Reductive thinking in computer science

Abstract

This paper discusses the role of reduction in computer science and describes a study on undergraduate students' perception of the concept of reduction. Specifically, based on an analysis of students' answers to questions addressing different computer science topics, we present several findings regarding the ways in which undergraduate students conceive of and apply reduction. These findings can be interpreted within the framework of the tension that exists between the following two factors: The need to think in terms of high levels of abstraction, on one hand, and the fact that reduction introduces a new approach to be used in problem-solving situations, on the other. In addition the paper suggests several teaching applications.

Reductive thinking in a quantitative perspective

“…We feel that these findings lend additional support to the recommendations we gave in a previous paper [2] regarding teaching reductive thinking. Specifically, we strongly believe that reduction should be taught as a fundamental idea, starting as early as CS1.…”

“…The findings indicated difficulties students encountered in applying reduction in the context of this course. The next study [2] was a qualitative, mostly interview-based study that examined the tendency of undergraduate CS students, at different stages of their studies, to use reductive solutions when solving problems taken from a variety of CS areas. The findings indicated an evolving development of reductive thinking: the first-year students hardly ever used reductive solutions, whereas the more mature students exhibited higher levels of awareness of the concept of reduction as well as its potential use in different problem-solving situations.…”

“…The current study is mostly based on the one preceding it in this series. The previous study [2] was qualitative, mostly interview-based, focusing on a small population. Through that study, we gained some insight into undergraduate students' perceptions of reduction, and specifically of black boxes.…”

Do all roads lead to Rome? (Orreductions for dummy travelers)

“…They argue that developing reductive thinking is important and should be emphasized. As a way to this, Armoni and Gal-Ezer (2005) suggest to present, and to encourage students to find, reductive solutions for language-theoretic problems on computational models courses. In they report empirical findings which indicate that university students have difficulties in fully perceiving the notion of reduction.…”

“…Michal Armoni and her co-authors have carried out extensive research on the teaching of reduction in computer science (Armoni, 2004;Armoni & Gal-Ezer, 2005, 2006Armoni, 2009). They argue that developing reductive thinking is important and should be emphasized.…”