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Session 2553

PROBLEM SOLVING IN TWO DIMENSIONS

G. F. Paskusz

University of Houston

ABSTRACT

Incoming freshmen are notoriously deficient in problem solving skills. In our freshman problem solving course we are primarily concerned with enhancing students’ skills in solving word problems, problems which yield to logical analysis, and finally problems requiring a good deal of imagination for their solution.

An excellent collection of word problems requiring only algebra in their solution can be found in Mildred Johnson’s “ How to Solve Word Problems in Algebra”.

The second type of problem, those requiring logical analysis for their solution, is easily obtained from a plethora of books on puzzles.

Certain types of puzzles lend themselves to be used as problems of the third type. But a really challenging problem can be design in Abbott’s “Flatland”. Abbott postulates a two dimensional world and in less than 100 pages describes this world, its inhabitants, some of its history and workings. Much is left unsaid and leaves room for postulating problems to be solved. Some examples are transportation, utilities, written communications, etc. These topics lend themselves to team based term projects.

COURSE OBJECTIVES

Incoming college freshmen are notoriously deficient in problem solving skills. They are compulsive memorizers and users of formulas and of teacher-certified algorithms. When confronted with a new type of problem, they tend to use a seemingly related algorithm without ever wondering if their solution makes sense. So, for example, in a pretest the problem statement,

Write an equation using the variables S and P to represent the following statement: “There are six times as many students as professors at this university.” Use S for the number of students and P for the number of professors

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Paskusz, G. F. (1998, June), Problem Solving In Two Dimensions Paper presented at 1998 Annual Conference, Seattle, Washington. 10.18260/1-2--7359