A cognitive core for common state standards

The purpose of this paper is to illustrate cognitive challenges introduced by Common Core State Standards for Mathematics (2010) with regard to conceptualizing fractions. We focus on a strand of standards that appear across grades three through five, which is best represented in grade four, by standard 4.NF.4a: “[Students should] understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).” We argue that supporting such conceptualizations is a critical challenge for teachers and researchers to address in US education, but one fraught with conceptual hurdles for students. We adopt a scheme theoretic perspective and share the case study of a sixth-grade student, to illustrate the ways of operating students need to develop for meaningful attainment of the new standards.     

工科数学试题库应具备的品质──来自用户的建议

工科数学试题库应具备的品质──来自用户的建议刘江国（郑州工学院）１工科数学试题库的意义和现状随着计算机应用的日益广泛和深入，计算机辅助教学（ＣＡＩ：ＣｈｌｌｌｏｕｔｅｒＡｉｄｅｄＩｎｓｔｒｕｃｔｉｏｎ）领域也呈现出方兴未艾的势头。在工科数学ＣＡｆ方面...     

Some modified mathematical analytic derivations of the annual total relevant cost of the inventory model with two levels of trade credit in the supply chain system

Several recent studies in supply chain system and related areas explored various economic order quantity (EOQ) models for noninstantaneous deteriorating items with imperfect quality and trade credit financing. In particular, in the year 2007, Teng et al investigated an EOQ model in which the supplier offers the retailer the permissible delay period M and the retailer, in turn, provides the trade credit period N (with ) to his/her customers. The main purpose of this article is twofold: (a) It modifies the annual total relevant cost TVC(T) in the study of Teng et al and presents the correct derivations of TVC(T) by applying mathematical analytic tools and techniques. (b) It exposes some logical and mathematical problems in the proof of Theorem 1 in Teng et al. It also corrects and overcomes all of the errors and shortcomings by systematically presenting the complete and mathematical solution procedures in order to locate all optimal solutions for the model in Teng et al.     

基于慢性病诊疗实践的参与式社区医生培训效果评价

目的 了解社区医生慢性病的诊疗知识水平,并对基于常见慢性病诊疗实践的交互式小组培训模式的效果进行评 价。方法 2013年7 月～2014年6月,对义乌市13家社区卫生服务中心的194名社区卫生服务中心一线工作人员及社区卫生服务站的责任医师进行慢性病诊疗知识问卷调查,并实施小班化互动式“二组二段式”新型培训模式,对培训效果进行评价。结果 （1）社区医生慢性病综合防治及社区管理能力水平较低,接受新型培训模式的医生慢性病危险因素知识及社区综合管理知识的平均答对率由31.8%提高到59. 0%（P＜0.01）。（2）接受新型培训模式的医生对高血压病、糖尿病和冠心病规范化诊疗水平、康复知识及社区管理知识的平均总分在培训前后均显著提高（P＜0.01）。结论 “以问题为中心,以病例为引导”的“二组二段式”小班化互动式新型社区医生慢性病规范化诊疗知识的培训模式简单实用,明显提高社区医师对慢性病的诊疗水平,可在社区医院或基层培训机构全面推广。     

不定最小二乘问题的改进的不完全双曲Gram-Schmidt预处理算法

应用改进的不完全双曲Gram-Schmidt(IHMGS)方法预处理不定最小二乘问题的共轭梯度法(CGILS)、正交分解法(ILSQR)与广义的最小剩余法(GMRES)等迭代算法来求解大型稀疏的不定最小二乘问题.数值实验表明,IHMGS预处理方法可有效提高相应算法的迭代速度,且当矩阵的条件数比较大时,效果更加显著.     

The collocation method for mixed boundary value problems on domains with curved polygonal boundaries

Summary. We consider an indirect boundary integral equation formulation for the mixed Dirichlet-Neumann boundary value problem for the Laplace equation on a plane domain with a polygonal boundary. The resulting system of integral equations is solved by a collocation method which uses a mesh grading transformation and a cosine approximating space. The mesh grading transformation method yields fast convergence of the collocation solution by smoothing the singularities of the exact solution. A complete stability and solvability analysis of the transformed integral equations is given by use of a Mellin transform technique, in a setting in which each arc of the polygon has associated with it a periodic Sobolev space. Received April 15, 1995 / Revised version received April 10, 1996     

基于广义判断形式的模糊排序方法

广义判断下的ＡＨＰ（ＧＪＡＨＰ）是一种广义ＡＨＰ。它是在研究不完全信息下的决策排序问题时，通过构造广义判断矩阵的数学模型而建立的一种广义ＡＨＰ。本文应用集值统计的方法，在区间判断标度基础上确定模糊判断矩阵元素的正模糊数表示。给出了基于模糊区间数排序权值向量的特征根算法。讨论了Ｆｕｚｚｙ环境下求解各种判断形式的模糊排序权值向量的方法。