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Unconventional ways of solving problems in mathematics classes

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Doulík P., Eisenmann P., Přibyl J., Škoda J.
The New Educational Review
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2016
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vol. 43
53-67
EN
The contribution enquires into possibilities of application of the heuristic methods in the teaching process, specifically its applications during the classes of mathematics in grammar school. In the frame of the research the influence was monitored of the unconventional way of solving problems during classes of mathematics in relation to the evaluation of educational advancements. Furthermore, pupils evaluated their attitude towards mathematical study including their viewpoint on problematic exercises in maths and the successfulness of solving these mathematical exercises was also evaluated. The results of the experimental group were compared to the same areas in the control group.
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Problem Solving in Mathematics and Scientific Reasoning

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Cihlář J., Eisenmann P., Hejnová E., Přibyl J.
The New Educational Review
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2020
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vol. 61
97-108
EN
The paper describes the results of a study whose aim was to explore correlations among the components of the construct Culture of problem solving (mathematical intelligence, reading comprehension, creativity and ability to use existing knowledge) and six dimensions of Scientific reasoning, which was tested by the Lawson’s Classroom Test. The total of 180 pupils from the Czech Republic aged 14-15 took part in this study. The results show that the dimensions proportional reasoning, control of variables and probability reasoning strongly correlate with the components mathematical intelligence, reading comprehension and ability to use existing knowledge.
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Technological devices in the development of pupils’ expertise in the use of selected heuristic strategies

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Eisenmann P., Novotná J., Přibyl J.
Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
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2023
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vol. 14
43-79
EN
This paper shows how technological devices can be integrated into the pupils’ use of four selected heuristic strategies in mathematical problem solving: Systematic experimentation, Introduction of an auxiliary element, Analogy, Solution drawing. Our research examined change in the pupils’ success rate and their attitude to problem solving as a consequence of being taught the four selected heuristic strategies while using technological devices actively. A statistically increased success rate of problem solving and a statistically significant decline in the frequency of the number of ‘no response’ cases (the solver does not start to solve the problem) were expected. The study was carried out about by 342 pupils from the 13-17 age group in the Czech Republic. The results of the study show the pupils’ success rate in the solution of problems effectively solvable using the strategies systematic experimentation and solution drawing improved significantly if the use of these strategies went hand in hand with the active use of technological devices. The number of ‘no response’ decreased significantly.
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