Abstract:

Since 2019, we started a project to analyze and improve the numerical strategies used by students when solving physics problems that require calculations and numerical methods. Our current research looks at the development of physical and mathematical concepts based on their relationship with arithmetic, and from this, we develop the numerical cutting strategies that students apply when solving basic physics problems. Our design considers the use of a learning cycle based on concept exploration activities, class discussions, practice problem solving, and problem solving (ACEP cycle).
In general, when solving exercises and activities, the emphasis is on using simple numerical strategies based on the concept of straight lines. Specifically, in problem-solving activities, students solve complex, non-routine situations that require a variety of algebraic skills and numerical approaches. As a result, students use physical concepts and calculus tools to model solutions to proposed problems, while using arithmetic and numerical strategies to solve problems. At the end of each learning cycle, students reflect on the connections between physics, analysis, and arithmetic with teacher guidance.

In this work, we show several complex problems and the analysis of answers of students. Some of the problems are planetary motion and Kepler and gravitation laws, rocket motion and conservation of physical laws, charged particle motion and Lorentz`s law, phase transitions and phase change materials.
The first question concerns students' concepts of planetary motion and its importance to understanding the universe and the formal development of mathematics and science. The second refers to the rocket's motion, which takes into account various physical factors such as change in mass and conservation of linear momentum. The third problem is to describe the motion in space of a charged particle in presence of electric and magnetic forces. The final problem is devoted to analyzing the physical behavior of phase change materials.

The obtained results show that students improve their understanding of physics and analytical concepts while learning classical numerical methods.

Keywords:

Dynamical systems, Tec21, Problem Based learning, Educational Innovation, Higher Education.