Didactics of mathematics as a scientific discipline

The European Proceedings of Social & Behavioural Sciences

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Effect of Concept Attainment Models and Self-Directed Learning (SDL) on Mathematics Learning Outcomes.

The paper discusses the deployment of cognitive and affective components for teaching languages in a blended learning university setting. A modified expectancy model of motivation was desig...

Psychodidactic approach in the development of language competences in university students within blended learning

The research is relevant as educational computer games are included in students’ mathematical activity and form additional opportunities to improve the quality of teaching mathematics in a digital school, to support the formation of the demanded professional competence - computational thinking. To form the appropriate skills that determine the essence of special computational thinking, the authors propose to include game educational spaces based on digital gamification resources into students’ mathematical activities. The research aims to resolve the contradiction between requirements of the modern economy for specialists’ high level of computational thinking and an insufficiently developed methodological base for training graduates that meets these requirements. The purpose of this research is to study the features of using gamification technologies in teaching mathematics to form the skills and abilities that make up the essence of computational thinking. The article describes directions of educational and cognitive mathematical activity based on the principles of gamification. The authors clarify the concept of “computational thinking”, which includes a system of actions for activating patterns, connections between them from human memory, and compile an effective algorithm for solving them: to obtain relevant information on advanced technological developments; to state the problem and model; to use a software product with mathematical content.

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Formation of Computational Thinking Skills Using Computer Games in Teaching Mathematics

The article discusses an innovative teaching technology that uses development-focused educational texts (DET Technology) to stimulate school pupils’ intellectual development in grades 5 to 9. It describes the psychological and psychodidactic framework of DET Technology. Development-focused educational texts are distinctive in that they use a framework of academic mathematical knowledge to build up the key components of pupils’ mental experience (cognitive, conceptual, metacognitive, and intentional). Such texts also provide the conditions for the development and usage of students’ personal learning styles. The article outlines the psychodidactic types of development-focused educational texts and the requirements that the psychodidactics proposes for educational texts.

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Development-focused educational texts as a basis for learners' intellectual development in studying mathematics (det technology)

IntroductionAdolescence is a distinct period of psychological development. On the one hand, it is a sensitive period of intellectual development as this is the time when conceptual thinking develops -"formal operational thought" (Piaget, 1969) or "thinking in concepts" (Vygotsky, 1934/1982); such thinking leads to a qualitative leap in the development of the intellectual resources of a child. On the other hand, there is a marked slowdown in intellectual development at this time (as compared with its dynamics in previous stages of ontogenesis) because of the onset of puberty.In research on childhood dysontogenesis a "normative approach" was dominant for many years. In this approach specific signs of psychological activity were seen as "standard," and the corresponding group of children was labeled as the "norm"; adolescents with development deviant to this norm and delayed intellectual development were described as having "deficits." Modern scholars rightly suggest that in the case of dysontogenesis one should speak not of developmental deficits but of developmental differences (Akhtar & Jaswal, 2013; Kapp, Gillespie-Lynch, Sherman, & Hutman, 2013; Norbury & Sparks, 2013).Among the most common forms of dysontogenesis are cerebral palsy (CP), attention deficit hyperactivity disorder (ADHD), and delayed intellectual development (DID). Many studies describe detailed features of the intelligence of children and adolescents with these types of deviant developments (Barkley, 1997; Peneda, Ardila, & Rosselli, 1999; Shipitsyna & Mamaychuk, 2001; Sonuga-Barke, Houlberg, & Hall, 1994; Swanson, Castellanos, Murias, LaHoste, & Kennedy, 1998). The interest of our study is that the state of intelligence of adolescent children with deviant developments differs greatly. In particular, adolescents with CP are a very diverse group in the development of intelligence -- they range from having quite good intelligence to having various forms of delayed intellectual development, including manifestations of intellectual disability. The range of symptoms of intellectual disorders in adolescents with ADHD also varies widely, up to signs of intellectual giftedness ("twice exceptional"). There are even broader boundaries of the DID syndrome: this form of dysontogenesis covers children with minimal brain dysfunction, children with learning disabilities (educationally disabled), slow learners, and children who have suffered social and cultural deprivation as a result of poor living conditions. The existence of such an amazing variety of levels of intelligence under the conditions of deviant development is apparently not accidental: it is evidence of the existence of complex compensatory mechanisms.However, there is still no clarity as to which intellectual qualities (abilities) can be regarded as a resource basis for the intellectual development of the atypical child. From our perspective, conceptual and metacognitive abilities can act as resource factors in the development of intelligence in normal adolescence and in the adolescence of children with dysontogenesis.Conceptual abilities are intellectual qualities responsible for the formation and evolution of semantic connections, the use of categories with different grades of generalization, the detection and discovery of implicit connections, and the generation of new ideas. In different studies, conceptual abilities are presented as "the ability to do abstract thinking" (Sattler, 1988), "conceptual intelligence" (Li, 1996), "generative thinking" (Ward & Sifonis, 1997), "thinking in concepts" (Vygotsky,Resource function of conceptual and metacognitive abilities in adolescents...1934/1982), and "semantic, categorial, and generative abilities" (Kholodnaya, 2012).Metacognitive abilities are intellectual qualities responsible for the involuntary and voluntary regulation of intellectual activity. Their main function is to control information processing. …

/pdf/resource-function-of-conceptual-and-metacognitive-abilities-4mq1vsyo1w.pdf

Resource function of conceptual and metacognitive abilities in adolescents with different forms of dysontogenesis

School textbooks as a medium for the intellectual development of children during the mathematics teaching process

The objectives of this study are to analyze the phenomenology of reflection, taking into account the relationship of the level of reflection with various intellectual and personal properties and the success of the activity. Along with this, the objectives of the study are to substantiate the role of metacognitive abilities as the basis of positive and negative manifestations of a high and low level of reflection, allowing us to talk about the light and dark sides of reflection and areflection. The results of the analysis describe the manifestations of the “splitting effects” of high and low reflection indicators. The pole of high reflection can hide both productive forms of self-regulation with positive consequences (such as increasing the success of activities, self-efficacy, systemic reflection), and maladaptive forms of self-regulation with negative consequences (decreased success in activities, rumination, hyperpersonal control, illusory control, introspection, quasi-reflection). In turn, the pole of low reflection also “splits” into two different components: productive forms of self-regulation with positive consequences (implicit learning, intellectual behavior of experts, secondary control, selective meaningfulness, creative process) and maladaptive forms of self-regulation with negative consequences (decreased success, learned helplessness, psychological encapsulation). In addition, the mechanism that provides the effect of splitting high and low indicators of reflection is metacognitive abilities (the ability to involuntarily and voluntarily control one's mental activity). The results of the study allow us to conclude the multidimensional (nonlinear) nature of reflection.

Light And Dark Sides Of Reflection And Areflection: Splitting Effect

Shadrikov V.D. (2021). The return of the soul: Theoretical foundations and methodology of psychological science. M.: Publishing House "Institute of Psychology of the Russian Academy of Sciences"

Marina A. Kholodnaya

Papers

Development-focused educational texts as a basis for learners' intellectual development in studying mathematics (det technology)

Resource function of conceptual and metacognitive abilities in adolescents with different forms of dysontogenesis

School textbooks as a medium for the intellectual development of children during the mathematics teaching process

Light And Dark Sides Of Reflection And Areflection: Splitting Effect

Shadrikov V.D. (2021). The return of the soul: Theoretical foundations and methodology of psychological science. M.: Publishing House "Institute of Psychology of the Russian Academy of Sciences"