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如果我们对有理数的加、减、乘、除、乘方运算仔细加以比较,就会发现,在有理数运算中,加减法是统一的,乘除法是统一的,而乘方运算则是特殊的乘法(相同因数相乘),只要理解了底数、指数的意义,乘方也就不难掌握了。由此可见,掌握有理数的加法和乘法运算是学好有理数运算的基础,而学会转化则是学好有理数运算的关键。 相似文献
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初等函数不论是在数学的理论上或是应用上都是经常遇到的,而且是极其重要的。一、初等函数的分类:通常把初等数学中所讨论的运算:加、减、乘、除、任意次的乘方和开方,以任意 相似文献
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刘东升 《初中生世界(初三物理版)》2014,(10):29-29
活动目的：为第五种运算的乘方创设一个简短的探究活动,帮助同学们认识乘方运算,并正确进行乘方运算,再讲一则故事引导大家感受乘方运算的奇异性.活动流程：一、回顾互逆运算的关系请同学们交流加、减运算,乘、除运算之间的关系,举例说明.设计意图：让同学们举例说明加减、乘除的互逆运算,感受运算之间的转化思想. 相似文献
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采用动态分配的字符数组存储长整数，0位置保存数的符号，其他位置保存整数的各位数值，另外记录整数的位数，实现了加、减、乘、除和乘方的运算函数并对各个函数的时间复杂度进行了分析． 相似文献
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周时和 《初中生世界(初三物理版)》2014,(10):23-23
初学有理数混合运算时,有些同学容易受到运算法则、符号、括号的干扰而出错,本文介绍一种分段意识,希望能对大家有所帮助.一、根据运算符号来分段有理数的基本运算有五种：加、减、乘、除、乘方,其中加减为第一级运算,乘除为第二级运算,乘方为第三级运算.所谓运算符号分段法,就是用低级运算符号把高级运算分成若干段. 相似文献
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姜重旭 《数理化学习(初中版)》2015,(2):2-4
我们知道,初中数学中的运算主要是加、减、乘、除和乘方、开方以及指数运算等,在现代数学中运算种类更多,特别是电子计算机的运用,使运算的内容更为丰富.纵观近年各地中考题,出现了一种定义新运算规则、给出一些新定义的运算符号从而推导出运算方法的题目,解答这类问题的关键是理解新运算的定义,严格按规定的计算法则代入计算,把定义新符号运算转化为熟悉的加、减、乘、除和乘方、开方以及指数运算.这种从未知到已知的思维过程,就是一种很好的转化数学思想的考 相似文献
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王小兰 《山西教育(综合版)》2003,(18):22-23
如果我们对有理数的加、减、乘、除、乘方运算仔细加以分析 ,就会发现在有理数运算中 ,加减法是统一的 ,乘除法是统一的 ,而乘方运算则是特殊的乘法 (相同因数相乘 ) ,只要理解了底数、指数的意义 ,乘方也就不难掌握了。由此可见 ,掌握有理数的加法和乘法运算是学好有理数运算的基础 ,而学会转化则是学好有理数运算的关键。有理数的加减法互为逆运算 ,它们既对立又统一。有了相反数的概念以后 ,有理数的加减法就可以互相转化 : 因此 ,在有理数范围内 ,加法和减法运算都可以统一为加法运算。有理数的乘除法也互为逆运算。在有了倒数的概念… 相似文献
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重点考点
（1）有理数、数轴、相反数、绝对值、有理数的大小比较、倒数、乘方的意义．有理数的加、减、乘、除、乘方以及混合运算． 相似文献
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如果我们对有理数的加、减、乘、除、乘方运算仔细加以分析,就会发现：在有理数运算中,加减法是统一的,乘除法是统一的,而乘方运算则是特殊的乘法（相同因数相乘）,只要理解了底数、指数的意义,乘方也就不难掌握了．由此可见,掌握有理数的加法和乘法运算是学好有理数运算的基础,而学会转化则是学好有理数运算的关键．有理数的加减法互为逆运算,它们既对立,又统一．有了相反数的概念以后,有理数的加减法就可以互相转化：因此,在有理数范围内,加法和减法运算都可以统一为加法运算．例如,（－3．78）＋（-4．05）－（－6．17）－… 相似文献
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同余概念是数论中的一个重要组成部分 ,利用同余的定义、定理及一些性质 ,可以检验整数的整除性及整数的加法 ,整数的乘积运算结果等 ;利用费马定理 ,进行素数、合数的判别是一个很有效的方法 相似文献
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Floyd R. Vest 《Educational Studies in Mathematics》1971,3(2):220-228
Summary The above catalog contains fifteen headings, each of which indicates a collection of families of models for multiplication and division of whole numbers. The catalog refers to somewhat more than sixteen families of models which are easily distinguished one from the other.Not included in the catalog thus far developed are several interpretations of multiplication and division that are also of interest. Among these are models based on the equivalency of denominations of money and various units of measurement. Other interpretations which are of historical interest are those of McLellan and Dewey [15] and Thorndike [24]. The relation between models of operations on whole numbers and models of operations defined on larger universal sets is also of interest. One aspect of this area of interest is the process of constructing models of multiplication and division of whole numbers from such models by altering the rules of the model or delimiting its universal set. For example, one can begin with one of Diénès' models of multiplication of integers [8, pp. 57–58] and make approapriate adjustments and result in a model of multiplication of whole numbers. Other interpretations developed by Diénès are of interest because they involve concretizations of whole numbers which are operators as opposed to states [8, pp. 12, 30; 9, p, 36].These are a great many strategies available for the use of models in teaching the operations on whole numbers. In one such strategy, an educator can define either multiplication or division on some basis (most likely in terms of a model) and then the other can be defined as its inverse.Another strategy is to define each operation in terms of a different model. For example, one might define multiplication in terms of the repeated addition model and division in terms of the repeated subtraction model.Still another type of procedure involves a multiple embodiment strategy in which several interpretations are taught as representing each operation.The choice of a particular strategy would depend upon a great many factors. Some of the factors would be the type of culture and students for which the program is written, the psychological assumptions adopted by the writer, and the writer's knowledge of the domain of models for the operations as well as their relation to the abstract mathematical domain which they represent. This article has contributed to a basis for intelligent decisions in this area by presenting a characterization of the domain of models for multiplication and division of whole numbers and their relation to the abstract operations. 相似文献
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从数据结构 算法的角度系统地给出的高精度数值计算的程序,可以突破计算机对数值表示范围的限制,从而使其具有任意位高精度数值的加、减、乘、除等强大的数值计算的功能。 相似文献
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12-and 13-year-olds were tested with two types of tasks to test their understanding of applications of the multiplication and division of positive numbers: (i) writing down calculations required to solve verbal problems, and (ii) making up stories to fit given calculations. Selected pupils were interviewed to investigate further the thinking processes involved. The results indicate (a) the pervasive nature of certain numerical misconceptions, (b) the effects of structural differences among the items; particularly whether multiplication can be conceived as repeated addition or not, and whether division has the structure of partition, quotition or rate, (c) specific effects of context attributable to such aspects as relative familiarity, and (d) various interactions between these three sets of factors.With the collaboration of Joanna Rigg and Malcolm Swan. 相似文献
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The division operation is not frequent relatively in traditional applications, but it is increasingly indispensable and important
in many modern applications. In this paper, the implementation of modified signed-digit (MSD) floating-point division using
Newton-Raphson method on the system of ternary optical computer (TOC) is studied. Since the addition of MSD floating-point
is carry-free and the digit width of the system of TOC is large, it is easy to deal with the enough wide data and transform
the division operation into multiplication and addition operations. And using data scan and truncation the problem of digits
expansion is effectively solved in the range of error limit. The division gets the good results and the efficiency is high.
The instance of MSD floating-point division shows that the method is feasible. 相似文献
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From classifications of word problems in international discussion of elementary mathematics instruction as well as from conceptual elaborations of didactical analyses in Germany, a classification of semantic structures of one-step word problems involving multiplication or division is proposed, comprehending four main classes: Forming the n-th multiple of measurers, combinatorial multiplication, composition of operators, and multiplication by formula. This classification is more comprehensive and differentiated than the classifications of Vergnaud (1983), Nesher (1988), and Bellet al. (1989) — aiming at a better assignment between diverse contextual circumstances and conceptual demands of mathematics and at compatibility with the well-known semantic structures of addition and subtraction word problems. 相似文献
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Effective strategies for mental and written arithmetic calculation from the third to the fifth grade
Daniela Lucangeli Patrizio E. Tressoldi Monica Bendotti Michela Bonanomi Linda S. Siegel 《教育心理学》2003,23(5):507-520
The strategies used to solve mental and written multidigit arithmetical addition, subtraction, multiplication and division were observed in 200 third, fourth and fifth grade children. A strategy was classified as effective if it resulted in the correct solution at least 75% of the time. For mental addition and subtraction, primitive strategies such as counting on fingers and counting on (mental counting from a specific point), and the more sophisticated strategy 1010 (solution of the calculation problem using tens and units separately) were more effective than the strategies learned at school. In written addition, subtraction and multiplication there was a shift from the CAR+to the CAR- strategy (tabulating with, or without, a carried amount) from the third to the later grades. Results show that typical strategies taught at school progressively substitute every other strategy both in mental and written calculation, but without reaching the criterion of effectiveness. The implications for maths curricula are discussed. 相似文献
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Researchers have speculated that children find it more difficult to acquire conceptual understanding of the inverse relation
between multiplication and division than that between addition and subtraction. We reviewed research on children and adults’
use of shortcut procedures that make use of the inverse relation on two kinds of problems: inversion problems (e.g., 9 ×24 ?24 {9} \times {24} \div {24} ) and associativity problems (e.g., 9 ×24 ?8 {9} \times {24} \div {8} ). Both can be solved more easily if the division of the second and third numbers is performed before the multiplication of
the first and second numbers. The findings we reviewed suggest that understanding and use of the inverse relation between
multiplication and division develops relatively slowly and is difficult for both children and adults to implement in shortcut
procedures if they are not flexible problem solvers. We use the findings to expand an existing model, highlight some similarities
and differences in solvers’ use of conceptual knowledge across operations, and discuss educational implications of the findings. 相似文献
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吴旭平 《南昌教育学院学报》2011,26(5):126-127
本文从数的概念起源、数的基础运算和数学的基本特征等方面来解析数学的本质。数的概念来自理性的抽象,现实中来源于可替代物。基础运算中加法是母法则,减法是唯一的分析判断,加减反映了量的连续性。而乘除反映了量的间断性。乘除的二次抽象性无法反映不确定性关系。数学创造力与艺术创造力完全不同。数学演绎中的理性盲点需要经验来弥补。 相似文献
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In order to give insights into cross-national differences in schooling, this study analyzed the development of multiplication
and division of fractions in two curricula: Everyday Mathematics (EM) from the USA and the 7th Korean mathematics curriculum (KM). Analyses of both the content and problems in the textbooks
indicate that multiplication of fractions is developed in KM one semester earlier than in EM. However, the number of lessons
devoted to the topic is similar in the two curricula. In contrast, division of fractions is developed at about the same time
in both curricula, but due to different beliefs about the importance of the topic, KM contains five times as many lessons
and about eight times as many problems about division of fractions as EM. Both curricula provide opportunities to develop
conceptual understanding and procedural fluency. However, in EM, conceptual understanding is developed first followed by procedural
fluency, whereas in KM, they are developed simultaneously. The majority of fraction multiplication and division problems in
both curricula requires only procedural knowledge. However, multistep computational problems are more common in KM than in
EM, and the response types are also more varied in KM. 相似文献