Polynomial calculus: rethinking the role of calculus in high schools

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in their definition and exposition. We develop the beginning concepts of differential and integral calculus using only concepts and skills found in secondary algebra and geometry. It is our underlining objective to strengthen students' knowledge of these topics in an effort to prepare them for advanced mathematics study. The purpose of this reconstruction is not to alter the teaching of limit-based calculus but rather to affect students' learning and understanding of mathematics in general by introducing key concepts during secondary mathematics courses. This approach holds the promise of strengthening more students' understanding of limit-based calculus and enhancing their potential for success in post-secondary mathematics.     

Generalized nets in neurology: an example of mathematical modelling

The purpose of this paper is to explain the basic theory of generalized nets (GNs) and their applications in the context of the differential diagnosis of neurological diseases. We define formally the concepts of a GN and transitions of a GN and also outline some remarks on their theory. The work here constructs an example which aims to trace the process of diagnosing different signs and symptoms in neurology. This will enable the interested reader to see the scope of nets in general as tools for the modelling, simulation, optimization and control of real processes.     

Cognitive opportunities in textbooks: the cases of grade four and eight textbooks in Israel

The cognitive domain in mathematics, defined as thinking and understanding in the process of learning mathematics, is a main focus of curricula in many countries. This study explores breadth and depth of understanding as addressed in mathematics textbooks certified as aligned to Israeli national mathematics curricula. We compare opportunities for students to engage with mathematics requiring different types and levels of understanding provided by the tasks in mathematics textbooks. Comparison of two fourth grade and two eighth grade mathematics textbooks showed significant differences in the opportunities to learn in the cognitive domain that each provides. These differences can be quantified; the quantification defines the cognitive demand of the textbook. The cognitive demand of the four textbooks varies. This reveals a potential source of inequity in students’ opportunities to learn mathematics. Results should prompt discussion around standardization and alignment of textbooks to the cognitive goals of the curriculum.     

数学分析中的一题多解问题

通过两个积分 (一个是不定积分 ,一个是定积分 )及一个极限 ,说明如何灵活使用积分法解决积分问题 ,方法灵活、巧妙 ,适用范围广 .     

Investigating the geometry curriculum in Palestinian textbooks: towards multimodal analysis of Arabic mathematics discourse

ABSTRACT

The analytical scheme used in the project The Evolution of the Discourse of School Mathematics (EDSM) was developed to analyse the change over time in examination texts. An adapted version of the EDSM scheme has been deployed to analyse the nature of mathematics construed in Palestinian schools’ textbooks and the mathematical activity expected of students in the geometry textbooks for students aged 10 to 16 years. The adaptation includes adding further tools for analysing visual components of texts, as well as accounting for some differences between English and Arabic. This article outlines these adaptations and illustrates the use of the adapted scheme with a different genre of texts from those studied in the EDSM project. Some of the challenges in the adaptation process in relation to Arabic mathematics discourse are discussed.     

Scalar and vector line integrals: A conceptual analysis and an initial investigation of student understanding

This paper adds to the growing body of research happening in multivariable calculus by examining scalar and vector line integrals. This paper contributes in two ways. First, this paper provides a conceptual analysis for both types of line integrals in terms of how theoretical ways of thinking about definite integrals summarized from the research literature might be applied to understanding line integrals specifically. Second, this paper provides an initial investigation of students’ understandings of line integral expressions, and connects these understanding to the theoretical ways of thinking drawn from the literature. One key finding from the empirical part is that several students appeared to understand individual pieces of the integral expression based on one way of thinking, such as adding up pieces or anti-derivatives, while trying to understand the overall integral expression through a different way of thinking, such as area under a curve.     

对恐怖袭击事件记录数据的量化分析与研究

恐怖主义是人类的共同威胁,利用数据挖掘可以为反恐防恐提供有价值的信息支持.基于数据挖掘的思路,从恐怖袭击事件中提取能描述危险程度的特征属性,构建量化分级模型,并考虑准确率评价指标进行优化.通过组内平方和法分析改进高斯混合模型(GMM),对恐怖组织进行聚类分析,侦查出潜在最相关的嫌疑人.建立相关模型结合统计分析,得到恐怖袭击发生的主要原因、时空特性和蔓延特性,并对未来全球反恐态势进行预测,帮助反恐组织提高反恐的精准性和打击能力.     

An investigation of assessment and feedback practices in fully asynchronous online undergraduate mathematics courses

Research suggests it is difficult to learn mathematics in the fully asynchronous online (FAO) instructional modality, yet little is known about associated teaching and assessment practices. In this study, we investigate FAO mathematics assessment and feedback practices in particular consideration of both claims and findings that these practices have a powerful influence on learning.

A survey questionnaire was constructed and completed by 70 FAO undergraduate mathematics instructors, mostly from the USA, who were each asked to detail their assessment and feedback practices in a single FAO mathematics course. Alongside these questions, participants also answered the 16-item version of the Approaches to Teaching Inventory. In addition, a novel feedback framework was also created and used to examine how feedback practices may be related to participants' approaches to teaching.

Results show that assessment and feedback practices are varied and complex: in particular, we found there was not a simple emphasis on summative assessment instruments, nor a concomitant expectation these would always be invigilated. Though richer assessment feedback appears to be emphasized, evidence suggests this feedback may not be primarily directed at advancing student learning. Moreover, we found evidence of a reliance on computer--human interactions (e.g. via computer-assisted assessment systems) and further evidence of a decline in human interactions, suggesting a dynamic that is both consistent with current online learning theory and claims FAO mathematics courses are becoming commodified. Several avenues for further research are suggested.     

城市环境质量多元统计分析──永安市城市环境质量综合评价

本文针对永安市城市环境质量综合评价，采用主成分分析法［１］，以福建省十个城市为样本进行横向比较，从而揭示永安市环境质量状况及其改进环境质量的突破口．使环境质量现状分析具有评价和控制的双重功能。     

数学模型在废黄河水质评价及预测中的应用

用多元统计分析中聚类分析的基本原理,对废黄河2004~2006年的水质进行评价,并用牛顿插值法进行水质预测,为环保工作提供有效参考.     

The European regional policy and the socio-economic diversity of European regions: A multivariate analysis

There are significant differences among the European Union regions, which have been heightened due to the most recent enlargement in 2004. This paper aims to analyse this diversity and to propose a classification of European regions that is adjusted to the different axes of socio-economic development and, simultaneously, is useful for European regional policy purposes. Multivariate statistical techniques allow the identification of clusters of socio-economic similarity, which are contrasted with the classes considered in the financial proposal of the European Commission (EC) for the period 2007–2013.     

因子分析在京杭大运河水质评价中的应用

用主成分分析的方法找出影响京杭大运河淮安段水质的主因子,求出因子得分函数,计算各样本的因子得分及水质综合评分,据此对京杭大运河淮安段各监测断面的水质进行评价.     

青海藏区社会经济发展水平动态评价研究

利用全局主成分分析(GPCA)、动态聚类分析等方法,根据经济发展水平、社会进步程度和社会经济综合水平3个方面对青海25个藏区县2002-2008年社会经济发展状况进行了定量评价和动态分析.指数化的评价结果表明,25个藏区县以上3个方面的发展水平逐年提高,社会经济综合实力综合指数均值从2002年的-0.8381上升到2008年的1.2796.     

DEA environmental assessment: Measurement of damages to scale with unified efficiency under managerial disposability or environmental efficiency

This study proposes a use of Data Envelopment Analysis (DEA) for environmental assessment. Firms usually produce not only desirable but also undesirable outputs as a result of their economic activities. The concept of disposability on undesirable outputs is separated into natural and managerial disposability. Natural disposability is an environmental strategy in which firms decrease their inputs to reduce a vector of undesirable outputs. Given the reduced input vector, they attempt to increase desirable outputs as much as possible. Managerial disposability involves the opposite strategy of increasing an input vector. The concept of disposability expresses an environmental strategy that considers a regulation change on undesirable outputs as a new business opportunity. Firms attempt to improve their unified (operational and environmental) performance by utilizing new technology and/or new management. Considering the two disposability concepts, this study discusses how to measure unified efficiency under managerial disposability and then discusses how to measure environmental efficiency. The proposed uses of DEA can serve as an empirical basis for measuring new economic concepts such as “Scale Damages (SD)”, corresponding to scale economies for undesirable outputs, and “Damages to Scale (DTS)”, corresponding to returns to scale for undesirable outputs.     

Multifunctional assessment and zoning of crop production system based on set pair analysis-A comparative study of 31 provincial regions in mainland China

In this study, we present a multifunctional indicator system for the performance evaluation of crop production system by set pair analysis method. Five functions were summarized to represent the multifunctionality of crop production system, including production function, supply function, ecological function, security function and economic function. Setting a case study of 31 provincial regions in mainland China, this paper conducted a comparison of each function in different regions, divided into 9 groups by cluster analysis. The results show that: the levels of multifunction in most regions are under a low degree balance; the production function has a high coordination with the economic function and security function in China; the supply function is lowly correlated with the other functions, especially the economic function has negative correlation with the supply function to some extent; some relevant policies and suggestions are deduced for multifunctional improvement. It is concluded that the multifunctional indicators and the set pair analysis method can serve as an effective method for the assessment of crop production system.