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Introduction. In this article we experimentally study wrong choices made during searching for a solution of difficult mathematical tasks and their influence on the result. The purpose of the article
is to find cause-effect relationships between mistakes made on different steps of problem-solving and the result of the process; to identify the steps where errors significantly increase the risk of unsatisfactory result at the output.
Materials and Methods. The synergetic, process and system approaches allowed us to describe the horizontal information streams of the system "searching for task solution", which reflect the actual aspects of search for the solution. The streams are divided into steps implementing different management functions. Every step of streams meets specified mistakes. We propose an experimental technique that studies the correlationbetween errors in the steps of the process and the results of the process. We use sociological methods (testing); methods of statistical processing of results, multidimensional regression, correlation and canonical analysis. The results of the experiment are compared with the results of empirical observations.
Results.Mistakes influencing results can be divided into “fatal” (leading to interruption of search process), “causing a defect” (leading to a wrong task solution) and “searching” (those which are an integral part of searching, including a control mechanisms, diagnostics and updating process improving results of searching).
For undesirable errors that statistically significantly affect the result there are steps forming 22% of search process and giving 76% of the output errors. It is connected with Pareto principle formulated for production processes.
Discussion. There is a discussion about the interaction of the teacher and the student in the event of errors in the various steps of the process of searching for task solution.
Conclusion.The conclusions of the article in application to pedagogical practice make it possible to improve student results. They can be used in learning to find solutions of difficult tasks.
searching for task solution, process of searching for task solution, interruption of search process, information streams,
mistakes, result, erroneous result
– The article describes the horizontal information flows of the system "searching for task solution", the steps of these flows, which implement various management functions.
– The authors propose an experimental technique that studies the correlationbetween errors in the steps of the process and the results of the process, including: interruption of search process, erroneous result, the correct solution.
– The article investigates cause-effect relationships between mistakes made on different steps of problem-solving and the result of the process. The steps forming 22% of search process and giving 76% of the output errors, are revealed.
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