Problem solving continues to be a major focus of K-12 mathematics education reform. This case study shows how a teacher's middle school mathematics instruction evolved from teaching problem solving as computation exercises to teaching how to select and implement combinations of problem solving strategies. The teacher's thinking about problem…

This article defines "higher level mathematical skills" and details an important class: that of "constructing instances" of mathematical objects satisfying certain properties. Comment is made on the frequency of higher level tasks in undergraduate work. We explain how such questions may be assessed "in practice" without the imposition on staff of…

Enzyme kinetics is a difficult subject for students to learn and for tutors to teach. During the practicals included in the biochemical courses at the Faculty of Chemistry of Universidad Nacional Autonoma de Mexico, we found that the students acquire good training in the calculations to obtain kinetic parameters such as K[subscript m], V[subscript…

This article discusses how children learn to understand the decimal system in very concrete ways, while having fun using beads. When counting the beads, the children learn 5,491 is not simply "five thousand four hundred and ninety-one" but actually 5 thousands, 4 hundreds, 9 tens, and 1 unit. They begin to understand that as they get 10 units,…

This microgenetic study investigated similarities and differences in use and discovery of addition strategies in children with and without mild mental retardation across 24 sessions. Nine children with mild mental retardation in third through fifth grade classrooms and 14 children without mental retardation in kindergarten classrooms were tested…

Federal student loans include a complex consolidation option that gives borrowers the opportunity to combine several loans into a single loan with a longer term to maturity and, for loans originated before July 2006, to convert from a variable- to a fixed-rate loan. The consolidation option adds substantial costs to the federal student loan…

This article explores how students learned to measure tall objects using a clinometer and some basic calculations. Such activities provide opportunities for students and teachers to learn the usefulness of linking mathematics content and science content to real-world problem-solving situations. (Contains 7 figures.)

In this article, rates of return to education for men and women have been estimated for the Spanish case, controlling for the biases appearing in the least squares estimation of the basic Mincerian equation. The results show that the returns for women are greater than those for men. The gender differential increases when taking into account the…

This paper estimates the returns to education for adult male workers in regular and casual wage employment using Indian national survey data at three points in time spanning almost two decades. Both standard and augmented Mincerian wage equations are estimated using a set of human capital measures and other controls after addressing the issue of…

The District of Columbia Tuition Assistance Grant Program (DCTAG), instituted in 1999, allows D.C. residents to attend public colleges and universities throughout the country at considerably lower in-state tuition rates. We use the sharp decline in the price of public colleges and universities faced by D.C. residents to estimate the effects of…

The abacus is a calculating tool that has been used in Asia for thousands of years. Mental abacus calculation is a skill in which an abacus image in the mind is used without the actual physical manipulation of the abacus. Using this method, people can perform extremely rapid and accurate mental calculations. Research indicates that abacus training…

In contrast to most other thermodynamic data, entropy values are not given in relation to a certain--more or less arbitrarily defined--zero level. They are listed in standard thermodynamic tables as absolute values of specific substances. Therefore these values describe a physical property of the listed substances. One of the main tasks of…

College students often experience difficulties in solving physics problems. These difficulties largely result from a lack of conceptual understanding of the topic. The processes of conceptual learning reflect the nature of the causal reasoning process. Two major causal reasoning methods are the covariational and the mechanism-based approaches.…

A longitudinal study was conducted on 82 children to investigate, firstly the numerical competence of young children and the predictive value of (pre)-numerical tests in kindergarten, and, secondly, whether children's knowledge of the numerical system and representation of the number size is related to their computation and logical knowledge and…

The 12th iteration of the International Conference on Educational Data Mining (EDM 2019) is organized under the auspices of the International Educational Data Mining Society in Montreal, Canada. The theme of this year's conference is EDM in Open-Ended Domains. As EDM has matured it has increasingly been applied to open-ended and ill-defined tasks…