Motivational tasks for learning the topic «Functions» by lyceum students

Abstract

In modern mathematics education, there is a gap between the abstract nature of mathematical concepts and their practical application in real life within the framework of implementing the New Ukrainian School (NUS) reform. In this regard, a pressing pedagogical issue is the development and implementation of a system of motivational tasks that would demonstrate the practical value of the topic «Functions» and contribute to the formation of students' key educational competences. The article investigates the methodological aspects of developing motivation and cognitive interest among lyceum students while studying the «Functions» content line in the school mathematics course.

The purpose of the article is to design and demonstrate examples of real-world and applied motivational tasks suitable for studying the topic «Functions» by lyceum students. We propose a system of competence-based tasks accompanied by detailed methodological comments for exploring the properties of power, trigonometric, exponential, and logarithmic functions. Using the methods of mathematical and computer modeling of problem-based situations, we integrate real-life and professional cases from contemporary fields such as wave engineering, the entertainment industry (GameDev), financial literacy, and IT entrepreneurship. The use of problem-based situations is demonstrated, specifically through the cognitive dissonance between school formulas for compound interest and the algorithms of real-world banking calculators, as well as the application of graphing calculators (such as GeoGebra, Desmos, etc.) to minimize routine calculations and shift the focus toward the deep analysis of mathematical models. Introducing such motivational tasks at the beginning of a topic eliminates the fear of studying the 'Functions' content line. The practical significance of the developed materials lies in the possibility of their direct use by mathematics teachers to enhance cognitive interest and foster critical thinking in lyceum students.