Jack Lochhead

DOES COMPUTER PROGRAMMING ENHANCE PROBLEM SOLVING ABILITY? SOME POSITIVE EVIDENCE ON ALGEBRA WORD PROBLEMS

Publisher Summary There is a common intuition among those in computer science education that programming encourages the development of good problem-solving skills. The term “problem solving” has a broader and deeper meaning than what is implied by its educational association with mathematics. This is an exciting idea, especially when one considers how the concept of problem solving has been synonymous with human endeavors of the best possible kind, with the mastery of the physical, social, and intellectual worlds we live in. Computer environments make it possible for students to experience some of the deeper ideas that underlie a correct understanding of what human problem solving entails. Students learn best in settings where they can move from the empirical to the theoretical and back again freely. This coincides with the way real problem-solvers function. Low-cost microcomputers make it possible to incorporate these ideas into mathematics curricula and also into new courses in computer science and computer literacy.

Positive effects of computer programming on students understanding of variables and equations

There is a common intuition among those in computer science that programming helps to develop good problem solving skills . Our work has attempted to isolate the specific factors in programming which enhance mathematical problem solving ability. We have found that a surprising number of college students have difficulty with very simple algebra word problems. However, significantly more students are able to solve these word problems correctly in the context of writing computer programs, than in the context of simply writing an algebraic equation. We obtained similar results in comparing the reading of algebraic equations within computer programs and the reading of algebraic equations by themselves. Computer programming apparently puts an emphasis precisely on the active , procedural semantics of equations that many students lack.

The Mathematical Needs of Students in the Physical Sciences

My task in this paper is to consider proposed changes in the mathematics curriculum from the point of view of a physics teacher. To do that I first need to distinguish between what students ought to be learning and what they do in fact learn. On the surface the present calculus curriculum is ideally suited to the needs of physics students; but a significant change seems in order when one examines the type of knowledge students are currently gaining. Thus the bulk of my paper will deal with certain problems in the calculus curriculum that I would hope will be effectively addressed by any new curriculum.

A Lower-Division Mathematics Curriculum Consisting of a Year of Calculus and a Year of Discrete Mathematics

The authors considered the problem of writing a curriculum for the first two years of college mathematics that would consist of a year of calculus and a year of discrete mathematics. They imposed the further constraint that it should be possible to take either year alone, and therefore to take both in either order. It was recognized that this constraint exacts certain costs, such as some need for repetition and fewer opportunities for cross-references; but it was intended that the additional flexibility should provide for the needs of a wide variety of undergraduate students, with the understanding that in many cases (e.g. for students concentrating in mathematics, computer science, engineering, or certain physical sciences) additional courses would be needed.