Development of Mathematical Knowledge in Young Children: Attentional Skill and the Use of Inversion

The principle of inversion, that a + b ? b must equal a, is a fundamental property of arithmetic, but many children fail to apply it in symbolic contexts through 10 years of age. We explore three hypotheses relating to the use of inversion that stem from a model proposed by Siegler and Araya (2005 Siegler , R. S. , &; Araya , R. ( 2005 ). A computational model of conscious and unconscious strategy discovery . In R. V. Kail (Ed.), Advances in child development and behavior (pp. 1 – 42 ). New York , NY : Elsevier .[Crossref] , [Google Scholar]). Hypothesis 1 is that greater calculational skill is related to greater use of inversion. Hypothesis 2 is that greater attentional skill is related to greater use of inversion. Hypothesis 3 is that the relation between attentional skill and the use of inversion is particularly strong among children with high skill in calculation. We found suggestive evidence for Hypothesis 2 and clear evidence for Hypothesis 3, indicating that for children who are strong at calculation, attentional flexibility is related to use of inversion.     

Mechanisms of motivation–cognition interaction: challenges and opportunities

Recent years have seen a rejuvenation of interest in studies of motivation–cognition interactions arising from many different areas of psychology and neuroscience. The present issue of Cognitive, Affective, & Behavioral Neuroscience provides a sampling of some of the latest research from a number of these different areas. In this introductory article, we provide an overview of the current state of the field, in terms of key research developments and candidate neural mechanisms receiving focused investigation as potential sources of motivation–cognition interaction. However, our primary goal is conceptual: to highlight the distinct perspectives taken by different research areas, in terms of how motivation is defined, the relevant dimensions and dissociations that are emphasized, and the theoretical questions being targeted. Together, these distinctions present both challenges and opportunities for efforts aiming toward a more unified and cross-disciplinary approach. We identify a set of pressing research questions calling for this sort of cross-disciplinary approach, with the explicit goal of encouraging integrative and collaborative investigations directed toward them.