Psychological Conditions of the Origin of Ideal Acts

Давыдов, В. В.; Andronov, V. P.

doi:10.2753/rpo1061-040519033

Cited by 7 publications

(4 citation statements)

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“…Based on our observations, we propose that there is a strong relation between experiencing numbers' part-part-whole relations and showing structured finger patterns, since this seems to provide an opportunity to see cardinality and ordinality simultaneously, in the task given. The necessity of awareness of numbers' cardinality and ordinality is not new (see Davydov 1982;Davydov and Andronov 1981;Fuson 1982), and Steffe et al (1982) described this dual meaning of numbers in terms of intuitive extension. However, the empirical findings in this study suggest the necessity of simultaneous experience of cardinality and ordinality.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…This does, however, depend on the ability to maintain the essential distinction of how fingers are used, to keep track of a sequence of number words or to represent a cardinal set. What becomes critical is then the simultaneous experience of numbers' ordinal and cardinal values, for example when adding on units to figure out a missing addend ("counting on") (Davydov and Andronov 1981).…”

Section: Finger Use In Arithmetic Problem Solvingmentioning

confidence: 99%

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Structuring versus counting: critical ways of using fingers in subtraction

Björklund

Kullberg

Kempe

2018

ZDM Mathematics Education

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The idea of using fingers as a key component in arithmetic development has received a great deal of support, much of which is based on neuroscientific evidence. However, this body of work pays limited attention to how fingers are used and possible different outcomes in arithmetic problem solving. The aim of our paper, based on an analysis of 126 observations of 4-5-yearolds solving a simple subtraction task, is to discuss different ways of using fingers, with some of the ways appearing more, and others less, powerful. The analysis suggests there is much more complexity to children's finger-related strategies than prior research has indicated. Empirical findings in our study point to the decisive effects of different ways of using fingers, and in particular for either keeping track of counted units or for presenting a structured awareness of number. Three ways of using fingers emerge in the analysis, which are discussed in relation to their rate of success in solving the subtraction task and with attention to why the differences matter for the success rate. Through this discussion we suggest that the complexity of how fingers are used must be considered.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Finger Use In Arithmetic Problem Solvingmentioning

confidence: 99%

Structuring versus counting: critical ways of using fingers in subtraction

Björklund

Kullberg

Kempe

2018

ZDM Mathematics Education

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“…Learning to use numbers and solve arithmetic problems is nevertheless a complex skill, which means that children have to understand some basic aspects of numbers. In particular, the significance of the number words' meaning of both ordinality and cardinality has been confirmed in many studies (e.g., Davydov & Andronov, 1981;Fuson, 1982). This implies children determining that numbers are associated with an exact set of items, either by counting and pointing one-by-one, or by first determining a set's quantity and then counting its units.…”

Section: Number Knowledge and Arithmetic Skills In Early Childhoodmentioning

confidence: 81%

Preschoolers’ reasoning about numbers in picture books

Björklund

Palmér

2020

Mathematical Thinking and Learning

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In this article we report on a study of children's attention to numerical content in picture books. Specific research questions are 1) how the content in a designed picture book directs children's attention to numbers, and 2) what kind of numerical reasoning the book reading entails. To answer these questions, we conducted an educational design research study in two cycles, with a specially designed picture book and two ways of reading: first without any prompting from the reading teacher, and second with teacher-child interaction. Nineteen preschool children (aged 3-5 years) and three teachers participated in video-observed individual reading sessions. The observations of the reading activities were analyzed with focus on the children's attention to numbers as well as on their numerical reasoning during the book talks. Based on the observations, we suggest that preschool children do direct their attention to aspects of numbers, but that the design of the pictures and the framing of the reading sessions influence which numerical aspects are discerned. Furthermore, teachers' support in transforming empirical clues into mathematical representations and comparisons seems critical for more advanced reasoning about numbers to occur.

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“…El'konin (El'konin, 1973; see also Amano, 1999) and V.V. Davydov (Davydov & Andronov, 1981;Davydov, 1995). Gradually, Gal'perin abandoned the idea of a strict sequence of steps in the teaching-learning process and started to emphasize the distinctive elements that form the basis of the process.…”

Section: Steps In the Formation Of Actionsmentioning

confidence: 99%

Outlining the teaching–learning process: Piotr Gal'perin's contribution

Haenen

2001

Learning and Instruction

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The Russian psychologist Lev Vygotsky was one of the most influential psychologists of the 20th century. As a psychologist following in his footsteps, Piotr Gal'perin could justifiably be called a Vygotskian, but he departed from Vygotsky's sociocultural theory and developed its educational implications. The formative role of education is significant in Vygotsky's notion of a zone of proximal development (ZPD). Gal'perin extended Vygotsky's "zone" to also include a teaching-learning model of the formation of mental actions. This model integrates the notions of mediation, activity and internalization. In doing so, Gal'perin outlines steps in the teaching-learning process, formulates a set of conditions for the development of mental actions and shows the teacher's role. This article summarizes Gal'perin's learning-psychological theory and discusses its use in today's classrooms.

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Psychological Conditions of the Origin of Ideal Acts

Cited by 7 publications

References 1 publication

Structuring versus counting: critical ways of using fingers in subtraction

Structuring versus counting: critical ways of using fingers in subtraction

Preschoolers’ reasoning about numbers in picture books

Outlining the teaching–learning process: Piotr Gal'perin's contribution

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