Word Problem Solving

Abstract

Education plays a vital role in shaping up one’s life. Education in early childhood includes learning from different activities where counting and other concepts of mathematics act as major building blocks. Mathematics is not just a subject to be taught in schools, but also it has myriad applications in our daily lives such as counting the total number of stationery items, calculating their individual prices, and adding them up for a purchase made in a grocery shop. This kind of real world situations are posited in mathematical word problems which are an essential part of a child’s learning that requires natural language understanding (NLU) as well as knowledge of mathematical operations. Mathematical Word Problem Solvers can assist both students and teachers. It is a challenging field and this thesis attempts to provide NLP solutions for math word problems in English and Indian languages. Our approach for developing word problem solvers follows a pipeline. For a word problem, first, we identify the relevant operands and required operations. In the second step, we form an equation from these identified components. The first two stages can be combined to generate equations at once using neural network based approaches. At the last stage, the equation is solved by a mathematical solver to get the final solution. We focus primarily on the first two stages of this pipeline. We developed solvers using three kinds of approaches: frame based, composition of classifiers based, and end-to-end neural based. We also shed light on the limitations of the current automatic solvers with respect to the data. We designed different data augmentation techniques to overcome the data scarcity problem. As a part of resource building, we developed word problem datasets and solvers for Indian Languages. In addition to this, we compared different models related to our developed approaches. We empirically show the difference in generation of various equation notation types. For this study, we present the results of equations in infix, postfix, and prefix notations. We also show two natural language processing tasks where components of word problem solvers can be utilized. In the first task, we studied the impact of simple number based pre-processing on the performance of machine translation systems. In the second task, we analyze speech transcript texts to extract equation spans. This kind of text is present mainly in transcripts from mathematical domain. For achieving this, we develop an equation identifier and convertor involving math notations for transcripts. This can make the transcripts easily readable for transcripts which have wide usage of mathematical terms.