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"Learning by doing" in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children's ability to "see" significant abstract structures in mathematical situations. The reflection necessary for such seeing is motivated by activities and contexts that emphasize affective and social aspects. Natural language, as a representation already familiar to children, is key in these activities, both as a means of mathematical expression and as a link between situations and various abstract representations. These tools support children's ownership of a mathematical problem and its expression; remote sharing of problems and data; software interpretation of children's own word problems; play with dynamically linked representations with attention to children's prior connect...

Understanding arithmetic word problems involves a complex interaction of text comprehension and mathematical processes. This article presents a computer simulation designed to capture the working memory demands required in “bottomup” comprehension of arithmetic word problems. The simulation's sentence-level parser and text integration component reflect the importance of processing the problem from its original natural language presentation. Children's probability of solution was analyzed in exploratory regression analyses as a function of the simulation's sentence-level and text integration processes. Working memory variables measuring the combined effects of concepts to remember and text integration inferences account for a significant proportion of variance in children's solution probabilities across the first four grade levels (K-3). Consistent with previous results from others, which highlighted the significance of small changes in problem wording, the simulation offers a process-oriented perspective as to why natural language presentation constrains the comprehension of mathematical relationships.

Theories and computational models of metaphor comprehension generally circumvent the question of metaphor versus “anomaly” in favor of a treatment of metaphor versus literal language. Making the distinction between metaphoric and “anomalous” expressions is subject to wide variation in judgment, yet humans agree that some potentially metaphoric expressions are much more comprehensible than others. In the context of a program which interprets simple isolated sentences that are potential instances of cross-modal and other verbal metaphor, I consider some possible coherence criteria which must be satisfied for an expression to be “conceivable” metaphorically. Metaphoric constraints on object nominals are represented as abstracted or extended along with the invariant structural components of the verb meaning in a metaphor. This approach distinguishes what is preserved in metaphoric extension from that which is “violated”, thus referring to both “similarity” and “dissimilarity” views of metaphor. The role and potential limits of represented abstracted properties and constraints is discussed as they relate to the recognition of incoherent semantic combinations and the rejection or adjustment of metaphoric interpretations.

A natural language interface has been developed to facilitate the use of statistical packages. Queries are parsed into “case frames” based on statistical primitives. A rule-based expert system uses the case frame to choose a statistical test and generate a batch file that, when executed, answers the query.