On the 100th anniversary of N.F. Talyzina

Background. The process of teaching mathematics represents a challenge for primary education, due to the different perspectives and disciplines involved. In addition, as an active and flexible process, it requires feedback on what the students actually achieved. An analysis of the different learning and development outcomes allows the teacher to understand the mathematical content and the method of teaching it in the classroom, with the objective of promoting the students’ conceptual development.

Objective. The objective of our study was to analyze the general skills for problem solving which students developed, by applying dynamic evaluation. 

Design. A verification method was used to identify the students’ abilities and difficulties. A protocol for evaluating the process of solving mathematical problems was organized. The assessment included four simple problems and four complex ones. The participants were 15 students in the third grade of primary school attending a private school located in Mexico City.

Results. The results showed that the students identified the types of mathematical operations (addition, subtraction, multiplication, and division) required to solve the problems as their objective. Therefore, their preparation of a solution plan, its execution, and its verification were based only on empirical thinking and quantitative information. 

Conclusions. We concluded that problem-solving is an intellectual activity that requires conceptual development to carry out a solution plan, execute it, and verify it, in addition to the  main objective of answering the question posed by the problem. We propose that these characteristics be included in the organization of mathematics teaching in order to develop mathematical thinking.

Background. Nina Fedorovna Talyzina was a Russian psychologist, whose theories have been applied in educational research in many countries around the world, including Brazil. Her name is mainly connected to the Activity Theory of Learning (ATL), which has been dubbed the Galperin-Talyzina system of developmental didactics.

Objective. Investigate how N.F. Talyzina’s ideas are applied in dissertations and theses developed in postgraduate programs in Brazil.

Design. Our research was a bibliographic review which used the state of the question method to examine how Talyzina’s ideas are applied in Brazilian academic publications. Data were gathered from three responsible databases – the Brazilian Digital Library, the CAPES Catalogue, and the Institutional Repositories (1987-2022). The method of content analysis was used for data analysis, according to pre-determined categories.

Results. We found a prevalence of research based on the methodology of formative experiments carried out at different educational levels. Skills, scientific concept- formation, and problem-solving were the objects of investigation in most of the studies. The ideas proposed by L.S. Vygotsky, A.N. Leontiev, P.Ya. Galperin, and V.V. Davidov were expressed through references to Talyzina’s work as the theoretical basis of many studies, thus evidencing a crucial dialogue with the Cultural-Historical School (CHS).

Conclusion. Our study points out the growing interest in Talyzina's ideas, specifically her Activity Theory of Learning, which can be attributed to comprehensive dialogues with the ideas of L.S. Vygotsky and A.N. Leontiev which predominate in Brazilian research.

Background. Activity Theory applied by the teacher to preschool education favors the development of new psychological formations, such as perception, attention, memory, thought, language, and voluntariness, which prepare the child for school.

Objective. To highlight the contributions of N.F. Talyzina based on Activity Theory applied to preschool education and to reflect on the theory’s use in the Brazilian education system.

Design. This article is theoretically built from research in a sandwich doctorate program in Puebla, Mexico and internship supervision practices for psychologist training at a public university in Brazil’s central-west region.

Results. Activity Theory is seldom applied to teaching, including in Brazil, and there is little knowledge about the scientific contributions of one of its practitioners, the late N.F. Talyzina. We chose the preschool stage as the focus of our reflections, and we maintain that the introduction of role-playing as the main activity in early childhood education promotes the development of psychological neoformations and prepares the child for the next stage of school. Finally, we present the internship practices in applied psychology in a Brazilian children’s group, with evidence of advances.

Conclusion. There is a need for expansion of the formative experiments reported here to the Brazilian population, for scientific dissemination of the results, and promotion of teacher training and qualification in Activity Theory.

Background. Piotr Ya. Galperin and his collaborator Nina F. Talyzina performed solid experimental work which led them to propose the theory of stage-by-stage formation of mental actions and concepts, as well as a method to investigate cognitive processes, whose conceptual and procedural streamlining demands analysis and systematization.

Objective. To investigate the formative experiment of P. Ya. Galperin and N.F. Talyzina, with the aim of analyzing their contributions to the method of psychological investigation of cognitive processes.

Design. The article is part of a theoretical research project on developmental didactics systems, of which the Galperin–Talyzina system is one. Russian works by the two authors and their translations into English, Spanish, and Portuguese, as well as works by other psychologists and educators from the Galperin–Talyzina school, were sources of the work.

Results. The experiments of P.Ya. Galperin and N.F. Talyzina studied, promoted, and analyzed the assimilation of new knowledge and mental actions, by introducing different conditions. The article systematizes the stages and procedures of such experiments, as well as the series and steps of diagnosis of the developmental level and the formation of mental actions and concepts, in relation to the type of Orienting Basis of an Action (OBA).

Conclusion. The theory was built on the basis of simultaneous production of a method to study the genesis of the cognitive processes and the theory of stage-by-stage formation of mental actions and concepts; it led us to define the method of P.Ya. Galperin and N.F. Talyzina as a gradual formation experiment.

Background. While the traditional method of teaching consists of repetition and memorization, the constructivist theory proposes independent discovery and free play. The cultural-historical approach, on the other hand, does not insist on the early introduction of formal mathematics as implicit or explicit knowledge. According to this outlook, important psychological developmental is necessary for the child before he/she can learn mathematics in primary school.

Objective. To present a methodology for organizing the play activity of children of preschool age by introducing symbolic means on the materialized and perceptual levels as an essential aspect of preparation for learning mathematical concepts in primary school.

Design. The experiment consisted in pedagogical work in the online modality by the authors at a private college in the city of Puebla, Mexico. Eighteen children from three levels of preschool education (from three to six years old) participated in 45-minute sessions three times per week. There were six children from each preschool level.

Results. It was shown that playing with roles online allows children at least partially to include different symbolic means in their activity. This allows the children not only to satisfy their curiosity and be positively engaged in the topic of the play, but also to develop symbolic functions as preparation for intellectual actions with numerical content in primary school.

Conclusion. The article shows a feasible way to organize preschool play with roles online and thus to scaffold the formation of children’s imagination and ability to use symbolic means, which is important for future learning. The cultural-historical approach offers useful guidelines here, although more research is needed to support the development of children’s symbolic function within math-specific activity, based on activity theory applied to learning.

Background. Using the Activity Theory of education (Galperin, 1992; Talyzina, 2018), this article examines the students’ actions that constitute the early stages of forming the concept of ratios. The psychological analysis of mastery of this concept shows that it essentially depends on understanding the coordination of the changes of two independent values (area, velocity, density, etc.).

Objective. The present research considers differences in students’ operations with numbers on various tasks, based on their comprehension of ratio relations (direct and inverse proportions); these differences are revealed through posing certain modified tasks, but may stay unnoticed in regular tasks. The goal of the study was to identify the criteria for adequate assessment of the sustainability of the students’ orientation in modified tasks.

Design. A test of 15 tasks was designed based on Galperin's classification of task variations: domain specific, logical, and psychological. The formulation of the tasks disguised the operations needed to achieve the right answer, and sometimes even prompted the wrong solution. There were 12 tasks on direct proportions – four sample and eight modified; and three inverse proportion tasks: one sample and two modified. One hundred sixty (160) students (5^th-6^th grade, 11-13 years old) took the test in writing.

Results. The comparison of students’ performance on the sample and modified tasks showed significant differences. Modifications impaired the students' performance on both types of proportion problems (direct and inverse). Logical and psychological modifications had the most impact on the quality of the students' orientation and thus proved to be most indicative in terms of students’ orientation quality assessment.

Conclusion. The data suggest the following: 1) that the concepts of proportionality which the students acquired from a regular school curriculum lack "generalization," and 2) that students’ ability to apply the ratio concept is very sensitive to the way the word problem is presented. These findings are essential for evaluating students’ multiplicative thinking: their actual level of comprehension cannot be revealed through their performance on regular tasks.

* We publish here the report by N.F. Talyzina to a Conference on Psychology in 1955 and released two years later in the proceedings of that conference (N.F. Talyzina [1957]. In B.G. Anan′yeva et al. [Eds.], Materialy soveshchaniia po psikhologii. July 1–6, 1955. Moscow: Publishing House of the Academy of Pedagogical Sciences of the RSFSR.) This report is of particular interest, since it describes some of the first formative experiments based on the theory of planned stage-by-stage formation of mental actions; the text does not yet discuss the formation of actions, but only the application of the attributes of concepts to solving problems. The text presents the results of a study of the formation of elementary geometric concepts according to the theory of planned stage-by-stage formation of mental actions and concepts. Twenty-two subjects from grades 6–9 formed geometric concepts such as “line,” “angle,” “angle bisector,” “perpendicular,” “adjacent angles,” and “supplementary angles.” These attributes were formed in the process of their application to solving different types of problems. Observational and then formative (training) experiments were performed individually. The article contains excerpts from the subjects’ protocols as they solved the problems. It was shown that stage-by-stage development (identifying attributes from a definition, saying them aloud, and then applying them to solving problems) leads to mastery not only of the geometric concepts themselves, but also of the method of action with definitions in general, allowing students to transfer the method they have learned to concepts from another field of knowledge.

Background. This article is dedicated to the 100-year anniversary of the birth of N.F. Talyzina and contains an assessment of the prospects for developing ways to master a scientific concept, in theories of learning according to the activity approach. The assessment takes into account achievements following the approach of L.S. Vygotsky, the “conceptual changes” approach, and theories of the psychology of insightful problem solving.

Objective. To demonstrate the necessity and productivity of the activity approach to scientific concepts that students learn as forms of constructive criticism.

Method. A comparative analysis of the theories of the activity approach to learning, the approach of L.S. Vygotsky, the “conceptual changes” approach, and theories of the psychology of insightful problem solving, from the standpoint of identifying the most effective way of mastering scientific concepts.

Results. The main substantiated thesis of the article is that mastery of a scientific concept is most effective when it is presented as a form of constructive criticism of another concept.

Conclusion. Taking into account the conceptual forms of constructive criticism allows us to outline the actual paths of development of the activity approach to learning. These forms were developed, on the one hand, through the methodology of science, and on the other, in a less developed way, through the psychology of insightful problem solving, with reliance on certain forms of “critical” action. In particular, when using a special kind of obstacle to teach a task, it is proposed to use the analysis of “full insight” to reveal a special type of reason for an erroneous action.