Approaches to the typology of the common mistakes of younger schoolchildren in the development of mathematical concepts

Sanina, S P; Sokolov, Vladimir Lvovich

doi:10.17759/jmfp.2021100413

Cited by 4 publications

(1 citation statement)

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“…For the study on arithmetic errors, it is a crucial step to identify the types of errors (Reisman, 1972;Ashlock, 1986;Morales, 2014;Pankow et al, 2018). The systematic handling of errors made by students is a vital stage in teacher's work, involving the spotting and explanation of errors (Rozak and Nurwiani, 2020;Ngcobo, 2021;Sanina and Sokolov, 2021). In further research on arithmetic errors, scholars have summarized the error types, including Errors of perseveration, Errors of association, Errors of interference, knowledge errors, and comprehension errors, etc.…”

Section: Mathematical Arithmetic Errorsmentioning

confidence: 99%

The effect of a Schema-based method on correcting persistent errors in mental arithmetic: an experimental study

Chen,

Liu,

Yan

et al. 2024

Front. Psychol.

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IntroductionArithmetic calculation is a fundamental skill for mathematical learning and daily life. However, elementary school students often make errors in practice.MethodsGrounded in the schema theory and the memory retrieval theory of mental arithmetic, this study employs a controlled experiment to investigate the effect of a schema-based method in correcting persistent errors in mental arithmetic, specifically in the context of simple addition operations. The experimental group utilizes a schema-based method to help participants rectify incorrect answers in memory retrieval, while the control group did not receive this treatment.ResultsThe results showed that significant differences emerged between the experimental and control groups in both the post-test performance and the reduction of persistent error count, indicating that the experimental group had rectified incorrect answers in memory; and persistent errors in simple addition were indeed caused by interference from incorrect answers during memory retrieval; and the schema-based method proves to be effective.DiscussionThe findings of this study contribute to enhancing practical mental arithmetic instruction, assisting students in correcting relevant errors, and improving their mental arithmetic abilities. Not only does it offer directive guidance for teaching practices, but it also provides an enlightening reference for promoting innovative teaching methods.

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Section: Mathematical Arithmetic Errorsmentioning

confidence: 99%

The effect of a Schema-based method on correcting persistent errors in mental arithmetic: an experimental study

Chen,

Liu,

Yan

et al. 2024

Front. Psychol.

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Psychological and Pedagogical Methods of Working on the Mistakes of Younger Schoolchildren in the Development of Mathematical Concepts

Sokolov

2023

Bulletin of Practical Psychology of Education

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The article continues a series of publications devoted to the methodology being developed for the development of students’ initial ideas to scientific concepts. The reasons for the mistakes made by younger schoolchildren when mastering mathematical concepts are considered. Examples of children’s mistakes are shown on the material of the topic “Subtraction”, their types are highlighted. The techniques of working on errors in the development of mathematical concepts are described. A method of organizing developmental assessment aimed at analyzing errors from the point of view of students’ misconceptions behind them is presented in detail. The stages of collecting error data, determining their type and causes, and eliminating error patterns are highlighted. Attention is paid to errors associated with a lack of reading skills. Recommendations are given on the organization of quasi-research activities and polylogue in elementary school math lessons, their mutual relationship is revealed. There are deficiencies in the skills of primary school teachers to organize an educational discussion and work with children’s hypotheses. The example of the topic “Subtraction with a transition through a digit” shows a way to create a problem situation and use numerical models. The prospects for the organization of quasi-research and polylogue in this lesson are outlined.

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Preparation of Primary School Teachers for Professional Activities for the Development of Mathematical Thinking of Younger Schoolchildren

Sokolov

2022

Psychological-Educational Studies

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The article discusses one of the aspects of the training of a teacher of primary general education – the ability to analyze the causes of students' mistakes made by them when mastering mathematical concepts. The special importance in the competence of the primary school teacher of understanding the value of the initial, initial representations of the child as a result of his own mental activity is noted. An overview of the concept of mathematical thinking in the psychological and pedagogical literature is given. The understanding of mathematical thinking as theoretical, carried out on mathematical material, is highlighted. The levels of development of mathematical thinking and its main components – analysis, planning and reflection – are recorded. The modules of the educational program for the training of primary school teachers are described, aimed at developing students' competencies that allow them to adequately assess the manifestations of mathematical thinking in younger schoolchildren on mathematical material traditionally studied in primary school. The sequence of actions aimed at identifying the error pattern is presented. Examples of tasks for students are given, showing ways of developing the educational action of control; determining patterns of mathematical errors.

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Approaches to the typology of the common mistakes of younger schoolchildren in the development of mathematical concepts

Cited by 4 publications

References 20 publications

The effect of a Schema-based method on correcting persistent errors in mental arithmetic: an experimental study

The effect of a Schema-based method on correcting persistent errors in mental arithmetic: an experimental study

Psychological and Pedagogical Methods of Working on the Mistakes of Younger Schoolchildren in the Development of Mathematical Concepts

Preparation of Primary School Teachers for Professional Activities for the Development of Mathematical Thinking of Younger Schoolchildren

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