Dimensionally Guided Synthesis of Mathematical Word Problems

Abstract

Mathematical Word Problems (MWPs) are important for training students' literacy and numeracy skills. Traditionally MWPs have been manually designed; an effective automated MWP generator can significantly benefit education and research. The goal of this work is to efficiently synthesize MWPs that are authentic (i.e., similar to manually written problems), diverse (i.e., covering a wide range of mathematical tasks), and configurable (i.e., varying difficulty levels and solution characteristics). This is challenging because a generated problem needs to both exhibit a well-founded mathematical structure and also an easily understood natural language story. Our key insight is to leverage the important role that dimensional units play in MWPs, both textually and symbolically. We first synthesize a dimensionally consistent equation and then compose the natural language story via a bottom-up traversal of the equation tree. We have realized our technique and extensively evaluated its efficiency and effectiveness. Results show that the system can generate hundreds of valid problems per second with varying levels of difficulty. More importantly, we show, via a user study with 30 students from a local middle school, that the generated problems are statistically indistinguishable from actual textbook problems for practice and examination.