Following the Template: Transferring Modeling Skills to Nonstandard Problems

This study seeks to analyze how students apply a mathematical modeling skill that was previously learned by solving standard word problems to the solution of word problems with nonstandard contexts. During the course of an experiment involving 106 freshmen, we assessed how well they were able to transfer the mathematical modeling skill that is used to solve standard problems to the solution of nonstandard ones that had an analogous structure. The results of our research show that students had varying degrees of success applying the different stages of modeling depending on whether they were solving a familiar problem (involving near transfer) or one that had an unfamiliar context (involving far transfer): in cases of near transfer, students applied the template formally even though it did not align with the text of the new word problem, which complicated further interpretation. In cases of far transfer, students chose to solve the problem by using an ordinary method of selecting a solution by trial and error in preference to the use of modeling. Thus, the application of the modeling skill as a multistage process is complicated when solving nonstandard problems involving either near or far transfer.     

Sample duration and type of stimuli in delayed matching-to-sample in rhesus monkeys

Two experiments were performed to determine the effect of sample duration (0.1, 2, and 4 sec), delay interval (.03, 4, 8, 16, and 32 sec), and type of stimulus (color and shape) on the matching performance of rhesus monkeys. In Experiment 1, the 15 possible delay-duration combinations were randomly presented in blocks of 15 trials. In Experiment 2, each duration was held constant and the five delays randomly presented. Then each delay interval was held constant with the three durations randomly varied. Matching performance increased as sample duration increased (ps < .01 and .005), while length of delay did not significantly affect performance. The type of stimuli paired in the matching test significantly affected performance (ps < .05 and .10) with the shape/shape choices leading to the poorest performance. Stimulus discriminability and amount of training with brief sample durations were implicated as significant determinants of matching performance.     

Children's internal organization of locative categories

4 locative categories were investigated to determine whether their examples were organized according to the prototype/nonprototype distinction. A ranking task was presented to 30 adult subjects to see whether they would judge those instances which had been designated as prototypes by the experimenter to be the best exemplars of each category. An elicited-drawing task was administered to see whether there was a preference for drawing adult-designated prototypical instances. A matching task was presented to determine whether fewer errors would occur in response to adult-designated prototypical instances. The latter 2 tasks were presented to 4-year-olds, 6-year-olds, and adults, with 17 subjects in each group. The results provide strong evidence of prototype/nonprototype organization in 3 of the locative categories and weak evidence in the fourth. Tentative conclusions regarding the development of such organization are drawn.