also compared the gaze paths, the number of visual fixations, and the time each group required to perform the tasks. The directions of the saccades were also analyzed, and our data showed that the vertical and horizontal saccades along the axes prevailed over saccades along other directions, a fact that may be considered as a trace of the ‘Cartesian plane’ concept. The data showed that experts performed the tasks faster and with fewer fixations and they also were able to use additional knowledge flexibly in organizing their perceptive actions. Our results show the fundamental interlacing of conceptual structures and visual processes, in which the latter are organized in accordance with prior knowledge. The specificity of the experts’ Cartesian plane perception corresponds to the late stages of the historical development of this concept. We consider this fact as an empirical confirmation of the relevance of the term “theoretical perception”.

This paper presents a psychotherapeutic method to work with the experience by drawing of symbolic forms. The guided drawing method was suggested and used in the existential-initial psychotherapy developed by K. Durckheim in the 1950s in Germany. The first part of the article describes the ways of guided drawing. The second part discusses some of the key concepts and provides a framework in which therapeutic work by guided drawing is considered as an approach to therapeutic experience. The author attempts to justify this technique based on the ideas of cultural-historical theory of LS Vygotsky. In the third part of the article the author makes an attempt to understand the mechanisms of metaphor and symbol in psychotherapeutic work with experience. The article discusses the difference between symbols and other symbolic forms and literary tropes. Symbolic forms that are used as part of this method are the tools that can be compared with metaphor and symbol. They allow the client to perform a reflexive action in relation to their own experience and thereby mediate the process of experience and master their emotional states and behavior. Psychotherapeutic work with experience, considered from the perspective of cultural-historical theory of LS Vygotsky, first appears in its intersubjective form as part of a dialogue between client and therapist, and only then becomes available to the client and moves onto intrasubjective level. Dialogue is constructed as therapist’s revealing support of the client's experience. The therapist performs a special interpretation work aimed at the development of the experience obtained in the process of drawing and client’s self-understanding begins to take the central place in that.

The article presents the results of adaptation of one of the latest versions of the Visual Aesthetic Sensitivity Test (VAST) on two Russian samples: school children aged 10-12 years (132 participants) and adults (107 participants).

1. There was no positive impact of age-related changes on the VAST results; however, the characteristics of the procedure used for the adult sample do not allow stating its complete absence.

2. In contrast to the data obtained by other authors (mostly when using an earlier version of VAST), our results do not support the asymmetry of the VAST scores.

3. VAST has satisfactory reliability: Cronbach’s Alpha is 0.86; correlation coefficient between odd and even items is 0.76.

4. Our results do not support the validity of VAST: average scores of professional artists did not exceed those of non-artists tested in similar conditions.

5. The assessment of school children showed that there was a weak positive relationship between aesthetic giftedness (to the extent that the results of VAST could be considered its valid indicator) and intelligence (as measured by Standard Progressive Matrices Plus (SPM Plus)).  A comparison of the results obtained in our study with the results obtained by other authors demonstrated stability of the psychometric properties of VAST across various studies.

The paper discusses two viewpoints on the usage of scientific theoretical ideas within the context of psychotherapy based on humanities. There are authors who believe that no psychotherapist can go without theoretical conceptions, and others who disagree with this position (in relation to the latter viewpoint the phenomenological approach of A. Puzyrei is reviewed). The author, an adherent of the first position, analyzes the work of P. Volkov that makes use of theoretical concepts of psychology and philosophy. He shows that theoretical notions provide a conceptual space that enables the creation of “therapeutic constructions” that can not be deduced from the theory but have to fit with it. Volkov’s approach is compared to the approach of G. Nardone that is currently popular among therapists, and it is shown that methodologically they are very close. The final part of the paper presents the principles of the theory of mental realities developed by the author who believes that this theory may help psychotherapists drawing from humanities to widen the scope of their scientific notions.

This paper addresses the problem of attitudes toward traits, a bipolar evaluative construct.  It is argued that attitude toward traits is a supplementary characteristic for conventional personality traits.  In this regard, a second dimension of personality traits emerges where each trait can be characterized on another level, a level of attitudes.  The study also demonstrates the psychometric utility of a Russian version of the Big Five Inventory (BFI; John, Donahue & Kentle, 1991; John, Naumann & Soto, 2008).  The secondary factor structure of the Big Five corresponding to the hypothesis on stability/plasticity (DeYoung, Peterson, & Higgins, 2002) was obtained.  The BFI was also shown to be employed as a tool to measure attitudes toward traits, and the five-factor structure was replicated as applied to attitudes toward traits.  Different traits demonstrated different sizes of relationships with attitudes toward respective traits.

This paper addresses memorization processes and functioning of memory abilities. The aim is to explore the dynamics of memory abilities with the increased difficulty of the task. We have attempted to uncover qualitative and quantitative characteristics of the system of mental operations used to memorize new material. The method suggested helped not only to identify the stage of immediate memorization and inclusion of mental operations into activity but also to uncover the subsequent development of the mental operations system in the process of memorization. We have studied the significance of qualitative and quantitative characteristics of the mental operations system of memory abilities. It has been concluded that memory activity includes different types of mechanisms, i.e. immediate memorization and memorization with the use of the system of mental operations. The link between those mechanisms has also been identified.

The article discusses the role of third-party strategies in resolving interpersonal conflicts, by which we mean the participants choosing to cooperate. In the experiment, three strategies of third-party behaviour were modelled – cooperative, neutral and aggressive. The study involved 156 subjects, 95 girls and 61 boys, all 10-11 grade high school students. 18 trained research assistants played the role of the third party. The study was conducted in two series corresponding to the two experimental conditions – in a group and in dyads due to the differences in the conflict parties’ behaviour. The essence of the experiment was to introduce a conflict situation by creating competition between the parties. This was done as part of a game through a simulation of struggle for a limited resource, which in our study was the highest grade and depended on the solution of biological crossword. Results of the study showed that the third-party strategy did have an impact on the process of resolving interpersonal conflict. It has been proved that there are differences in the effectiveness of third-party behaviour depending on the conditions of the conflict – in a group or in a dyad. The results showed that the aggressive strategy of third party encouraged participants to cooperate in a dyad within a social group. The results can be used to create guidelines for teachers, often acting as a third party in the resolution of conflicts, and for the adolescents themselves.

This paper is a continuation of the article “Bullying as an object of research and cultural phenomenon” (Psychology. Journal of the Higher School of Economics, 2013, vol. 10, №3, p. 149-159) and focuses on bullying on the Internet. Widespread use of the Internet and teenagers’ addiction to social networks in conjunction with the deficit of user competence and lack of understanding of the need to maintain a certain ethics of Internet communication make cyberbullying one of the greatest social risks in adolescents. We consider the psychological aspects of cyberbullying that are associated with the specificity of the virtual environment and that make it different from traditional bullying – such as the anonymity of the bully and their continued access to the possibility of prosecution, fear of deprivation of access to the computer of the victim as a motive of concealing information about cyberbullying from their parents, countless and anonymous witnesses, lack of feedback in bully-victim communication and the phenomenon of disinhibition. We consider the basic forms of cyberbullying (flaming, griefing, trolling, defamation, impersonation, the disclosure of secrets and fraud, exclusion / ostracism, cyberstalking and sexting) in order to show the specificity of online bullying behavior. Means to stop and prevent cyberbullying include technical aspects (account lockout, privacy settings, etc.) but otherwise are similar to dealing with bullying outside of the Internet: these are increase of the user awareness in terms of acceptable behaviors, understanding of the need to maintain respectful relations between users (including unmoderated Internet sites and websites that don’t have official rules of conduct), as well as exclusion and possible termination of unsafe, degrading statements and images.