Practice Makes (Nearly) Perfect: Solving ‘Students‐and‐Professors’‐Type Algebra Word Problems

Abstract

Three experiments with university students (Ns = 40, 36, and 36) who were non-math majors explicitly examined whether repetition in performing 'students-and-professors'-type algebra word problems, which have been shown in the past to be vexingly difficult even for more advanced students, would spontaneously lead to higher rates of correct answers. Word order and situation model specificity were also examined to determine their effects on the rate of improvement. The strongest predictor of students producing correct equations (i.e., not producing the typical 'reversal error') was practice: In all experiments, participants spontaneously improved in equation accuracy almost to ceiling levels as they progressed, despite receiving no feedback. Tentative support is provided for the pedagogical value of repetition in solving problems, along with varying the wording of the problems.

Synthesis of discipline-based education research in physics

“…Cohen and Kanim [109] studied occurrences of the algebra "reversal error" in both algebra and physics contexts, concluding that sentence structure was the most influential factor in guiding translation of sentences expressing relationships among variables into equations. More recently Christianson, Mestre, and Luke [163] found that the reversal error essentially disappears as students practice translating algebraic statements into equations, despite never being given feedback on whether or not their equations were correct.…”

Influence of additive and multiplicative structure and direction of comparison on the reversal error

“…However, word order matching supposes the existence of an automatism which leads directly from the surface level to the model of the problem without producing a reflection about the situation model. In this case, we adopt the term Bsituation model^from Christianson, Mestre, and Luke (2012) as Bthe global representation of a given text that is built up in the mind of a reader or listener as words are recognised and sentences are parsed^(p. 811). This representation differs substantially from a text-level representation, and in fact, situation models Bmay incorporate previous experiences, and hence also previous textbases, regarding the same or similar situations.…”

Gesture and Vocabulary Learning in a Second Language

“…We added item order to the analysis (cf. Christianson, Mestre, & Luke, 2012) to identify potential interference effects as well as to determine whether any observed interference effects varied as a function of gesture condition.…”