Difficulty level estimation of mathematics problems using machine learning

Abstract

The aim of this research is to design an automatic system that can estimate the difficulty level of mathematics problems in the way that is similar to human judgment. This system helps reduce the teacher workload in the question bank construction and also helps students who want to practice the problems with varieties of difficulty levels for self-learning. Our system started with extracting features from the mathematics problem directly and then using machine-learning algorithms to estimate the difficulty level so that the desired value is consistent with the estimation made by human experts. The designed system extracts feature from the mathematics problems by simulating the human calculation process and counting the number of applying formulas during the optimal path of the problem-solving process, then the features are used for training naive Bayes, neural network, regression, and support vector machine (SVM). The comparative result from the 4 model prediction on the differential calculus dataset shows that the regression model is the best predictor, where the mean absolute error between the machine learning predicted value and the labels from human experts is approximately 0.57 level out of 1 - 5 scales.