The authors define two mathematical cognitive verbs which are fundamental to the development of mathematical thinking and reasoning. They distinguish between 'describing' and 'explaining' in relation to doing mathematics, rather than using them interchangeably.

Experiments are reported in which semantically interrelating sentences were presented to subjects as discrete items, and inference tests were given to measure the degree to which the similar information had been stored in the same memory system. Results suggest that verbal information is sometimes encoded into an episodic system. (Author/RM)

Investigated third and sixth graders' understanding of factive presupposition using two tasks: one requiring an abstract truth judgment of the verb complement, the other calling for informal judgment of consistency between the target sentence and the negation of its complement. Results indicated the development of factive presupposition is an…

Investigated the effect of problem wording on solving arithmetic word problems by first graders. Found that wording is a crucial component in solving difference problems. Results suggest that further research on word problem-solving processes focus on the interaction between linguistic comprehension and mathematical reasoning. (AA)

This study had two purposes: (1) to determine when children distinguish ambiguous from precise messages and when they can resolve ambiguity through additional questioning, and (2) to identify whether implicit messages were more difficult to identify than explicit ones. All children found ambiguous messages significantly more difficult to…

Two experiments assessed whether children's difficulty with word problems can be attributed to difficulty in comprehending abstract or ambiguous language. The subjects were 38 first-, 36 second-, and 36 third-graders. The resulting theory of arithmetic word problem solving may represent a theoretical problem-solving model. (TJH)