Reduction -- an abstract thinking pattern

Abstract

Abstraction has been the focus of many researches in mathematics education and to some extent in computer science education. Abstract thinking characterizes the theoretical foundations of computer science, where reduction is one important abstract thinking pattern. In a previous work, we discussed the issue of reductive thinking among high school students in relation to computational models -a theoretical unit. This unit requires abstract thinking in many aspects. Our findings in relation to reductive thinking showed that many students preferred direct, non-reductive solutions, even if reductive solutions could have significantly decreased the design complexity of the solution. This study motivated the current study where we examine the issue of reductive thinking among university students. The findings of this preliminary study are demonstrated by students' solutions to questions in assignments given in the computational models course. We found that even among university students in a very prestigious academic institution with very high entrance requirements abstraction is a real obstacle as reduction is not easily understood and used. This encourages us to further investigate this phenomenon.