Abstract:

The aim of the research is the importance of the applied tasks for the motivation, the engagement, the development of the cognitive skills, the analytical thinking, the functional literacy of the students. The mathematics in the high school course aims to get acquainted with science, axiomatics, theorems and rules. It creates skills for following algorithms, finding logical connections and combining models to solve problems. Students often ask why they need knowledge of functions. Only later in university or in their work do they understand the importance of the ability to analytically read more complex texts and analyse graphically presented information. Along with the memory of hard practical tasks, adults often regret that they did not make enough effort at school to understand such problems. The big challenge is for teachers – to teach not only mathematics, but also its application, in a limited number of hours. These difficulties are relevant even for educational systems with traditions in the inclusion of practical tasks in mathematics courses.

The applied tasks are important for the development of 21st Century skills – critical thinking, creativity, information and technology literacy. The practical problems are introduced after mastering the necessary theoretical material. There is no clearly defined methodology and the process is based on multiple examples with which students can gain experience and learn how to apply the theory in practical tasks. The teacher can guide, build in students a vocabulary to facilitate the transition from text to mathematical model.

The study aims to monitor the level of analytical insight into the text of a voluminous task, the problem-solving approach, the impact on engagement, critical thinking and self-esteem.

For the purposes of the research, two adapted tasks are considered, which serve as a tool for observing the skill of applying the theory, understanding the complex textual content and discovering the connections between theory and practice. They differ radically in wording. One (Option A) clearly specifies characteristic points of a function whose coefficients must be determined. It assesses the level of knowledge of the relevant mathematics material. The second (option B) consists of descriptive text and illustrative graphic. On the basis of analytical reading of the text, combined with the graph, the conditions for finding the same coefficients must be separated. The restrictions set in both tasks are the same. Both problems lead to the construction of the same mathematical model and, accordingly, have the same final solution.

The observation is conducted in high schools with different hours of mathematics – a public language school, a mathematical gymnasium, a private mathematical gymnasium and a public general education high school. The experiment aims to examine students with different levels of mathematical interest. Adapted tasks do not assess academic performance, but aim to track students' analytical skills.

The classes are evenly divided into two groups, each receiving different problems. After completing the task, both groups receive an additional questionnaire for the assessment of the problem on several parameters, as well as for self-assessment. The parallel analysis of the results by tasks and by schools is indicative of the level at which the students make the connection theory-practice in high school.

Keywords:

Text problems, applied mathematics, 21st Century skills, problem-solving, motivation, experiment.