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David Khaliqi 《School science and mathematics》2016,116(4):199-211
The U.S. educational system is undergoing rapid and substantial changes with many states grappling with the adoption of the Common Core State Standards in Mathematics (CCSSM). Important research questions remain unanswered regarding the potential efficacy of the CCSSM to improve student math performance compared with students around the globe. This article utilized TIMSS 2007 8th‐grade math assessment results and curricular frameworks to (1) measure the degree of overlap between the CCSSM and TIMSS standards, and (2) use this finding to create a predictive model to determine the potential efficacy of the CCSSM in improving the U.S. 8th‐grade student math performance compared with six culturally matched, TIMSS‐assessed countries, provinces, and states. Comparisons of CCSSM and TIMSS‐assessed jurisdictions show that the CCSSM holds many items in common with TIMSS‐assessed jurisdictions, but lacks rigor in some key areas. The CCSSM deficiencies include algebraic knowledge and problem solving at the 8th‐grade level, and are a significant detractor from the CCSSM when compared with TIMSS. 相似文献
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Dirk Horstmann 《Journal of Nonlinear Science》2011,21(2):231-270
In this paper we extend the famous Keller–Segel model for the chemotactic movement of motile species to some multi-species
chemotaxis equations. The presented multi-species chemotaxis models are more general than those introduced so far and also
include some interaction effects that have not been studied before. For example, we consider multi-species chemotaxis models
with attraction and repulsion between interacting motile species. For some of the presented new models we give sufficient
conditions for the existence of Lyapunov functionals. These new results are related to those of Wolansky (Scent and sensitivity:
equilibria and stability of chemotactic systems in the absence of conflicts, preprint, 1998; Eur. J. Appl. Math. 13:641–661, 2002). Furthermore, a linear stability analysis is performed for uniform steady states, and results for the corresponding steady
state problems are established. These include existence and nonexistence results for non-constant steady state solutions in
some special cases. 相似文献