Performance characteristics of retarded and normal students on pattern recognition tasks

The purpose was to compare the performance of normal and educable mentally retarded children on pattern recognition tasks. Pattern recognition was assessed by the administration of 96 pattern tasks which measured the ability of children to find: (a) duplicate patterns and same elements as presented in model pattern sequences; (b) opposite patterns and same elements as presented in model pattern sequences; and (c) duplicate patterns but different elements than presented in model pattern sequences. The normal and mentally retarded children were matched on mental age derived from individual and group intelligence tests. Results indicated significant differences in performance measures between groups and various pattern tasks. The data support the suppositions that: (a) mentally retarded children and normal children show the same type of progression through the hierarchical arrangement of pattern tasks; and (b) mentally retarded children show a slower progression through the hierarchy than normal children when matched on mental age. Educational implications from this study are discussed.     

Latent growth curves within developmental structural equation models

This report uses structural equation modeling to combine traditional ideas from repeated-measures ANOVA with some traditional ideas from longitudinal factor analysis. A longitudinal model that includes correlations, variances, and means is described as a latent growth curve model (LGM). When merged with repeated-measures data, this technique permits the estimation of parameters representing both individual and group dynamics. The statistical basis of this model allows hypothesis testing of various developmental ideas, including models of alternative dynamic functions and models of the sources of individual differences in these functions. Aspects of these latent growth models are illustrated with a set of longitudinal WISC data from young children and by using the LISREL V computer program.     

The Impact of a Science Education Game on Students’ Learning and Perception of Inhalants as Body Pollutants

This study investigated the knowledge gains and attitude shifts attributable to a unique online science education game, Uncommon Scents. The game was developed to teach middle school students about the biological consequences of exposure to toxic chemicals in an environmental science context, as well as the risks associated with abusing these chemicals as inhalants. Middle school students (n = 444) grades six through eight participated in the study consisting of a pre-test, three game-play sessions, and a delayed post-test. After playing the game, students demonstrated significant gains in science content knowledge, with game usability ratings emerging as the strongest predictor of post-test content knowledge scores. The intervention also resulted in a shift to more negative attitudes toward inhalants, with the most negative shift occurring among eighth grade students and post-test knowledge gains as the strongest predictor of attitude change across all grade levels. These findings suggest that the environmental science approach used in Uncommon Scents is an efficacious strategy for delivering both basic science content and influencing perceived harm relating to the inhalation of toxic chemicals from common household products.     

Zooming in on infinitesimal 1–.9.. in a post-triumvirate era

The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be alternative ways in which one could formalize mathematical ideas about infinity. We discuss the key ideas about infinitesimals via a proceptual analysis of the meaning of the ellipsis “...” in the real formula \(\hbox{.999\ldots = 1}\). Infinitesimal-enriched number systems accommodate quantities in the half-open interval [0,1) whose extended decimal expansion starts with an unlimited number of repeated digits 9. Do such quantities pose a challenge to the unital evaluation of the symbol “.999...”? We present some non-standard thoughts on the ambiguity of the ellipsis in the context of the cognitive concept of generic limit of B. Cornu and D. Tall. We analyze the vigorous debates among mathematicians concerning the idea of infinitesimals.