以物质的量为核心的化学计量系统构建及其产生式教学策略

从认知心理学知识学习角度分析以物质的量为核心的化学计量系统,从教学策略角度,可以将其划分为知识系统和操作系统2大部分,其知识系统主要属于陈述性知识,而操作系统则主要属于程序性知识。按照陈述性知识的认知特点设计体现物质的量相关知识系统网络结构功能的探究教学;按程序性知识的认知规律设计产生式自展过程等较高层次的思维运作。从而形成了以物质的量为核心的化学计量系统知识建构的探究教学方法与实际问题解决的小步子产生式策略。其意义在于以结构化系统替代零散知识,用逻辑性思维替代常识比喻,以智能化产生替代机械运算,为以物质的量为核心的化学计量系统教学探索更加有效的策略与方法。     

Generative Art with Swarm Landscapes

We present a generative swarm art project that creates 3D animations by running a Particle Swarm Optimization algorithm over synthetic landscapes produced by an objective function. Different kinds of functions are explored, including mathematical expressions, Perlin noise-based terrain, and several image-based procedures. A method for displaying the particle swarm exploring the search space in aesthetically pleasing ways is described. Several experiments are detailed and analyzed and a number of interesting visual artifacts are highlighted.     

Developing flexible procedural knowledge in undergraduate calculus

Mathematics experts often choose appropriate procedures to produce an efficient or elegant solution to a mathematical task. This flexible procedural knowledge distinguishes novice and expert procedural performances. This article reports on an intervention intended to aid the development of undergraduate calculus students’ flexible use of procedures. Two sections of the same course were randomly assigned to treatment and control conditions. Treatment students completed an assignment on which they resolved derivative-finding problems with alternative methods and compared the two resulting solutions. Control students were assigned a list of functions to differentiate. On the post-intervention test, treatment students were more likely to use a variety of solution methods without prompting than the control. Moreover, the set of treatment section solutions were closer to those of a group of mathematics experts. This study presents evidence that not only is flexible procedural knowledge a key skill in tertiary mathematics, it can be taught.     

Kinetic analysis of TG data XXXVI: Influence of procedural variables upon the apparent kinetic parameters of the thermal deamination

A number of 7 complexes of the [Co(DH)₂(amine)₂)]I type (DH₂ stands for dimethyloxime) have been studied by means of thermogravimetry and differential scanning calorimetry in nitrogen atmosphere, by using heating rates of 2.5, 5 and 10 K min^–1. In all cases an endothermal deamination reaction occurs leading to the relatively stable [Co(DH)₂I(amine)] intermediate. For this reaction apparent kinetic parameters have been derived. The influence of heating rate is discussed. The validity of a linear and a non-linear kinetic compensation law was verified.This revised version was published online in November 2005 with corrections to the Cover Date.     

Evaluating students’ conceptual and procedural understanding of sampling distributions

Introductory statistics courses, which are important in preparing students for their daily lives, generally derive inferential statistics from informal knowledge. In this transition process, sampling distributions have an important place, yet research has shown that students often have difficulties with this concept. In order to increase their understanding of sampling distributions, students should have a strong conceptual foundation that is balanced with procedural knowledge. To address this issue, this study was designed to examine the relationship between college students’ procedural and conceptual knowledge of sampling distributions. With this aim in mind, an achievement test consisting of two sections – procedural and conceptual knowledge – was prepared. In answering the questions related to procedural knowledge, the participants were more successful in identifying the relationship between standard deviation of a population and sample means. However, they lacked theoretical knowledge about statements that they had heard or knew intuitively. Simulation activities provided in statistics courses may support students in developing their conceptual understanding in this regard.     

罪与罚——司法公正的统计学分析

本文用统计学中的假设检验方法对司法审判中的定罪过程作一个比较分析,从另外一个角度来理解司法公正的内涵。     

The mathematics textbook at tertiary level as curriculum material – exploring the teacher's decision-making process

This paper reports on a study about how the mathematics textbook was perceived and used by the teacher in the context of a calculus part of a basic mathematics course for first-year engineering students. The focus was on the teacher's choices and the use of definitions, examples and exercises in a sequence of lectures introducing the derivative concept. Data were collected during observations of lectures and an interview, and informal talks with the teacher. The introduction and the treatment of the derivative as proposed by the teacher during the lectures were analysed in relation to the results of the content text analysis of the textbook. The teacher's decisions were explored through the lens of intended learning goals for engineering students taking the mathematics course. The results showed that the sequence of concepts and the formal introduction of the derivative as proposed by the textbook were closely followed during the lectures. The examples and tasks offered to the students focused strongly on procedural knowledge. Although the textbook proposes both examples and exercises that promote conceptual knowledge, these opportunities were not fully utilized during the observed lectures. Possible reasons for the teacher's choices and decisions are discussed.     

The numerical evaluation of the error term in Gaussian quadrature rules

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.     

A comparative analysis of British and Taiwanese students’ conceptual and procedural knowledge of fraction addition

This study examines students’ procedural and conceptual achievement in fraction addition in England and Taiwan. A total of 1209 participants (561 British students and 648 Taiwanese students) at ages 12 and 13 were recruited from England and Taiwan to take part in the study. A quantitative design by means of a self-designed written test is adopted as central to the methodological considerations. The test has two major parts: the concept part and the skill part. The former is concerned with students’ conceptual knowledge of fraction addition and the latter is interested in students’ procedural competence when adding fractions.

There were statistically significant differences both in concept and skill parts between the British and Taiwanese groups with the latter having a higher score. The analysis of the students’ responses to the skill section indicates that the superiority of Taiwanese students’ procedural achievements over those of their British peers is because most of the former are able to apply algorithms to adding fractions far more successfully than the latter. Earlier, Hart [1 Hart KM. Children's understanding of mathematics: 11–16. Oxford: Alden Press; 1981. [Google Scholar]] reported that around 30% of the British students in their study used an erroneous strategy (adding tops and bottoms, for example, 2/3 + 1/7 = 3/10) while adding fractions. This study also finds that nearly the same percentage of the British group remained using this erroneous strategy to add fractions as Hart found in 1981.

The study also provides evidence to show that students’ understanding of fractions is confused and incomplete, even those who are successfully able to perform operations. More research is needed to be done to help students make sense of the operations and eventually attain computational competence with meaningful grounding in the domain of fractions.