Abstract
The article describes the study of the effectiveness of methodological techniques used in classes with students training to become teachers of mathematics in elementary schools in accordance with the methods of teaching mathematics to elementary school students. The methods proposed by the authors activate the mutual connection between logical thinking and several non-cognitive abilities of students. This reciprocal relationship is seen as a means to diagnose and develop students’ combinatorial abilities. The study uses testing methods with subsequent mathematical processing. The non-cognitive factors (level of general cultural development, general humanitarian training, features of the micro-environment, as well as the level of general psychosocial development, etc.) are assessed through the methods of academic success diagnostics, expert assessment of the level of general cultural development, and assessment of the level of psychosocial development. The obtained data were compared with the level of development of students’ logical thinking determined through the Raven test. The formative stage deployed original methodological methods allowing to stimulate students’ interest in composing textual mathematical tasks. The proposed methodological solutions to the problems of diagnosing and developing combinatorial thinking understood as a combination of logical thinking and several non-cognitive factors in future teachers show themselves effective. The proposed hypothesis is that composing textual mathematical tasks for elementary school students is an effective means of developing combinatorial abilities in students. The main conditions stimulating the effectiveness of non-cognitive factors are the increase in the level of an individual’s general cultural development, the expansion of their outlook, and the development of knowledge base, the creation of the “right” atmosphere for creativity, and stimulation of metaphorical thinking in the learning process.
Highlights
The article describes the study of the effectiveness of methodological techniques used in classes with students training to become teachers of mathematics in elementary schools in accordance with the methods of teaching mathematics to elementary school students
The combination of cognitive and non-cognitive factors creates the basis for combinatorial thinking that presents a system of ways of allocating different options, permutations, combinations, and placements of elements in the relationships determined by the conditions of the task and its purpose
Our study is based on the idea that for the development of combinatorial abilities in future teachers, of special importance is the combination of two characteristics: logical, consistent unidirectional thinking that develops in the process of education typically at the conscious level and serves as a basis for the acquisition of declarative knowledge and implicit knowledge hidden in the depths of the subconscious and acquired during general psychosocial development and students’ mastery of various academic disciplines
Summary
The combination of cognitive and non-cognitive factors creates the basis for combinatorial thinking that presents a system of ways of allocating different options, permutations, combinations, and placements of elements in the relationships determined by the conditions of the task and its purpose. Considering the relevance of the problem of developing combinatorial thinking, researchers primarily draw attention to the close connection between the ability to solve problems using combinatorial abilities and academic and overall life success [1,2,3,4,5,6]. Modern teachers require combinatorial abilities to solve a variety of professional tasks of both theoretical and practical nature. Important evidence of the development of combinatorial abilities is the productivity of thinking in solving tasks of divergent type as it creates opportunities for achieving original results by analyzing, comparing, and combining a large number of options [7, 8] etc
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