This article reviews two aspects of human learning: (1) people draw inferences that appear to rely on hierarchical conceptual representations; (2) some categories are much easier to learn than others given the same number of exemplars, and some categories remain difficult despite extensive training. Both of these results are difficult to reconcile…

Many geoscience phenomena cannot be perceived at human temporal or spatial scales. As a consequence, we can only understand many processes that drive geological phenomena through analogical reasoning. Building deep conceptual understanding requires instruction that activates the appropriate source analogs and allows students to build useful…

Practicing teachers as well as researchers, mathematicians, and teacher educators have offered opinions and theoretical critiques of the multiple models used to teach integer arithmetic. Few studies, however, have investigated what students learn with models or empirically compared affordances and constraints of integer models. This led me to…

As the largest international study ever taken in history, the Trend in Mathematics and Science Study (TIMSS) has been held as a benchmark to measure U.S. student performance in the global context. In-depth analyses of the TIMSS project are conducted in this study to examine key issues of the comparative investigation: (1) item flaws in mathematics…

The instructional metaphor is an important bridge to understanding, particularly when students are undertaking tasks that are conceptually difficult and outside their previous experience. It is suggested that the limitations of the implicit metaphor of the procedural control languages are the main cause of the problems experienced with delivering…

This paper proposes a methodology to calculate both the difficulty of the basic problems and the difficulty of solving a problem. The method to calculate the difficulty of problem is according to the process of constructing a problem, including Concept Selection, Unknown Designation, and Proposition Construction. Some necessary measures observed…