A new approach: Computer-assisted problem-solving systems

In this research, the author presents the selected and modified three steps in the problem solving strategy based on the problem solving strategies reported by the researchers mentioned before. The developed IPSS (Integrated Problem Solving Strategy Steps) could be summarized as follows:

I. Identifying the Fundamental Principle(s): In the first and most important step, a student should accurately identify and understand the problem. A student should examine both the qualitative and quantitative aspects of the problem and interpret the problem in light of his/her own knowledge and experience. This enables a student to decide whether information is important and what other information may be needed. In this step students must: (i) simplify the problem situation by describing it with a diagram or a sketch in terms of simple physical objects and essential physical quantities; (ii) restate what you want to find by naming specific mathematical quantities; and (iii) represent the problem with formal concepts and principles.

II. Solving: A student uses qualitative understanding of the problem to prepare a quantitative solution. Dividing the problem into subproblems is an effective strategy for constructing the solution. Thus, the solution process involves repeated applications of the following two steps: (i) choosing some useful subproblems and (ii) carrying out the solution of these subproblems. These steps can then be recursively repeated until the original problem has been solved. The decisions needed to solve a problem arisen from choosing subproblems. The two main obstacles can be: (i) lack of needed information and (ii) available numerical relationships that are potentially useful, but contain undesirable features. These choices are promoted if there are only few reasonable options among which a student needs to choose. An effective organization of knowledge has crucial importance in making easy the decisions needed for problem solving. The organization done after applying the particular principle is facilitated by all of a student’s previously gained technical knowledge. The final step contains plugging in all the relative quantities into the algebraic solution to determine a numerical value for the wanted unknown quantity (ies).

III. Checking: In the final step, a student should check the solution to assess whether it is correct and satisfactory and to revise it properly if any shortages are detected by following this checklist: (i) Has all wanted information been found?; (ii) are answers expressed in terms of known quantities?; (iii) are units, signs or directions in equations consistent?; (iv) are both magnitudes and directions of vectors specified?; (v) are answers consistent with special cases or with expected functional dependence?; (vi) are answers consistent with those obtained by another solution method?; (vii) are answers and solution as clear and simple as possible?; and (viii) are answers in general algebraic form?

Those IPSS are expected to eliminate the potential drawback of the LON-CAPA problems/homework and make all students experienced problem solvers in computer-based problems. In the Appendix, a sample problem is presented with these Integrated Problem Solving Strategies steps (IPSS) as screenshots. In the first screen, students are asked to understand and choose related fundamental concept(s). The second display leads to the students’ selecting the correct diagram or sketch to make the concept clear and then to restate the specific mathematical quantities. In the third window, students are expected to fill the equation blanks by selecting parameters from symbolic/mathematical expression boxes and to calculate the numerical quantities with units. The fourth screen encourages students to check the solution steps with the checklist; if the entry is correct on the previous screen, and at the bottom of the page they confirm the numerical result. On the last page the students review the instructor’s solution key.

The current (LON-CAPA) and new design (IPSS) of computer-based problem solving systems was investigated with a pilot study that is detailed below. Also, the perceptions of the volunteer students who attended this pilot were observed.