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.
