MIT researchers and colleagues at the University of Washington have developed a computer system that can automatically solve the type of word problems common in introductory algebra classes.
According to Nate Kushman, a graduate student and lead author on the new paper, the work is in the field of “semantic parsing,” or translating natural language into a formal language. “In these algebra problems, you have to build these things up from many different sentences,” he says. “The fact that you’re looking across multiple sentences to generate this semantic representation is really something new.”
The researchers’ system exploits two existing computational tools. One is the computer algebra system Macsyma, developed at MIT in the 1960s, which can distill algebraic equations into a few common templates. The other is a sentence parser, which represents the relationships between words in a sentence as a treelike diagram.
To train their system to map elements in the parsing diagram onto Macsyma’s equation templates, the researchers used hundreds of examples from an online discussion site. The system analyzed hundreds of thousands of “features” of those examples, such as the syntactical relationships between words or words’ locations in different sentences. Kushman also included a few “sanity checks,” such as whether the solution yielded by a particular equation template was a positive integer.
The work could lead to educational tools that identify errors in students’ reasoning and to systems that can solve more complicated problems in geometry, physics, and finance.