Abstract:

Problem-solving is a power tool to enhance the understanding and test the acquisition of concepts in technical and scientific matters, in particular in Physics courses. Indeed, some Intelligent Tutoring Systems have been realized in order to guide students, while they solve problems in the context of introductory courses. Such systems are each time equipped with a teacher’s set of solving equations, which is analyzed and compared with the student’s ones, in order to give advising and evaluation.
We present a computer based problem-solving environment for Physics, which aims to stimulate self-assessment and learning. The assistant can also produce an automatic evaluation of the whole solution worked out by the student, that can be indeed useful for the teacher. The idea is to treat problems at University first and second year level, which are typically solved by means of algebraic and differential equations. We restart from what is reported in two recent papers, describing assistants for learning of spreadsheet and database problem-solving techniques. There, a line is adopted such that guidance and assessment mainly take place by comparison of the results from the student’s solution with respect to the teacher’s one.
Our assistant presents two different interfaces: one for the teacher and one for the student. The teacher must describe the problem and give a solution for it. Then, the student works out his solution with the help of the computer system, which is able:
- to show the correct results, as number values and graphics of functions yielded by the teacher’s solution;
- to give automatic assessment of the student's results (numerical and functional);
- to offer suggestions prepared by the teacher.
After having posed the problem as a set of possibly correlated questions, the teacher assigns a weight to each question, and a cost to each suggestion. Obviously, the final score is diminished of the cost of the used hints. Thus, the student get a fair and impartial assessment of his overall performance.
In a physical system, several regimes with various interesting behaviours can be identified. In our working environment, the teacher can record specific situations as suitable data samples. The student will be able to recover in turn such samples, in order to appreciate peculiar aspects of the problem, always with the help of the assistant.
Our computer assistant is based on Microsoft Excel, enhanced with a numerical integrator of differential equations and derivation capabilities, while the Solver component of Excel is used to treat algebraic equations. The ability of the computer system to solve algebraic and differential equations, is by itself an aid for the student, who can be relieved from tedious calculation burdens. Moreover, it becomes possible to consider aspects of physical phenomena, which are described by equations difficult to solve with traditional analytical methods, such as the motion of a projectile with air friction force.
The assistant exploits Excel graphic capabilities to show the functions obtained by integration or derivation. It is also possible to observe the motion of material points on their trajectories. All inspections can be done for different initial data, and of course with respect to teacher’s data samples. As verified in several class lessons and assessment tests, the approach stimulates to deepen the understanding of physical features, just trying to retrieve the solution of the problem.

Keywords:

Problem-solving assistants, Tutoring Systems, Assessment, Physics problems, Excel working environment.