Understanding and solving arithmetic word problems: A computer simulation

In this paper, I describe a computer program, WORDPRO, which simulates the psychological processes involved when third-grade children understand and solve simple arithmetic word problems. Both the implementation of the program and its performance on a set of sample problems are presented. WORDPRO is a useful research tool in that it demonstrates the sufficiency of the theory upon which it is based, assists in communicating that theory to other researchers, and provides a sources of empirical predictions for experimental tests of the theory.     

Achromatic color categories

Sternheim and Boynton’s (1966) continuous judgmental color-naming technique was used to assess the elemental nature of achromatic colors. Results from three subjects indicate that the names “black” and “white” are necessary and sufficient to describe achromatic test lights associated with the name “gray.” On the basis of the criteria that establishes a color as elemental, black and white were confirmed as elemental, whereas gray was not. These findings support the assumption of various opponent processing models that there are only two elemental achromatic sensations. In addition, the results support Hering’s (1920) view that black and white differ from the paired-chromatic opponent colors in that they are not mutually exclusive.     

Short-term memory processes in counting

Four experiments examined the memory processes used to maintain location in a counting sequence. In Experiment 1, subjects who rapidly counted forward omitted many repeated-digit numbers (e.g., 77), as found previously with backward counting. Subjects in Experiment 2 counted backward with normal auditory feedback or with headphones through which white noise was channeled. In both cases, repeated-digit errors predominated, suggesting that the contents of short-term memory, rather than auditory sensory memory, are checked during counting. In Experiment 3, subjects silently wrote counting responses, and the omission errors resembled those in vocal counting. Repetition errors were also found and attributed to phonological recoding failures. Articulatory suppression in Experiment 4 greatly increased the number of repetition errors in the written counting task. A model of the counting process was proposed according to which subjects keep track of their location in the counting sequence by monitoring phonologically coded short-term memory representations of the numbers.     

Differential effects of high-level and low-level postpassage questions

This experiment compared the effects of high-level and low-level postpassage questions, when presented immediately after the passage segment containing the answer to the question, on college students' free recall of expository prose passages. Low-vocabulary subjects' recall of high-level information not specifically quizzed by the postpassage questions was significantly greater in the condition in which the questions quizzed a high-level unit than in the low-question and no-question conditions, p less than .05. These results are interpreted as being consistent with a direct-access explanation which assumes that questions presented in close temporal contiguity to the quizzed information directly access that information in memory and that fewer associative links have to be traversed in the spread of activation from high-level units to other related information in the hierarchy. The effect of type of question in this experiment was compared with that found in an earlier experiment (Wilhite, 1982) involving delayed question presentation.