基于模糊综合评判的大学数学考核方式改革

独立高校数学课程的开设旨在让学生掌握数学知识的基础上,提高数学应用能力.然而现行的考核方式存在重考试结果,轻学习过程等问题.从传统考核方式入手,指出其不足之处,基于模糊综合评判法建立新型评价体系和数学模型,通过试点运行验证了新的考核方式的可行性、客观性、合理性和科学性.     

Laying groundwork for an understanding of academic integrity in mathematics tasks

ABSTRACT

To date, the way that academic misconduct is manifested in undergraduate mathematics coursework has been unexamined in the literature, with the consequence that policy and preventive education can fail to address it appropriately. This paper describes the particular features of the responses expected in mathematical tasks and provides concrete examples of what lapses of integrity look like in this context. The intent is to lay groundwork for discussion and a response to this issue from within our discipline.     

How do we understand mathematical practices in non-mathematical fields? Reflections inspired by cases from 12th and 13th century China

Recent studies of the history of mathematics have shed light on the diversity of mathematical practices in the ancient world. In this article, I address this issue from two perspectives. First, I analyze different mathematical instruments used in different domains in 12^th and 13^th century China. Second, by analyzing how the text is related to the problems written down in the same period, I argue that there existed two categories of mathematical problems. As a result, I suggest that problems, textual procedures, and material operations should be considered together when regarding various mathematical practices in mathematical and non-mathematical fields.     

Media pressures on Welsh language preservation

Despite compulsory school instruction in the Welsh language and strong cultural incentives to acquire the language, the most recent UK Census showed a downward trend in the number of speakers. The asymmetry in explicit language acquisition incentives is here considered to be offset by the media dominance of the English language. This dominance is modeled by the introduction of time-dependent connectivity and infectivity among English speakers into an adapted epidemiological model. Extrapolations up to 2050 are made, this being the announced date of a Welsh Assembly language-planning target of one million Welsh speakers.     

Expanding conceptions of utility: middle school students’ perspectives on the usefulness of mathematics

This research explores how adolescents conceptualize the usefulness of mathematics. Integrating sociocultural theory with the study of utility value, this study uses open-ended survey items and interview tasks to examine conceptions of usefulness among a group of predominantly Latinx middle school students. Findings reveal that students primarily conceptualized the usefulness of mathematics in two ways. First, students considered the applicability of mathematics content, focusing on applications of mathematics in everyday life and future jobs/careers. Second, students considered the usefulness of features of the learning experience, such as the form of interaction and structure of the activity. Both conceptions are compared to existing conceptions of usefulness in the literature, and implications for classroom practice and future research are discussed.     

Optimal intervention under stress scenarios: A case of the Korean financial system

We consider optimal intervention methods under budget constraints when financial systems face economic shocks. We propose two policies formulated by mixed-integer linear programs where regulators inject cash into institutions. One is to minimize systemic losses, and the other is to minimize the number of defaulting institutions. Using publicly available data on the Korean financial system, we construct its entire network and apply stress scenarios to the system to compare the performances of intervention strategies and derive insights on their workings.     

Evolving a three-world framework for solving algebraic equations in the light of what a student has met before

In this paper we consider data from a study in which students shift from linear to quadratic equations in ways that do not conform to established theoretical frameworks. In solving linear equations, the students did not exhibit the ‘didactic cut’ of Filloy and Rojano (1989) or the subtleties arising from conceiving an equation as a balance (Vlassis, 2002). Instead they used ‘procedural embodiments’, shifting terms around with added ‘rules’ to obtain the correct answer (Lima & Tall, 2008). Faced with quadratic equations, the students learn to apply the formula with little success. The interpretation of this data requires earlier theories to be seen within a more comprehensive framework that places them in an evolving context. We use the developing framework of three worlds of mathematics (Tall, 2004, Tall, 2013), based fundamentally on human perceptions and actions and their consequences, at each stage taking into account the experiences that students have ‘met-before’ (Lima and Tall, 2008, McGowen and Tall, 2010). These experiences may be supportive in new contexts, encouraging pleasurable generalization, or problematic, causing confusion and even mathematical anxiety. We consider how this framework explains and predicts the observed data, how it evolves from earlier theories, and how it gives insights that have both theoretical and practical consequences.     

澳门博采收入增长影响因素分析

通过对2005年1月至2013年7月份的澳门博采毛收入数据进行季节分析,显示澳门博采毛收入有显著的中国节假日特征.其次分析入境澳门旅客数、酒店住客数、劳动力参与率、消费指数以及突发事件是否是澳门博采毛收入迅速增长的原因,通过计量经济学分析,得到酒店住客数、劳动力参与率、中国的节假日三个因素对澳门博采毛收入有显著的正向影响关系,而2008年世界金融危机对博采毛收入有显著的负的影响.最后结合实际给出了提高博采收入的政策建议.     

Dynamic investigation of triangles inscribed in a circle,which tend to an equilateral triangle

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner.

First, using geometrical software, we investigate four theorems that represent interesting geometrical properties, after which we present formal proofs that rest on a combination between different fields of mathematics: trigonometry, algebra and geometry, and the use of the concept of standard deviation that is taken from statistics.