Translation of algebraic equations and its relation to formal operational reasoning

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Abstract

A large proportion of science major college students are unable to translate even simple sentences into algebraic equations. Given the following sentence: There are six times as many students (S) as professors (P) at this university, most students write the following equation: 6S = P, referred to as the reversal error. In order to overcome the reversal error students need to operate in a hypothetico-deductive manner, i.e., performing a hypothetical operation that makes the group of professors six times larger than it really is (S = 6P). The objective of this study is to investigate the relation between student ability to translate sentences into equations, equations into sentences, and student performance in the following variables: formal operational reasoning, proportional reasoning, and introductory freshmen-level chemistry course. The results obtained show that as the student ability to translate sentences into equations and equations into sentences increases, their mean scores in Chemistry I, formal operational, and proportional reasoning increases. This study has found support for the hypothesis that students who lack formal operational reasoning skills (hypothetico-deductive reasoning) may experience more problems in the translation of algebraic equations.

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