Recently, there has been a growing interest in learning approaches that combine two
phases: an initial problem-solving phase followed by an instruction phase (PS-I). Two often …

A long tradition of research on mathematical thinking has focused on procedural knowledge,
or knowledge of how to solve problems and enact procedures. In recent years, however …

This book takes stock of the state of affairs of the teaching and learning of mathematical
modelling with regard to research, development and practice. It provides a conceptual …

The topic of this paper is mathematical modelling or—as it is often, more broadly, called—
applications and modelling. This has been an important topic in mathematics education …

Mathematical competence rests on develo** knowledge of concepts and of procedures (ie
conceptual and procedural knowledge). Although there is some variability in how these …

Develo** adaptive expertise with arithmetic problem solving is a much desired aim of
primary school mathematics education. However, there are very few practical tools for …

When learning a new math concept, should learners be first taught the concept and its
associated procedures and then solve problems, or solve problems first even if it leads to …

Cognitive flexibility is an important characteristic that helps humans pursue complex tasks,
such as multitasking and finding novel, adaptable solutions to changing demands. Yet it is …

Being told procedures and concepts before problem solving can inadvertently undermine
the learning of deep structures in physics. If students do not learn the underlying structure of …

After more than 100 years of interest and study, knowledge transfer remains among the most
challenging, contentious, and important issues for both psychology and education. In this …