Effective technologies for learning and doing mathematics should be based on sound cognitive theory, be empirically tested against alternatives, and be primarily addressed at mathematics as a modeling language. I will discuss the status and promise of researchbased "intelligent" systems that support students in mathematical modeling and tool use. Such systems are beginning to reshape the mathem...

Mathematics programs in high school, graduate and undergraduate university classes, confront students with realworld problems to be solved with software tools, through a modeling process which requires mathematical concepts. We propose an e-learning application for an educational mathematics environment, whose aim is to build a bridge between mathematics world and application world. It is going...

Mathematics) Modeling Oscillations in the cAMP-PKA Network Within Budding Yeast by Kevin E Gonzales Department of Mathematics Duke University

In this paper we explore the hypothesis that constrained uses of imagination are crucial to economic modeling. We propose a theoretical framework develop thesis through number specific hypotheses test and refine six new, representative case studies. Our ultimate goal is philosophical account practice oriented informed by empirical evidence. To do this, deploy an abductive reasoning strategy. st...

Proof theory began in the 1920’s as a part of Hilbert’s program, which aimed to secure the foundations of mathematics by modeling infinitary mathematics with formal axiomatic systems and proving those systems consistent using restricted, finitary means. The program thus viewed mathematics as a system of reasoning with precise linguistic norms, governed by rules that can be described and studied...