The efficiency of algorithms—misconceptions

Abstract

The implementation of a new computer science (CS) curriculum in high schools which includes all the basic elements of traditional CS programs, motivated a research to determine how students conceive the very fundamental notion of efficiency. Since this was the first time that algorithm efficiency was integrated into a high school curriculum, our study was crucial for further implementation of the program. This paper describes a study that revealed misconceptions in perceiving the efficiency of algorithms by high school students. We discuss the results, provide some indication of the roots of these misconceptions, suggest ways to prevent them, and recommend further research.

Introduction

A new computer science (CS) curriculum has been designed and is now being implemented in high schools (Gal-Ezer, Beeri, Harel, & Yehudai, 1995). While there has been considerable activity regarding CS curricula on the college and university levels over the years, on the high school level, development has been somewhat slower, due in part to the lack of adequate separation between CS and computer literacy or computer applications. The new curriculum currently being implemented is in a sense a break-through since it combines conceptual and practical computing issues in a zipper-like fashion, with an emphasis on the basics of algorithmics, and introducing, for the first time, notions of algorithmic correctness and efficiency.

The design of efficient algorithms to solve algorithmic problems is one of the most important research fields in CS. Good algorithm design is crucial to the performance of all software systems and therefore essential in every CS program of study. The study of algorithms gives the learner insight into the problems involved in providing techniques for solutions that are independent of programming languages or other implementational aspects.

Efficiency and complexity are pervasive themes throughout the study of algorithms, however they are considered advanced issues and therefore were not included in high school CS curricula in the past. Even in many university programs, they were not usually included in the introductory course, but only when teaching data structures. Thus, it was important to design a study to examine whether the curriculum suits high school students and to suggest ways to revise the materials if that was found to be necessary, depending on the outcomes of the research.

Recognizing the important contribution that research on misconceptions in relation to mathematics and science education made to the teaching of these fields (Eylon and Lynn, 1988, Fischbein, 1987, Hart, 1981, Osborne and Freyberg, 1985, Perkins and Simmons, 1988, Stavy and Tirosh, 1996a, Stavy and Tirosh, 1996b), we believed that exposing misconceptions in relation to the concept of efficiency was crucial to the examination of the CS high school curriculum.

Initial observations of the implementation of the program, interviews with teachers and students, and examination of students' achievements, confirmed our assumption that efficiency is a difficult concept to grasp. The goal of our study was to find out what misconceptions students hold regarding the notion of efficiency. We did not attempt to uncover the source of the misconceptions, nor did we systematically examine ways to prevent them. We will, however, provide some assumptions and clues regarding reasons for the misconceptions together with some ideas on how to prevent them; however, these need to be further investigated.