Why are Algebra word problems difficult? Using tutorial log files and the power law of learning to select the best fitting cognitive model

Abstract. Some researchers have argued that algebra word problems are difficult for students because they have difficulty in comprehending English. Others have argued that because algebra is a generalization of arithmetic, and generalization is hard, it’s the use of variables, per se, that cause difficulty for students. Heffernan and Koedinger [9] [10] presented evidence against both of these hypotheses. In this paper we present how to use tutorial log files from an intelligent tutoring system to try to contribute to answering such questions. We take advantage of the Power Law of Learning, which predicts that error rates should fit a power function, to try to find the best fitting mathematical model that predicts whether a student will get a question correct. We decompose the question of “Why are Algebra Word Problems Difficult? ” into two pieces. First, is there evidence for the existence of this articulation skill that Heffernan and Koedinger argued for? Secondly, is there evidence for the existence of the skill of “composed articulation ” as the best way to model the “composition effect” that Heffernan and Koedinger discovered?