巧设情境,计算有理数加减法

有理数是初中数学的最重要的部分之一,而有理数加减法运算是有理数运算的基础,所以学好有理数的加减运算至关重要,那么如何才能提高运算能力呢,关键是要记住运算法则,掌握运算方法.人教版7年级数学教材上对有理数的运算法则是这样规定的:1.同号两数相加,取相同的符号,并把绝对值相加.2.绝对值不相等的异号两数相加,取绝对值较大的加数的符号,并用较大的绝对值减去较小的绝对值.互为相反数的     

进行有理数运算要注意什么

升入初中之后，同学们明显地感觉到数的范围扩大了，由小学时学的数一下子扩大到既有符号又有绝对值的有理数，由此带来了在进行有理数的运算时的复杂和易错．那么，怎样避免这些问题呢?     

《有理数》复习指导

有理数是在小学学过的正数和零的意义及运算的基础上学习的，本章内容可以概括为有理数的概念与有理数的运算，具体体现为一个工具——数轴；两个概念——相反数、绝对值；三种数学思想——分类思想、数形结合思想、转化思想：四种运算——加（减）、乘（除）、乘方和近似计算．这些是我们今后进一步学习数和式的运算的基础．也为学好数学培养良好的学习习惯，进而会用数学思维方式学习数学．     

让学生经历知识的形成过程——谈“有理数的加法”的问题设计

1．1目标解读 有理数加法是算术数集扩充为有理数集之后学生学习的第一种运算,它是算术数加减法的拓展与延伸．借助有理数的性质、符号及绝对值概念,有理数的加法运算可以转化成算术数的加减运算．有理数加法法则的探索过程不但考查了学生灵活运用所学知识（如正负数、绝对值、算术数的运算、数轴等）解决未知问题的能力,[第一段]     

第2讲 实数的运算和非负数性质

要点复习 1．运算法则 （1）同号两数相加，取____的符号，并把____相加，绝对值不相等的异号两数相加，取绝对值____加数的符号，并用____的绝对值减去____的绝对值．     

加碱运算中的“整队集合”

在有理数的加减运算中，形式复杂种类多变，要想提高计算速度，增加准确度，在加减运算之前先根据数的特征进行“整队集合”是十分必要的．     

《分式的运算》测试题

特殊化与一般化是辅助解题的重要工具.——波利亚(匈牙利数学家,1887—1985)问题导引:1.你知道分式的乘除、乘方、加减运算法则吗?你能根据这些运算法则熟练进行分式的混合运算吗?2.你知道负整数指数幂的运算性质吗?你会用科学记数法表示绝对值小于1的数吗?     

让学生经历知识的形成过程——谈“有理数的加法”的问题设计

1 解读教材 1.1 目标解读有理数加法是算术数集扩充为有理数集之后学生学习的第一种运算,它是算术数加减法的拓展与延伸.借助有理数的性质、符号及绝对值概念,有理数的加法运算可以转化成算术数的加减运算.有理数加法法则的探索过程不但考查了学生灵活运用所学知识(如正负数、绝对值、算术数的运算、数轴等)解决未知问题的能力,而且还充分体现了分类、转化、数形结     

《数学课程标准》第一学段“数与代数”具体目标阐释（二）

二、数的运算本学段数的运算的主要内容有:认识四则运算的意义;能计算简单的整数加减法与乘除法;会计算简单的分数、小数加减运算;能运用不同的方法解决生活中的简单问题等。这些内容是数的运     

我教有理数的加减法

为了生活及生产的需要,在学习了负数之后,数的范围已扩展到有理数,我们将在有理数范围内研究数的表示、大小比较与运算等;前两节借助数轴学习了相反数与绝对值的概念,这为有理数的运算奠定了基础,有理数的加减法是后面学习整式的加减、解一元一次方程等内容的基础,它的作用至关重要.一、有理数的加法教学难点是异号两数相加,对于从未接触过"异号两数相加"的七年级学生来说增大了思维强度,尤其是需要通过绝对值大小的比较来确定和的符号和加     

Systematic Mathematical Errors and Cognitive Load

The hypothesis that the intrinsic nature of algebraic bracket tasks causes an uneven distribution of cognitive load during computation was tested in three experiments with grades 8 and 9 students. In Experiment 1, students were given problems which required two successive brackets to be expanded; each bracket required two operations (computations) to be completed. It was discovered that more errors were made during the calculation of the second bracket than the first, and more errors were made during the second operation than the first operation within each bracket. Verbal protocols collected in Experiment 2 indicated that most errors were caused by failures in working memory rather than poorly learned rules. In Experiment 3, a dual-task methodology showed that the cognitive nature of brackets affected working memory performance. It was concluded that the cognitive load experienced by problem solvers on these tasks varied across operations and caused the observed error pattern. Copyright 2001 Academic Press.     

一维无限深势阱的辛算法解分析

利用辛算法计算一维无限深势阱的含时薛定谔方程，解得的波函数的图象与其绝时误差的图象完全相似，这说明各点的相时误差趋向于一个固定值。经计算相时误差在各个X格点处完全相同。波函数相时误差随时间的演变表现出一定的规律性，其实数部分和虚数部分的相时误差周期性地在正负之间来回变化。波函数的实数部分和虚数部分的相时误盖之间有类似于测不准原理的关系，一个相时误差趋向于极小时另一个相时误差趋向于极大，两的乘积为一稳定的小数，随着时间的推进这一小数的绝时值缓慢增大。     

南疆小学生数学运算错误类型及分析——基于新疆大规模测评数据

结合新疆大规模测评数据,针对南疆小学生数学运算中错误进行了微观分析.研究发现,南疆小学生在整数乘法、整数除法、整数混合运算、小数加法、小数减法和小数混合运算6个方面出现错误类型主要表现为概念性错误,即混淆运算符号、不理解小数概念、混合运算中运算顺序混乱和运算律使用错误等问题.出现概念性错误的原因主要包括复杂运算的算法与算理的理解问题,对位值的理解问题和混合运算中运算规则的理解问题.     

高中生"数学运算"素养的落地之策

数学运算是六大数学核心素养之一,是解决数学问题的基本手段,为了减少或避免学生在数学运算中出现的失误,从数学运算的内涵角度提出五个解决问题的策略:明晰运算对象,解析对象实质;掌握运算法则,展示形成过程;探索运算思路,优化运算方法;理解运算算理,设计运算程序;调整运算策略,反思运算结果.     

基于 WebGL 的换热器三维 Web 应用设计与开发

Web application in industrial engineering design process has been discussed with the aim to improve the calculation speed involved,avoid errors in manual calculation,improve reusability,and realize 3D real-time preview of design. Taking the design of heat exchanger for air conditioning and refrigeration as an example,this paper introduces the Web application and WebGL in industrial engineering design,including pre-processing,calculating and post-processing. In the post-processing,the 3D preview of refrigeration design has been realized based on WebGL. The drawing sheet for the heat exchanger have been completed through Web application. The practice shows that the Web application can effectively reduce the manual calculation workload in the design process of heat exchanger,also reduce the manual calculation workload in the trial calculation. And two-dimensional or three-dimensional drawing sheets could be directly generated via the Web application,so as to avoid the calculation error via manual calculation,and to avoid the modification of drawing sheets manually when working conditions are changed.     

A principle of concretization permanence for the formation of arithmetical concepts

The celebrated principle of the permanence of the rules of calculation is contrasted here with another principle, called concretization permanence principle (c.p.p.). Both apply to situations where some arithmetical operation known to children for numbers of a certain kind is to be extended so as to include further numbers (these numbers are already known to the children). In such a case, c.p.p. advises that a suitable concretization schema and a suitable paradigmatic example be chosen and then extended so as to include numbers of the broader domain; students should explore what the given concept becomes in the new situation and in this way find values of the extended operation for a sequence of examples with fixed concretization (or fixed concretization schema) and varying numbers.     

The acquisition of subject-verb agreement in written French: From novices to experts' errors

Recent studies have shown that many subject-verb agreement errors consist of making the verb agree with the immediately preceding noun, as in The smell of the rubbish-bins are foul. Assuming that it is the automaticity of the agreement operation which is responsible for these attraction errors in expert writers, the present studies aimed at demonstrating the gradual automatization of this operation in young writers by examining developmental changes in the occurrence of agreement errors. In three experiments we found that subjects' performance moves from systematic errors in number agreement in young children (e.g., no use of plural marks) to attraction errors in fifth graders and older adults through an intermediate phase characterized by an attention-demanding and easily disrupted computation of verb agreement displayed by some second graders. Attraction errors are a byproduct of the automatization of the implementation of the agreement process.     

日本学生汉语中介语写作偏误分析及教学对策

日本学生在用汉语进行写作的过程中,在语言表达、语篇建构、文化内涵三个层面上存在着一些规律性的偏误,为了防止这些偏误的产生,帮助学生提高汉语写作水平,教师应采取相应的教学对策。     

压力损失可靠性计算和研究

在工程机械、矿山机械、机械加工等设备中广泛使用液压传动，而液压在动力传动中都要产生压力损失。本文就液体在油管内流动时的压力损失计算方法进行了分析和研究，提出了正确计算公式，以免在液压传动系统设计与计算时产生错误和误差，保证其计算准确与可靠性。     

Unraveling the gap between natural and rational numbers

The foundations for more advanced mathematics involve a good sense of rational numbers. However, research in cognitive psychology and mathematics education has repeatedly shown that children and even adults struggle with understanding different aspects of rational numbers. One frequently raised explanation for these difficulties relates to the natural number bias, i.e., the tendency to inappropriately apply natural number properties to rational number tasks. This contribution reviews the four main areas where systematic errors due to the natural number bias can be found, i.e., their size, operations, representations and density. Next, we discuss the major theoretical frameworks from which rational number understanding is currently investigated. Finally, an overview of the various papers is provided.