数学

Because the mathematical linguistics are one kind by the mathematical symbol, mathematics terminology and the scientific language which is composed after the improvement natural language, therefore in mathematics teaching, the teacher not suitable direct use mathematical linguistics achievement teaches the language generally, but must act according to student's knowledge foundation and the psychological feature, transforms the mathematical linguistics as easily the language which is accepted by the student.

由于数学语言是一种由数学符号、数学术语和经过改进的自然语言组成的科学语言，因此在数学教学中，教师一般不宜直接使用数学语言作为讲授语言，而必须根据学生的知识基础和心理特征，将数学语言转化为容易被学生所接受的语言。

Language is the carrier of communication and understanding, learning math is math thinking, mathematics and mathematical language is a tool for thinking, so to master the language of mathematics is a smooth and effective conduct of mathematics learning activities of one of the important foundation.

语言是沟通与理解的载体，数学学习活动基本上是数学思维活动，而数学语言是数学思维的工具，所以掌握数学语言是顺利地、有成效地进行数学学习活动的重要基础之一。

In this study, we try to provide the examples of the application of mathematics to music; the application of golden ratio to musical structure; the calculation and derivation of Pythagoras scale、pure scale and twelve-tone equal temperament scale; the application and analysis of mathematics in fifth-degree co-generation method; and the two-dimension research of the interval and scale. These discussions apparently show the strong correlation of mathematics and music.

本文藉由数学与音乐的多元对话，探讨音乐领域中数学的应用范例；黄金比例在乐曲结构之应用；运用数学推演和计算毕氏音阶、纯律音阶和十二平均律音阶的组成；探讨五度相生律的应用范例与数学的密切关系；归纳和分析音程和音调的数学二元图表，在在都显示出数学与音乐密不可分的关系。

After a further analysis based on the empirical results,a trial probe on the cognitiveprocessing mechanism of the problem representation of the word problem in two types of MLDwas made by the author.The MRD performed much poorer than the MLD only in the mostdifficult equation listing of word problem and the medium and most difficult problemrepresentation of word problem,which showed no difference in computation and comprehensionof simple meaning of the problem,but the gap between two types of MLD became wide as afunction of difficulty and cognitive loading.It indicated that the MLD only had some advantage over MRD for they used more cognitive skills to solve the problem.

基于以上实验的结果，对两类数学困难小学生的应用题问题表征的认知机制作如下推断：混合型数学困难学生仅在高难度水平的应用题列式成绩和中高难度水平应用题问题表征水平上比单纯型数学困难学生得分显著低下，表明两类数学困难小学生在计算能力与理解简单题意的能力上并无差异，但随着难度提高，认知负荷加重，两类数学困难学生在应用题解题上的差异得以突显，表明当需要运用更多的认知能力解决问题时，单纯型数学困难学生比混合型困难学生更具优势。

In the historical evolution of mathematic thought, content and method, m athematic truth has assumed some postmodern characteristics.The targets of the pursuit of mathematic truth have changed from the objectives and valu es of metaphysics to the relative and varied theoretical constructions.Mat hematic truth is an open system with different levels and frameworks. It h as transcended the scope of natural truth and has generated a new dimensio n,i.e.,selectivity.Both formalization and non-formalization are effec

在数学思想、内容与方法的历史性变革过程中，数学真理的观代性开始发生转向，逐步表现出一些后现代特征：数学真理从追求形而上学的目标与价值转向追求相对的、多样化的理论构建；数学真理是一个具有不同层次性和等级结构的开放体系；数学真理超越了自然真理的范畴，开始生长出一种新维度——可选择性；形式化与非形式化都是获得数学真理的有效手段。

So it is highly beneficial for maths treachers to study phylosophy and apply it in their teaching and in their research of mathematical methodics.

哲学是学习数学、认识数学的理论指导，数学工作者进行哲学研究，有益于数学与数学教育辨证性质的研究；有益于数学方法论的深入研究。

We will introduce some definitions in the Mathematics Ecology and the mathematical theories and methods. Methods for studding the population ecology or the more ordinary ecology are by setting up the mathematical modelings. We will give the examples of the single population models and the population with interaction models.

简单介绍数学生态学中的一些常用的名词和研究问题所用的数学手段-通过数学建模的方法，将一个实际的生态问题量化为一个数学问题，给出常用的单种群增长的数学模型和具有种间关系的多种群数学模型。

The purposes of this study were:(1) to explore whether there were interactions between "Feedback" and "Goal-setting" on both students' mathematical performance and test anxiety;(2) to compare the differences of students' mathematical performance and test anxiety between students' self-set goals and teacher-assigned goals;(3) to compare the differences of students' mathematical performance and test anxiety between students of different predicting abilities.

本研究的目的有三：一为探讨「回馈方式」与「目标设定」二因子之间是否有交互作用效果存在；二为比较学生自订目标与教师指定目标间，学生在数学作业表现或是数学测试焦虑分数上的差异；三为分析学生自订目标中，不同预测能力的学生在数学作业表现或是数学测试焦虑分数上的差异。本研究的受试来自台北市、台北县六所国小261名五年级学生，使用的工具有数学乘除法测验及数学测试焦虑量表。

The major findings were as follows:(1) There were significant interactions between Feedback and Goal-setting in both students' mathematical performance and test anxiety;(2) No significant differences were found in mathematical performance and test anxiety between the student self-set goal condition and the teacher-assigned goal condition when feedback was presented;(3) There were significant differences in students' mathematical performace between correct-predicting students' and incorrect-predicting students, but no difference was found in students' test anxiety between the two groups of students;(4) High-estimating students and low estimating students showed significant differences in mathematical performance, but no difference in test anxiety.

在有回馈的情形下，学生自订目标与敎师指定目标间，其学生在数学作业表现或是在数学测试焦虑分数上均无显著差异存在。3。学生自订目标中，预测正确组与预测不正确组学生在数学作业表现上有差异存在，在数学测试焦虑分数上无差异存在。4。学生自订目标中，高估组与低估组学生在数学作业表现上有差异存在，在数学测试焦虑分数上无差异存在。

Going at the teaching of mathematical thought and method during high school is an important means by which the school in the 21th century cultivate the person with innovative spirit and practical bility.Moreover going in for the teaching study of the mathematical thought and method in high school can make ours absorb well the international and national mathematical thought and methodology knowledge,and improve the cognition to the importance of the teaching about mathematical thought and method,so that they are able to practise consciously and selfconsciously the teaching .

中学阶段进行数学思想方法的教学是21世纪学校培养具有创新精神与实践能力的人才的重要手段，而进行中学数学思想方法的教学研究更能使我们中学数学教师充分吸收国内外数学思想方法论知识，提高对数学思想方法教学重要性的认识，从而能够有意识、自觉地实践数学思想方法教学。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。