Mathematical Word Problem Generation from Commonsense Knowledge Graph and Equations

There is an increasing interest in the use of automatic mathematical word problem (MWP) generation in educational assessment. Different from standard natural question generation, MWP generation needs to maintain the underlying mathematical operations between quantities and variables, while at the same time ensuring the relevance between the output and the given topic. To address above problem we develop an end-to-end neural model to generate personalized and diverse MWPs in real-world scenarios from commonsense knowledge graph and equations. The proposed model (1) learns both representations from edgeenhanced Levi graphs of symbolic equations and commonsense knowledge; (2) automatically fuses equation and commonsense knowledge information via a selfplanning module when generating the MWPs. Experiments on an educational gold-standard set and a large-scale generated MWP set show that our approach is superior on the MWP generation task, and it outperforms the state-of-the-art models in terms of both automatic evaluation metrics, i.e., BLEU-4, ROUGE-L, Self-BLEU, and human evaluation metrics, i.e, equation relevance, topic relevance, and language coherence. A mathematical word problem (MWP) is a coherent narrative that provides clues to the underlying correct mathematical equations and operations between variables and numerical quantities (Verschaffel et al., 2000; Cetintas et al., 2010; Moyer et al., 1984). Table 1 shows one such problem where students are asked to infer the counts of chickens and rabbits. Mathematical Word Problem Equations Solutions Chickens and rabbits were in the yard. Together they had 27 heads x y 27 x 11 and 86 legs. How many chickens and rabbits were in the yard? In this paper, our objective is to automatically generate well-formed MWPs.