The review article examines the field of scientific research devoted to the analysis of errors in mathematics. The problem of mastering mathematical concepts by younger schoolchildren continues to be relevant in pedagogical psychology. Systematic work with students' mistakes is an important stage in the teacher's work. The review shows the significance of the analysis of mathematical errors. The importance of not only detecting systematic mistakes of students, but also the misconceptions about concepts behind them is substantiated. The reasons for the typology of errors are revealed in the context of a discussion about the relationship between conceptual and procedural knowledge. Various approaches to the typology of mathematical errors are described. The typology of errors based on the identification of error patterns, which has become widespread in research, is considered in detail. In this typology, three large groups of mathematical errors are distinguished: factual, procedural and conceptual. Examples of these errors are given on the material studied by younger schoolchildren.

Развитие компетенций учителя начальных классов в процессе решения профессиональных задач Санина С.П., кандидат педагогических наук, доцент кафедры педагогической психологии факультета психологии образования, ФГБОУ ВО МГППУ, Москва, Россия, saninasp@mgppu.ru Обсуждается проблема развития профессиональных компетенций учителя начальных классов в части умения организовать и формировать у младших школьников навыки учебного сотрудничества. Приводятся результаты исследования, направленного на изучение представлений учителей о продуктивных способах взаимодействия учителя и ученика и на развитие профессиональных компетенций педагога начальной школы. Проверяется гипотеза о том, что тип взаимодействия, основанный на принципах учебного сотрудничества, способствует развитию компетенций учителей начальных классов. Показан принцип разработки обучающих профессиональных задач, названных конструктивными. Приведен пример задачи, нацеленной на изучение эффективных способов взаимоотношений между учителем и учениками и позволяющей организовать продуктивный способ взаимодействий между обучающимися. Доказана эффективность использования профессиональных задач в развитии компетенций учителей в рамках дополнительного профессионального образования.Ключевые слова: профессиональный стандарт, профессиональная деятельность, учитель, компетенции, повышение квалификации, начальная школа, учебное сотрудничество, совместная учебная деятельность, профессиональная задача. Для цитаты:Санина С.П. Развитие компетенций учителя начальных классов в процессе решения профессиональных задач [Электронный ресурс] // Психологическая наука и образование psyedu.ru.

The modular principle of the educational process organization is considered in which practical work, training and introductory, educational practice, SSRP are included into the module, along with the theoretical content. The aim of the article is to consider possibilities of modular education in developing professional competencies of future primary school teachers. In the article experience of the module section approbation "Organization of students’ learning activities at Arts and crafts lessons" is presented. Two models of the teacher's activity in the teaching process are described: the “instruction” model of the teaching process and the teacher’s "controlling" activity. Experience of implementing the model of modular education at all stages is presented: an example of the task for students for educational and introductory practice is given; examples of questions discussed in reflexive work are given; how classroom studies are conducted taking into account the specificity of the subject "Arts and crafts". Examples of a test task and a case for the midterm assessment of students are provided. The effectiveness of the modular organization of the educational process in developing students’ professional competencies of applied bachelor degree course is shown.

The article provides research data on the impact of skills and abilities of teachers in training successful learners. For example, it regards the teacher’s diagnostic competence and its role in overcoming academic failure of students. The article presents the results of scientific research from the United States, Germany, Norway, Russia, etc. We introduce an overview of approaches to definition of diagnostic competence of the teacher. Special attention is paid to the diagnosis of learners’ understanding of educational material. For example, the math illustrates how you can analyze children's reasoning, what you can see and understand from the students ' erroneous decisions. The discussed data show how to build math diagnostic tests that can be used by the teacher of primary school to create his/her own tests. We also introduce the different view on the diagnostics, which is described as aimed at studying and correcting students’ behavior. The case is presented as a tool for development of diagnostic competence of teachers. The described model can be used as a practical guide for building diagnostic action of the teacher in the classroom. An efficient way of teaching students and training teachers with the help of multimedia is described. All the studies analyzed in the article are of great importance for the practice of education, are aimed at the development of diagnostic competence of teachers as a means of overcoming academic failure of students

The article focuses on the designing of disciplines, based on the competence and activity approach to the content and methods of training of future teachers in the research psycho-pedagogical master’s program. Particular attention is paid to the creation of problematic situations, in which research master students find themselves in the position of supervisors examining the educational activity. The authors provide examples of how students perform expert-analytical tasks based on analysis of training activities developed in the theory of developmental education by Davydov scholar school. There are samples of test items to assess how students have learned the content of the discipline, as well as to determine their ability and willingness to perform professional activities. These tasks were performed by master students as well as developing training teachers in elementary school and secondary school teachers. Testing the «Design and research of learning activities in the science lessons in secondary school» course allows us pre argue that psycho-pedagogical research master program allows to train future research training specialist using professional tasks related to expertise and design of training activities. Master students reach an acceptable level of competence for the performing the expert-analytical tasks. We propose to discuss if natural-scientific training of master students is one of the conditions for full cooperation between future research training specialist and teachers in order to improve the education of adolescents in the field of natural sciences.