Abstract:

Research and analysis of solving strategies used in the process of mathematical tasks solution provide important information about the way of reasoning of the solver thinking. Pupils approach the solution of mathematical problems on an intuitive, manipulative level, and apply various representations of task elements. In the process of solving problems, it is appropriate to use different models of representations in the context of Bruner's theory (1960) - i.e., from manipulative (enactive), through iconic to symbolic. It turns out that future teachers at the primary level of education are unaware of the existence of different approaches to solving tasks in mathematics. We consider it important that teachers should be able to reflect on the student´s thought processes. An essential prerequisite is knowledge of the principles of different solving approaches applied in the process of solving mathematical problems.

The results of a qualitative analysis of written solutions to the mathematical problems solved by students (n=52), a group of future teachers in the 1st stage of primary school are presented in the poster. The main aim of qualitative analysis was to find answers to research questions:
(1) What strategies do students use when solving non-standard mathematical problems?
(2) What type of task representation do students apply when learning individual solutions to the task?
(3) Is a comment explaining the solver's thought process part of the written solution to the task?

The analysis of the written tasks showed that the students are able to produce different approaches and solving strategies. In most cases, in the examined written solutions, the used models were at the pictorial (iconic) level, in some cases, it was a symbolic type of representation. No verbal comment was part of the solution to the analyzed written tasks solutions. Students do not consider it necessary to explain their procedure if it is not explicitly stated in the assignment. Different solving strategies of mathematical problems are important tools for developing mathematical thinking. The type of used strategy in the process of solving problems has an influence on the academic performance of the student teachers (Guzman, 2018). Analysis of various solution approaches is the starting point for further direction in the subject area of research.

Keywords:

The mathematical task, Solving strategy, Mathematics Education.