Abstract:

Beside teachers’ explanations, problem solving is the traditional way to acquire physics concepts. This paper refers to the use of computer tools in order to enhance the efficacy of problem solving in physics learning.
Let us distinguish three typical stages of problem solving activities, which we will name Exploration, Solution, and Verification. They are depicted below, together with some well-known software that we propose as support in these three stages in physics learning.

(1) Exploration
The problem is usually posed by a textual description, possibly with pictures. In our idea, the teacher presents the problem in the form of an already worked out virtual experiment (i.e. computer simulation) together with a list of questions. In order to gain familiarity with the problem, the student explores the simulation, looking at the dynamics of the system components and variables in the light of the given questions.

(2) Solution
The student is asked to set down a mathematical model, i.e. a set of equations, to capture the behavior of the physical system, and then carry out the necessary algebraic and/or numerical calculations. In this phase, we exploit computer algebra systems to save the student time and mental energy.

(3) Verification
At the end, the correctness of the solution must be checked. Here we propose that the student return to the virtual experiment and compare his results with the virtual ones. If the comparisons succeed with respect to diverse initial conditions, confirmation is obtained that the solution is correct.
We are now trying the above work scheme for first Physics courses at university level at the Naval Academy of Leghorn, using Interactive Physics and Maxima. Benefits from this kind of systematic use of computer supports have emerged. In particular:
(a) Engagement and autonomy
The use of virtual experiments facilitates a personal grasp of the problem, as well as avoiding possible misunderstandings of textual descriptions. Final comparisons between the student’s own results and those of the virtual experiments enhance the awareness of the reliability of one’s own solution, without additional teacher intervention. This can sensibly augment homework effects.
(b) Solution insight
When, as often happens, the first solution attempt is either incorrect or incomplete, the student must necessarily go back to the Exploration and/or Solution steps. Thus, a cycle is entered to revise the mathematical model, which can indeed lead to a real comprehension of the problem with its solution. Without computer support, however, even a few refinements can appear highly time and energy consuming, so that the student might be tempted to abandon the task prematurely. Conversely, with computer algebra, the time required by the three learning stages is reduced to an amount which can be willingly sustained by the student.
The feeling of autonomy, with the perception of being relieved from tedious technical efforts, proves to be highly motivating and encourages the student to seek a full understanding of the problem. Actually, by lessening technical efforts, reflection on and comprehension of true physical aspects are amplified. In a sense, what is (and always has been) desirable seems to become quite viable due to the use of computer tools.

Keywords:

Physics learning, problem solving, computer support, virtual experiments, computer algebra.