According to the National project “Education”, the main goals for the Russian Federation is to become one of the top 10 countries by quality of general education and to create the ‘conditions for the upbringing of a harmoniously developed and socially responsible individual’. Analysis revealed that after completing elementary school, Russian students consistently show high results in the Progress in International Reading Literacy Study (2011: 2nd; 2016: 1st), and good results in elementary and secondary schools in the Trends in International Mathematics and Science Study (2019: 6th in mathematics; 3rd in natural science literacy). However, according to the Programme for International Student Assessment, some students (more than 20 percent in 2018) are not reaching the threshold levels of reading, mathematical, and natural science literacy [6, 7].

The research question of the study: What is the percentage of elementary school teachers who see conceptual and procedural mistakes in mathematics and natural sciences in problem solving by students and children’s initial representations behind them and offer to avoid or develop them? 

Objective: To create the method of children’s concepts development from initial representations to scientific concepts in mathematics and natural sciences in elementary school.

Theoretical framework

The research provides psychological and pedagogical background for a technique aimed at transforming children’s initial representations in mathematics and natural sciences into scientific concepts in elementary school. The methodological basis underlying this technique is largely shaped by L.S.Vygotsky’s ideas of the holistic and unified development of concepts in the process of learning [13]. We emphasize the key ideas of designing tools for working with students’ initial representations in elementary school and transforming them into mathematical and natural scientific concepts: identification and joint discussion of children’s naive representations, reflective assessment of different views on the explored subject concept, coordination of opinions and assessments. We analyze the main approaches and practices of working with the students’ initial representations developed in foreign and Russian psychological and pedagogical research. 

Two alternative approaches to understanding the essence of initial representations and their role in learning have been identified: 1) conceptual change (S. Vosniadou) [1, 2, 11, 12], 2) “Knowledge in Pieces” (A.A. diSessa) [3].

Psychological analysis shows that most of the students' mistakes are not random, but regular in nature and are associated with the students' initial representations about the content being studied, which differs from scientific concepts. Incorrect generalizations that have developed in the preschool period or already in the course of training and are mechanically transferred to new learning situations lead to naturally occurring mistakes. 

The implementation of such an action is based on the need for the teacher to have not only a deep knowledge of the subject but also an understanding of how the student's thinking develops in the learning process, which implies the need for special psychological and pedagogical competencies. The mastering of such competencies by a teacher in the course of his methodological training, therefore, has a high potential for improving the level of both subject and meta-subject student’ learning outcomes [4]. 

The survey was conducted in 2021 and involved 2.6 thousand elementary school teachers from 7 subregions of the Russian Federation: the Kabardino-Balkarian Republic, the Republic of Buryatia, the Krasnoyarsk Territory, and four regions - Volgograd, Vologda, Nizhny Novgorod, and Sverdlovsk. In first part of the survey participants were offered case studies in mathematics and natural sciences on various topics: multiply numbers, calculating the length of a side of a similar rectangle, comparison of objects of the same shape made from different types of materials. Preliminary results of the survey show a statistically significant correlation between teachers' answers to questions about what type of mistakes are present in students' problem solving, and how teachers intend to work with initial representations. In the second part of the survey participants were offered to describe the best practice of work with the mistakes in mathematics and natural sciences in problem solving by students and children’s initial representations behind them. Almost the same proportions of participants indicated as the best practice: practical work, including experiments, using the observation method, analysis of problem situations (11%), laboratory work, involving students in the performance of specific tasks (10%). 8% of survey participants singled out experimentation and consolidation of previously studied material as the best practice. Less part of teachers believes that to develop the initial ideas of students in the lessons it is optimal to use the method of observation. Less than 5% of teachers named among the best practices: didactic games, analysis of examples of life situations, organization of joint activities, development of functional literacy.

1. It is concluded that the best practices of pedagogical activity in developing the initial ideas of students are built based on the psychological components of the methodological competence of teachers of primary general education. 2. It is worth noting that there is no universally recognized technique for transforming students’ initial representations into scientific concepts in elementary school; nonetheless, there are several effective methods in pedagogical practice that we outline [5, 8, 9, 10]. 3. Finally, we stress the importance of training teachers to work with children’s initial representations in the course of developing their scientific concepts within the learned subject. 4. Proposals were developed for the methodology for developing the initial representations of students to scientific concepts in mathematics and natural sciences in elementary general education. The methodology is based on five psychological components of pedagogical activity: the teacher's ideas about the importance of working with the students' initial representations, the organization of students' quasi-research activities aimed at identifying the limitations of the initial representations in the framework of specially organized laboratory and experimental situations with structured support and organization of this activity from the teacher; organization of an educational discussion in the classroom (polylogue), in which all students participate; implementation of developmental assessment technology in the learning process; the formation of universal learning activities as a condition for the development of initial representations.

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