A machine learning approach for the identification of learners' misconceptions in algebraic problem-solving

Misconceptions play a significant role in the learning process as they reflect an inaccurate understanding of a particular concept. Error diagnosis can help teachers and intelligent learning environments determine the most appropriate type of student assistance. Previously, misconceptions were identified using rule-based expert systems (bug libraries) and clustering algorithms. Bug libraries demand extensive work from developers to identify all potential misconceptions and code rules for each one in advance. Additionally, these solutions cannot detect misconceptions for which rules were not explicitly programmed. Clustering-based solutions overcome these drawbacks by automatically identifying misconceptions based on students' most common errors. To effectively and efficiently identify misconceptions, clustering solutions must have a suitable representation of the problem and its steps, and employ machine learning algorithms capable of discerning patterns from them. This paper proposes a solution that utilizes expression trees to represent algebraic problem-solving steps and the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm to identify misconceptions by clustering similar errors in a database containing 1064 steps from 112 students. This database was collected from an intelligent learning system designed to assist in solving first-degree equations. In our final solution, a Natural Language Processing tokenizer was employed to represent each term numerically, which identified 178 homogeneous clusters with minimal noise and few outliers.