From natural language to mathematical representations: A model of ‘mathematical reading'

Mathematical representations such as equations can account for or unify a large class of semantic structures of arithmetic word problems, each of which can in turn be expressed linguistically. In this paper we describe how a computer-based learning environment, which addresses linguistic and conceptual difficulties that children experience in understanding and solving word problems, is helping elementary-level students to 'see' linguistic descriptions in quantitative or mathematical terms. Past cognitive models have avoided the process of reading, but here a conceptual word analyser parses word problems into unambiguous conceptual representations of the quantities and actions in the word problem. Reading comprehension thus overlaps with mathematical comprehension. Instructional tools allow students to explore connections between representations by manipulating icons. Dynamic linkage of representations allows students to manipulate one representation and see the effect on analogous representations of the problem immediatly. A prototype version of some of these graphics tools is providing preliminary evaluation as to students' learning choices and future design characteristics of the learning environment.