Анализ практических задач по математике: теоретическая модель и опыт применения на уроках
PISA results show that math problems with everyday context are typically difficult for Russian students. Are these difficulties caused either by exactly everyday context or by lack of some general problem solving skills required when solving unusual contextual problems? In a qualitative study we analyzed mistakes of 8-10-graders (n=60) and showed that a minor part of their mistakes was due to requirements to make math model that are specific requirements of contextual problems. Vast majority of mistakes was due to general problem skills such as visual representation skills, monitoring of solving process, validating of decision.
The patterns of knowledge application in new situations are explored from the perspectives of modeling and transfer. We provide an overview of studies to compare these two conceptions and get a comprehensive idea of which psychological processes are involved in knowledge application, what will change in research and teaching practices if the conceptual frameworks change, and how these conceptions can contribute to each other. We show that analyzing the problem structure and comparing problem models in different representational systems are the key prerequisites for a successful knowledge application in both conceptions. Based on the data obtained, we draw conclusions about approaches to education promoting effective knowledge application and about training problem assessment criteria.
Institutions affect investment decisions, including investments in human capital. Hence institutions are relevant for the allocation of talent. Good market-supporting institutions attract talent to productive value-creating activities, whereas poor ones raise the appeal of rent-seeking. We propose a theoretical model that predicts that more talented individuals are particularly sensitive in their career choices to the quality of institutions, and test these predictions on a sample of around 95 countries of the world. We find a strong positive association between the quality of institutions and graduation of college and university students in science, and an even stronger negative correlation with graduation in law. Our findings are robust to various specifications of empirical models, including smaller samples of former colonies and transition countries. The quality of human capital makes the distinction between educational choices under strong and weak institutions particularly sharp. We show that the allocation of talent is an important link between institutions and growth.