Thermodynamical Arguments Against Evolution

The argument that the second law of thermodynamics contradicts the theory of evolution has recently been revived by anti-evolutionists. In its basic form, the argument asserts that whereas evolution implies that there has been an increase in biological complexity over time, the second law, a fundamental principle of physics, shows this to be impossible. Scientists have responded primarily by noting that the second law does not rule out increases in complexity in open systems, and since the Earth receives energy from the Sun, it is an open system. This reply is correct as far as it goes, and it adequately rebuts the most crude versions of the second law argument. However, it is insufficient against more sophisticated versions, and it leaves many relevant aspects of thermodynamics unexplained. We shall consider the history of the argument, explain the nuances various anti-evolution writers have brought to it, and offer thorough explanations for why the argument is fallacious. We shall emphasize in particular that the second law is best viewed as a mathematical statement. Since anti-evolutionists never make use of the mathematical structure of thermodynamics, invocations of the second law never contribute anything substantive to their discourse.     

A framework for analyzing the collaborative construction of arguments and its interplay with agency

In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and discuss their influence on the building of mathematical arguments and student agency. The framework is exemplified using data from a study of the development of mathematical reasoning in an urban sixth-grade informal after-school program.     

Combinatorial proofs and algebraic proofs — I

It is sometimes the case in mathematics that the same result can be proved in two or more essentially different ways (a luxury of mathematical riches, you might say). A recurrent theme in this context is the tension between combinatorial proofs and algebraic proofs. Inthis two-part article we describe some results which allow for proofs of both kinds and give us an opportunity to contrast them. We shall see some beautiful examples of both kinds of proofs. In Part I we dwell on results that deal with the binomial coefficients and with Fibonacci numbers. We will not be overly zealous in our usage of the term ‘combinatorial’: we will allow a proof to be so categorized if it is largely combinatorial, with only a ‘small’ component of algebra. However, that small part may well be an essential component of the proof. The simplicity of counting arguments can be deceptive. In recent times, Paul Erd?s has shown just how subtle and powerful such arguments can be, and how far they can reach.     

如何用数学模型定量评价进程调度算法的性能

通过建立调度算法的数学模型 ,探讨了对进程调度算法的调度性能进行定量分析和深入研究的方法     

Weighing up the Influence of Context on Judgements of Mathematical Literacy

Mathematical literacy, viewed as a set of ideas involving applications of mathematics to real-world contexts, has recently featured in curricular discussions about the aims for mathematics education. This article explores the effect that differences in the way that a mathematical task is contextualised can have on students’ mathematical arguments and, therefore, on their perceived levels of mathematical literacy. Seventy-two students’ responses to three similar measurement tasks are described according to Kaiser and Willander’s levels of mathematical literacy. The arguments used for assigning each level of mathematical literacy are then investigated for the presence of specific macro- and micro-linguistic features. The context of the task affects what students perceive to be most relevant approaches to use, which are reflected in the arguments they give; this, in turn, affects external judgements of their level of mathematical literacy.     

数学建模的一般认知过程研究

运用口语报告分析、深度访谈分析和理论分析方法建立数学建模的一般认知过程模型.该模型尝试模拟数学建模的一般认知过程,力图揭示数学建模行为过程的基本阶段及其联系,试图表征实现数学建模行为操作过程各阶段的一般认知操作过程及其方式,旨在为数学建模教学的有效实施提供认知理论基础.但该模型尚需通过更深入的理论研究与更广泛的实证研究优化与完善.     

从“元曲四大家”的演变看戏曲批评的发展

古代不同时期的戏曲批评家对＂元曲四大家＂及地位存在不同的见解,这其实反映了他们不同的戏曲批评观。从这不同的戏曲批评观中,我们可以梳理出古代戏曲批评观的变化情况,总的来说,经历了重音韵的顺畅,到重音律标准和曲词的情感本色,到最后注重剧本创作这样一个过程。     

A Dynamic Model for Education of Doctoral Students and Guidance of Supervisors in Research Groups

In the department of mathematics of the Luleå University of Technology in Sweden, a dynamic model for the education of doctoral students and guidance of supervisors in research groups has been developed and applied for several years now. Presently groups in mathematics as well as a group in mathematics education are working according to this model and treated in the same way. Moreover, both the students and the supervisors get some education and experience also in elements, which usually are not included in more traditional models for supervision in the mathematical sciences in Sweden. In this paper, we describe our model as well as some experiences of it. Moreover, the results of a questionnaire addressed to and answered by all doctoral students (both finished and still in the program) are presented, evaluated and compared with some related investigations in Sweden. We claim that the students in general are very satisfied to be supervised and guided in this way. In principle, there have been no cases of dropping out of the Ph.D. programs, students obtained their degrees within the stipulated time and the careers after the studies have been successful. We hope that this positive experience will stimulate other universities to test and evaluate our model (or relevant parts of it) under different conditions.     

Articulation of Conceptual Knowledge and Argumentation Practices by High School Students in Evolution Problems

The oral arguments of 12th grade students while solving tasks related to evolution are examined. Two groups (N = 45), taught by the same teacher, were studied during a complete teaching sequence. The paper focuses on data from the last sessions, devoted to solving problems in small groups, problems related to different dimensions of the evolutionary model. Data include video recordings, the students’ written productions and the researcher (first author) field notes. The objective is to examine the process of articulation of students’ argumentation practices with their use of evolutionary models. The results show that participants were able to apply notions such as common ancestors, radiation, or gradualism to different contexts. The arguments required the articulation of evolution notions with argumentative practices as coordinating evidence with claims at different epistemic levels. The influence of the teacher’s strategies in the students’ role is discussed.     

Exploring Mathematical Definition Construction Processes

The definition of ‘definition’ cannot be taken for granted. The problem has been treated from various angles in different journals. Among other questions raised on the subject we find: the notions of concept definition and concept image, conceptions of mathematical definitions, redefinitions, and from a more axiomatic point of view, how to construct definitions. This paper will deal with ‘definition construction processes’ and aims more specifically at proposing a new approach to the study of the formation of mathematical concepts. I shall demonstrate that the study of the defining and concept formation processes demands the setting up of a general theoretical framework. I shall propose such a tool characterizing classical points of view of mathematical definitions as well as analyzing the dialectic involving definition construction and concept formation. In that perspective, a didactical exemplification will also be presented.     

Tables turned: Physics in the service of mathematics

E T Bell, the famous author of ‘Men of Mathematics’, has described mathematics as the ‘Queen of Arts and Servant of Science’. What he meant is that mathematics serves science by entering into the picture as soon as a proper mathematical model is set up by the scientist, and then after a purely mathematical analysis of the model, the final mathematical step is interpreted scientifically. The purpose of the present article is to convince the readers that sometimes the roles of science and mathematics are reversed, and a mathematical problem is interpreted as a physics problem; the laws of physics are utilized for a physical analysis, and the final result of the physical analysis is interpreted mathematically. We shall illustrate this by means of few examples.     

An Investigation of Pre-service Middle School Mathematics Teachers’ Ability to Conduct Valid Proofs,Methods Used,and Reasons for Invalid Arguments

The purposes of this study are to investigate Turkish pre-service middle school mathematics teachers’ ability in conducting valid proofs for statements regarding numbers and algebra in terms of their year of enrollment in a teacher education program, to determine the proof methods used in their valid proofs, and to examine the reasons for their invalid arguments. A proof questionnaire containing three proof statements was administered to 115 pre-service middle school mathematics teachers in a large state university in Ankara, Turkey. The results showed that more than half of the pre-service teachers were able to conduct valid proofs for the given statements. In terms of year levels, it was seen that the seniors were the least successful group in conducting valid proofs for each statement. When pre-service teachers’ valid proofs were analyzed, it was concluded that mathematical induction and direct proof were the mostly used methods for the given statements. When pre-service teachers’ invalid arguments were analyzed, it was seen that “inserting numbers to verify the given statement” and “rewriting the givens in the statement” were the common reasons for stating invalid arguments.     

Applied mathematical problem solving,modelling, applications,and links to other subjects — State,trends and issues in mathematics instruction

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.Written version of a Survey Lecture given jointly at the Sixth International Congress on Mathematical Education (ICME-6, Budapest 1988). A condensation was published in a volume with contributions from the ICME-6 Theme Groups on Problem Solving, Modelling and Applications and on Mathematics and Other Subjects (Blum/Niss/Huntley 1989, pp. 1–21).     

无线电信号传输的区域覆盖

以一个无线电信号覆盖圆域的工程问题为例,建立了用若干个小圆覆盖大圆区域的数学模型并求出其最优解,同时还给出了实现最优方案的充分条件和必要条件。对于较少用户情形,以覆盖效率为指标确定实现面积覆盖的最少小圆数目;对大容量用户,综合考虑用户密度和覆盖密度进行网格设计,在保证完全覆盖的同时避免了通信设备的闲置和拥堵,使方案达到最优。采用的方法可推广到一般情形,对通信工程中信号传输覆盖问题有一定的指导作用。     

叶燮诗歌发生论——以《原诗》为中心

叶燮在《原诗》中论及了诗歌发生问题。他关于这一问题的根本学说,可以概括为＂我四物三＂说。在这一根本学说之外,先有胸襟说、触物起兴说、诗无定法说这三个具体说法值得注意。＂我四物三＂说是叶燮诗歌发生论的＂纲＂,而先有胸襟说、触物起兴说和诗无定法说这三说则是＂目＂,它们是对＂我四物三＂说的进一步补充和完善。这一＂纲＂三＂目＂比较圆满地实现了叶燮的理论目的。     

Drawing space: mathematicians’ kinetic conceptions of eigenvectors

This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of eigenvectors depends strongly on both time and motion—hence, on physical interpretations of mathematical abstractions—which are dimensions of thinking that are typically deliberately absent from formal, written definition of the concept. We shall also show how gesture and talk contribute differently and uniquely to mathematical conceptualisation and further elaborate the claim that diagrams provide an essential mediating role between the two.     

Socioeconomic and Political Context of Current English Educational Policy

In the following we shall try to present a brief statistically based sketch of the present trends in Great Britain's economic development* and their effects on the employment structure. Our purpose in presenting these statistics is to illustrate and provide a general background for the socioeconomic processes to which the expressions "scientific and technical progress" or "technical and social change" refer. This approach is also made necessary, we feel, by the fact that references to present social and economic trends have been an important part of the various arguments adduced to justify reforms in education. In other words, reforms bearing on the education of the future work force — that is, its occupational and social training — are justified or rejected on the basis of references to these trends and their actual or projected effects.     

The Development of Teacher Knowledge in Support of Student Mathematical Inquiry

Abstract

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities from multiple courses in the program, we offer general principles of instruction for supporting mathematical inquiry at all grade levels. We contend that an awareness and application of the multiple facets of mathematical knowledge for teaching can be critical to supporting mathematical inquiry across the K-16 spectrum.     

Providing written feedback on students’ mathematical arguments: proof validations of prospective secondary mathematics teachers

Mathematics teachers play a unique role as experts who provide opportunities for students to engage in the practices of the mathematics community. Proof is a tool essential to the practice of mathematics, and therefore, if teachers are to provide adequate opportunities for students to engage with this tool, they must be able to validate student arguments and provide feedback to students based on those validations. Prior research has demonstrated several weaknesses teachers have with respect to proof validation, but little research has investigated instructional sequences aimed to improve this skill. In this article, we present the results from the implementation of such an instructional sequence. A sample of 34 prospective secondary mathematics teachers (PSMTs) validated twelve mathematical arguments written by high school students. They provided a numeric score as well as a short paragraph of written feedback, indicating the strengths and weaknesses of each argument. The results provide insight into the errors to which PSMTs attend when validating mathematical arguments. In particular, PSMTs’ written feedback indicated that they were aware of the limitations of inductive argumentation. However, PSMTs had a superficial understanding of the “proof by contradiction” mode of argumentation, and their attendance to particular errors seemed to be mediated by the mode of argument representation (e.g., symbolic, verbal). We discuss implications of these findings for mathematics teacher education.     

危机,创新与知识产权之道

1　Introduction　Chinese economy is facing a new round ofdevelopmental fastigium, featuring the shift fromquantity centered development model in scale toquality centered sustainable development model, thetransition from industrialization model first stage tomid term stage, and the new development model ofsystem innovation and value innovation.Correspondingly, China’s economy is facing a newround of development peri…