The effect of mathematical vs. verbal formulation for finite automata

Abstract

This study examines the capability of high-school students to solve problems related to the Computational model of finite deterministic automata. Specifically, we compared student's achievements when solving verbal "story like" questions to solving the similar problem but formulated mathematically. A questionnaire composed of two questions, each formulated in two ways (verbal and mathematical), was given to the students as part of an exam. Generally, average or weak students got lower grades when they had to solve verbal questions. It was also found that the gap between the student achievements in verbal vs. mathematical questions widened for weaker students and when the teaching and practicing time was reduced. The student mistakes originated from their difficulties to extract a formal language from the story and to translate constrains given in the verbal formulation of the questions correctly. It was also found that when the students were unfamiliar to the content and the context of the story they had difficulties comprehending the text. This in turn caused the student to inaccurately describe the formal language (alphabet and constrains) and thus to design an incorrect automata.