Abstract:

University students of several technical and science-oriented programs (not only) in physics-oriented courses regularly encounter numerical data showing some trend. Depending on the difficulty of the given class, we can call the given trend a relation of physical quantities, a physical dependence, or a (mathematical) function. Our previous theoretical analyzes showed that several situations with a physics context lead students to dependence of quantities, which has an exponential character. However, after talking with several physics teaching students, we discovered that the students perceive the exponential function mainly on an intuitive level. Conscious work with a given concept is rare. The interviews pointed to the fact that students' experiences with the exponential function are mainly based on physics lessons and less on mathematics lessons. In mathematics education, the exponential dependence explicitly occurs only in the later stages of the educational program - experience with physics and natural intuition, therefore, precede conscious math experience and purposeful work with a specific mathematical function. However, recent research results indicate that when solving physics problems, it is essential to know both the concept (here, it is an exponential function) and the context (which is a specific situation using the given function). In this paper, we focus on selected current trends related to the change of the paradigm of physics and mathematics education, which are gradually abandoning the teaching of comprehensive concepts and moving towards gradually building concepts using a stimulating, intelligently designed environment for student learning. As part of the gradual construction of concepts, one inevitably uses prior knowledge, including knowledge one does not even know he has, even in ways that appear to be without apparent logical reasoning or analysis. We will take a closer look at the intuitive concepts related to the exponential function in physics contexts among recent high school graduates, i.e., students of introductory university courses.

Keywords:

Tacit knowledge, exponential function, college physics, concept formation.