Classroom sociomathematical norms for proof presentation in undergraduate in abstract algebra

This paper is a case study of the teaching of an undergraduate abstract algebra course with a particular focus on the manner in which the students presented proofs and the class engaged in a subsequent discussion of those proofs that included validating the work. This study describes norms for classroom work that include a set of norms that the presenter of a proof was responsible for enacting, including only using previously agreed upon results, as well as a separate set that the audience was to enact related to developing their understanding of the presented proof and validating the work. The study suggests that the students developed a sense of communal and individual responsibility for contributing to growing the body of mathematical knowledge known by the class, with an implied responsibility for knowing the already developed mathematics. Moreover, the behaviors that norms prompted the students to engage were those that literature suggests leads to increased comprehension of proofs.     

On an Extremal Problem About the Arc-Length of Algebraic Polynomials

In this work we investigate polynomials of maximal (minimal) arc-length in the interval [−1, 1] amongst all monic polynomials of fixed degree n with n real zeros in [−1, 1].     

Effectiveness of Two Generative Learning Strategies in the Science Classroom

The purpose of this study was to assess the effectiveness of two generative learning strategies, concept mapping and laboratory experiments involving object manipulation, to determine if either one is more‐effective with individual learners or learning groups in a science classroom. Eighty sixth‐grade science‐students were randomly assigned to group or individual conditions and to one of two experimental treatments. Experimental treatments were changed between a first and second posttest. Long‐term retention was evaluated with a third, delayed posttest. Students starting with concept maps showed higher achievement on the delayed posttest than students beginning with the laboratory experiment. No difference was found between students working as individuals or in groups, but a significant interaction between generative learning strategy and grouping condition was revealed. Implications for sequencing generative learning strategies are discussed.     

A cycle for validating a learning progression illustrated with an example from the concept of function

A learning progression, or learning trajectory, describes the evolution of student thinking from early conceptions to the target understanding within a particular domain. As a complex theory of development, it requires conceptual and empirical support. In earlier work, we proposed a cycle for the validation of a learning progression with four steps: 1) Theory Development, 2) Examination of Empirical Recovery, 3) Comparison to Competing Models, and 4) Evaluation of Instructional Efficacy. A group of experts met to discuss the application of learning sciences to the design, use, and validation of classroom assessment. Learning progressions, learning trajectories, and how they can support classroom assessment were the main focuses. Revisions to the cycle were suggested. We describe the adapted cycle and illustrate how the first third of it has been applied towards the validation of a learning progression for the concept of function.     

课程思政理念指导下的高等数学过程考核实施方案

在融入课程思政前,利用调查问卷的结果做了 一些准备工作,目的是了解学生意愿及需求,找好切入点.接着开始实际操作,进行"高数那些事儿"环节教学改革设计,并平稳有序的开展一学期试行.然后为了更好了解学生对教改的反馈及学生学习态度,对两个平行教学班进行了相关内容的问卷调查,所得结果相近,以其中一班为例说明多项令人满意的重要内...     

Item efficiency: an item response theory parameter with applications for improving the reliability of mathematics assessment

Many large universities, community colleges and some smaller four-year colleges are turning to hybrid or online instruction for remedial and entry level mathematics courses, often assessed using online exams in a proctored computer lab environment. Faculty face the task of choosing questions from a publisher's text bank with very little, if any, background in test theory and design. We present a new item parameter, item efficiency, that is calculated from the results of an item response theory analysis of a comprehensive college algebra final examination and show that this new parameter may be used to identify items better suited for similar comprehensive final assessments. Further, by relating Item Efficiency to classical test theory item statistics, we propose guidelines that can be used to identify suitable items prior to testing with little or no background in psychometric theory.     

An “inverse” relationship between mathematics identities and classroom practices among early career elementary teachers: The impact of accountability

This qualitative case study guided by portraiture examines the relationships between three early career elementary teachers’ beliefs about themselves in relation to mathematics (mathematics identities) and their classroom practices. Through autobiographical inquiry, reflective practice, classroom observations, interviews, and artifacts, findings show that all three second grade teachers appeared to have an “inverse” relationship between their mathematics identities and their classroom practices. In this relationship, as negative as they felt about themselves with regards to mathematics, they expended that much more effort to ensure that their students would have positive experiences with it and not be stigmatized by it as they had been. Accountability to schools, students, and parents, to increase student achievement appeared to play an important role in this relationship. Implications for preservice teacher education, inservice professional development, and research on beliefs and practices are discussed.     

基于LS-SVM的现代战斗机空战效能评估模型研究

现代战斗机空战是当前空中力量遂行作战任务的主要模式,其空战效能的评估问题也是研究的难点之一.在分析现代战斗机空战模式及七个关键影响因素的基础上,引入人工智能技术的思路和方法,运用LS-SVM支持向量机方法对现代战斗机空战效能进行了多级评估LS-SVM支持向量机分类器设计并建立智能评估模型,结合实例进行了计算和分析,为进一步研究空战效能的评估问题提供了一种新的思路.     

Problem structuring methods ‘in the Dock’: Arguing the case for Soft OR

Problem structuring methods (‘soft’ OR) have been around for approximately 40 years and yet these methods are still very much overlooked in the OR world. Whilst there is almost certainly a number of explanations for this, two key stumbling blocks are: (1) the subjective nature of the modelling yielding insights rather than testable results, and (2) the demand on users to both manage content (through modelling) and processes (work with rather than ‘on behalf’ of groups). However, as evidenced from practice there are also a number of significant benefits. This paper therefore aims to examine the case of Soft OR through examining the case for and against problem structuring methods.     

广州大学数学专业分析类课程评价方式现状与有效性分析报告

本文采取问卷调查的方法,对广州大学数学专业三门分析类课程考核方式与有效性进行了调查,并根据所得的数据进行分析,在考核内容、考核方式方面提出了对策与建议。通过对课程评价方式进行改革研究与实践,对于科学全面地评价学生的综合素质,提高人才培养质量不无帮助。     

基于多Agent的心理战效果评估方法研究

心理作战系统是典型的复杂适应系统。以复杂适应系统理论为指导,运用多Agent建模仿真方法,建立了心理战效果评估模型,开发了心理战智能体仿真平台PSYOPASP,对5种心理战防御方案进行仿真实验。     

C3I系统知识库的类特征模式

在Ｃ３Ｉ系统知识库中引入了条件事件推理规则以及类与特征的概念,并给出了进行动态管理知识库的有效方法。     

Behavior of the Free Boundary Near Contact Points with the Fixed Boundary for Nonlinear Elliptic Equations

The aim of this paper is to study a free boundary problem for a uniformly elliptic fully non-linear operator. Under certain assumptions we show that free and fixed boundaries meet tangentially at contact points.     

On the stability of the unsmoothed Fourier method for hyperbolic equations

Summary. It has been a long open question whether the pseudospectral Fourier method without smoothing is stable for hyperbolic equations with variable coefficients that change signs. In this work we answer this question with a detailed stability analysis of prototype cases of the Fourier method. We show that due to weighted -stability, the -degree Fourier solution is algebraically stable in the sense that its amplification does not exceed . Yet, the Fourier method is weakly -unstable in the sense that it does experience such amplification. The exact mechanism of this weak instability is due the aliasing phenomenon, which is responsible for an amplification of the Fourier modes at the boundaries of the computed spectrum. Two practical conclusions emerge from our discussion. First, the Fourier method is required to have sufficiently many modes in order to resolve the underlying phenomenon. Otherwise, the lack of resolution will excite the weak instability which will propagate from the slowly decaying high modes to the lower ones. Second -- independent of whether smoothing was used or not, the small scale information contained in the highest modes of the Fourier solution will be destroyed by their amplification. Happily, with enough resolution nothing worse can happen. Received December 14, 1992/Revised version received March 1, 1993     

Improved smoothing-type methods for the solution of linear programs

Summary. We consider a smoothing-type method for the solution of linear programs. Its main idea is to reformulate the primal-dual optimality conditions as a nonlinear and nonsmooth system of equations, and to apply a Newton-type method to a smooth approximation of this nonsmooth system. The method presented here is a predictor-corrector method, and is closely related to some methods recently proposed by Burke and Xu on the one hand, and by the authors on the other hand. However, here we state stronger global and/or local convergence properties. Moreover, we present quite promising numerical results for the whole netlib test problem collection. Received August 9, 2000 / Revised version received September 28, 2000 / Published online June 7, 2001     

Large-Time Behaviour of Solutions of the Exterior-Domain Cauchy–Dirichlet Problem for the Porous Media Equation with Homogeneous Boundary Data

The title of this paper states precisely what the subject is. The first part of the paper concerns the radially-symmetric problem in the exterior of the unit ball. It is shown that in time the solution of the problem converges to one of two specific self-similar solutions of the porous media equation, dependent upon the dimensionality of the problem. Moreover, the free boundary of the solution converges to that of the self-similar solution. The critical space dimension is two, for which there is no distinction between the self-similar solutions, and the form of the convergence is exceptional. The technique used is a comparison principle involving a variable that is a weighted integral of the solution. The second part of the paper is devoted to the problem in an arbitrary spatial domain with no conditions of symmetry. A special invariance principle and the results obtained for the radially-symmetric case are used to determine the large-time behaviour of solutions and their free boundaries. This behaviour is decidedly different from when the boundary data are fixed and not homogeneous.