LeActiveMath (Language-Enhanced,User-Adaptive, Interactive eLearning for Mathematics) is an interdisciplinary European effort that develops an internationalized Web-based intelligent e-Learning system for mathematics that can be used in high school and university as well as for self study.Themany technological innovations serve amoderate constructivist and competency-based pedagogical approach....

Jianfeng Lu, Jian-Guo Liu, and Dionisios Margetis Department of Mathematics and Department of Physics, Duke University, Durham, North Carolina 27708, USA Department of Chemistry, Duke University, Durham, North Carolina 27708, USA Department of Mathematics, and Institute for Physical Science and Technology, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, ...

In common teaching practice the habit of connecting mathematics classroom activities with reality is still substantially delegated to word problems. But besides representing the interplay between mathematics and reality, word problems often are the sole example of realistic mathematical modeling and problem solving. During the past decades, a growing body of empirical research (e.g. Freudenthal...

In Cognitive Science, conceptual blending has been proposed as an important cognitive mechanism that facilitates the creation of new concepts and ideas by constrained combination of available knowledge. It thereby provides a possible theoretical foundation for modeling high-level cognitive faculties such as the ability to understand, learn, and create new concepts and theories. Quite often the ...

Fuzzy control and modeling use only a small portion of the fuzzy mathematics that is available; this portion is also mathematically quite simple and conceptually easy to understand. In this chapter, we introduce some essential concepts, terminology, notations, and arithmetic of fuzzy sets and fuzzy logic. We include only a minimum though adequate amount of fuzzy mathematics necessary for unders...

In this paper we use the Triangular and Trapezoidal Fuzzy Numbers as tools for assessing student Mathematical Modelling (MM) skills. Fuzzy Numbers play a fundamental role in fuzzy mathematics analogous to the role played by the ordinary numbers in classical mathematics, On the other hand, MM appears today as a dynamic tool for teaching and learning mathematics, because it connects mathematics w...

This commentary discusses the Bauer and Curran (2002) investigation of growth mixture modeling. Single-class modeling of non-normal outcomes is compared to modeling with multiple latent trajectory classes. New statistical tests of multiple-class models are discussed. Principles for substantive investigation of growth mixture model results are presented and illustrated by an example of high scho...