Determining the Sources of Error in a Translation from Sentence to Equation

At least one out of three college students is likely to translate a sentence of the type “There are n times as many x as y ” into y = nx , where n is a given number (e.g., 6) and x , y are English words (e.g., students, professors). Possible sources of this reversal error were explored in a series of six studies. The principal sources were haste, failure to think of checking the equation, failure to base the equation on the meaning of the sentence, and use of nonalgebraic symbols. Students could successfully check when prompted. After a 10-minute classroom intervention on the need for basing the equation on sentence meaning and for checking, immediate success was nearly 100%. A discussion suggests ways to ensure lasting effects.