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1.
We examined the use of balance and inverse methods in equation solving. The main difference between the balance and inverse methods lies in the operational line (e.g. +2 on both sides vs ?2 becomes +2). Differential element interactivity favours the inverse method because the interaction between elements occurs on both sides of the equation for the balance method but only on one side of the equation for the inverse method. In an experimental study, 63 students (mean age = 13) were randomly allocated to either balance or inverse group to undertake a pre-test, study an instruction sheet, complete acquisition equations, sit for a post-test and a concept test. Procedural knowledge was assessed on performance on practice equations and post-test, whereas conceptual knowledge was assessed on performance on the concept test. The inverse group outperformed the balance group on practice equations but not the post-test. Both the balance and inverse groups scored higher on the inverse concept test than the balance concept test. Positive association between performance on procedural knowledge and performance on conceptual knowledge was found for the inverse group but not the balance group. Overall, the evidence obtained indicates a number of educational implications for implementation. 相似文献
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Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side only. In an experiment, middle school students (N?=?71) were randomly assigned to the balance and inverse methods to complete a pre-test, an acquisition phase and a post-test. Pre-test and post-test comparisons found that the inverse group outperformed the balance group for those equations that involved high element interactivity. Instructional efficiency measures further confirmed that the balance method imposed higher cognitive load. The inverse method was capable of reducing cognitive load due to the interacting elements. 相似文献
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The contradiction between the worked example effect that occurs when learners presented with more instructional guidance learn more than learners presented with less guidance and the generation effect that occurs when the reverse result is obtained can be resolved by the suggestion that the worked example effect is obtained using materials high in element interactivity, whereas simpler, low element interactivity materials result in the generation effect. A 2 (guidance: low vs. high) × 2 (element interactivity: low vs. high) × 2 (expertise: low vs. high) experiment investigated this hypothesis with high school trigonometry learners. On an immediate test, high guidance reflecting a worked example effect was found for novices, but a generation effect was obtained for more knowledgeable learners. In contrast, on a delayed test, a three-way interaction between guidance, element interactivity and expertise was found. This interaction was caused by a worked example effect for material high in element interactivity and a generation effect for material low in element interactivity for novices while for more knowledgeable learners, a generation effect was obtained for both low and high element interactivity materials. These results suggest firstly, that both the worked example and generation effects may be more likely on delayed than immediate tests and secondly, that the worked example effect relies on high element interactivity material while the generation effect relies on low element interactivity material. 相似文献
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In this paper, we summarize some recent activities in the field of metamaterial research at the National University of Singapore （NUS）. Integral equations are applied for electromagnetic modelling of supernatural materials. Some special characteristics of the metamaterials are shown. Moreover, quasi-static Lorentz theory and numerical method （i.e., the method of moments for solving the electric field integral equation） and the transmission line theory are both presented to obtain the effective constitutive relations of metamaterials, respectively. Finally, feasibility of fabricating metamaterials based on analysis of equivalent transmission line model in the microwave spectrum and even higher is also shown and correspondingly some broad-bandwidth and low-loss metamaterial structures are designed and synthesized. 相似文献
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INTRODUCTION Conventional materials have positive magnetic permeability and mostly positive electrical permittiv- ity. Veselago (1968) initially assumed a material with negative permittivity and permeability simultane- ously and theoretically demonstrated the abnormal electromagnetic properties. This material, referred to as left-handed material (LHM) or metamaterial, re- verses a basic feature of light, such as, the reversal of the Doppler shift for radiation, and negative refractive in… 相似文献
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使用齐次平衡方法，得到了（2＋1）维破裂孤子方程的一些新多孤子解，齐次平衡方法，能使复杂的（2＋1）维破裂孤子方程转化为简单的线性偏微分方程和双线性偏微分方程，然后通过特定的拟解，便可构造出（2＋1）维破裂孤子方程的丰富的孤子结构。 相似文献
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Joëlle Vlassis 《Educational Studies in Mathematics》2002,49(3):341-359
The use of concrete models for teaching students how to solve equations is often debated in scientific literature. This article aims to examine the balance model and to identify the issues that divide scientists. We based our reflections on the results of an empirical study and analysis of the various arguments put forward by supporters and opponents of the model. We describe learning situations that were the subject of the empirical study, which involved forty students in two 8th-grade classes. The aim was to teach the formal solving method, which involved performing the same operations on both sides of the equation using, notably, the balance model. Analysis of students' reasoning showed that the presence of negative numbers gave rise to many errors. The difficulties presented by negative numbers were reviewed, eight months later, during an interview with five students, chosen from those who took part in the experiment. Within that context, we discuss the relevance of the balance model and analyse the arguments put forward by researchers who either defend or reject its use.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
8.
While the kinematics of the parallel manipulatorhas been studied extensively during the past two dec-ades, more and more papers can be found on the dy-namics of the parallel manipulators now[1—7]. The dy-namics of robotcan be used forthe simulation, controland optimization. It plays an important role inachieving high-speed performance. There are twotypes of dynamical problems for the parallel robot: di-rect dynamics and inverse dynamics. The direct dy-namical problem is to find the response v… 相似文献
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非线性发展方程是人们认识和解释自然界许多现象时得到的数学模型,研究这些模型的解的性态十分重要,其显式解更是人们研究所必需的.F-展开法是求解非线性发展方程精确解的非常有效的方法之一.利用F-展开法,并借助于Riccati方程的精确解,导出(2+1)-维EW方程4种不同形式的精确解. 相似文献
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本文介绍了研究振动方程时的几种分析方法,并讨论了方程解的物理意义。自然界中最基本的振动是简谐振动,讨论简谐振动是研究复杂振动现象的基础,对其研究和分析方法很多,本文介绍几种求解振动方程的几种分析方法：1.常系数线性微分方程的一般求解法;2.拉普拉斯逆变换法;3.简谐振动的矩阵求解法,并讨论了方程解的物理意义。 相似文献
11.
王小明 《温州职业技术学院学报》2002,2(4):25-30
本用反函数多项式展开法导一组求解高次方程或超越方程的计算公式。这组公式包括了牛顿－拉夫森求根公式以及其它一我具有更高精度的求根公式。采用这些高精度的计算公式解方程，常常无须迭代计算即可一步得到理想的结果。这对于不便于迭代计算的方程的求解有较大的应用意义。 相似文献
12.
运用一种新的双曲截断展开方法 ,求得了非线性Schr dinger (NLS)方程新的显式精确解 ,其中包括孤子解、行波解和关于时间t的奇异解 ,并对求解中可能出现的一般性问题进行了讨论 相似文献
13.
A fractal approximation algorithm for inverse initial-value problems of nonlinear differential equations 总被引：1，自引：0，他引：1
唐艳 《重庆大学学报(英文版)》2003,2(2)
1. Introduction Initial-value problems (IVP) for the differential equations are often confronted with in many fields of science, and are particularly common in engineering. These problems are characterized by a governing differential equation and its associated initial conditions. Methods for solving direct IVP have been known for many decades in the area of differential equation. A few of the more popular methods of solution have proven to provide sufficient and even efficient mechanisms … 相似文献
14.
Within the framework of cognitive load theory, the element interactivity and the expertise reversal effects usually are not treated as closely related effects. We argue that the two effects may be intertwined with the expertise reversal effect constituting a particular example of the element interactivity effect. Specifically, the element interactivity effect relies on changes in element interactivity due to changes in the type of material being learned, while the expertise reversal effect also relies on changes in relative levels of element interactivity but in this case, due to changes in relative levels of expertise. If so, both effects rely on equivalent changes in element interactivity with the changes induced by different factors. Empirical evidence is used to support this contention. 相似文献
15.
利用对称约化理论和文[28～30]的思想,提出一种推广形式的双曲函数截断展开方法,并将它应用到广义Camassa-Holm系统和(3+1)维Jimbo-Miwa系统中,求得了GCH方程的精确解及其特解-Peakon解,得到了(3+1)维Jimbo-Miwa方程的孤子解、周期解和关于时间t的奇异解. 相似文献
16.
Why are some students able to learn to use the trial and error method to balance chemical equations while others are not? To test the hypothesis that formal reasoning is required to balance even simple one-step equations, while formal reasoning and a sufficiently large mental capacity are required to balance more complex many-step equations, a sample of science students was tested to determine level of intellectual development, mental capacity, and degree of field dependence/field independence. Students were then given classroom instruction in using trial and error to balance equations. As predicted, a posttest revealed significant correlations between developmental level and equation balancing ability for both simple and complex equations. Also, as predicted, mental capacity correlated significantly with complex equations but not with simple equations. Field dependence/field independence played no significant role in performance. Educational implications are drawn. 相似文献
17.
利用双曲函数方法 ,研究Burgers-Fisher方程的精确解 ,得到了若干其它方法不曾给出的新的精确解 这种方法的基本原理是利用非线性波动方程的局部特点 ,将方程的精确解表示为双曲函数的多项式 ,从而将非线性波动方程的求解问题转化为非线性代数方程组的求解问题 相似文献
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为了对处于环境温、湿度中的混凝土的收缩变形进行有效数值模拟分析,提出了一种数值解析与有限元分析相结合的方法.根据多孔介质热质传输原理描述混凝土中湿热迁移过程的耦合偏微分方程组,借助Laplace变换及传递函数将其简化为拉氏域内的简单微分方程并求解,然后通过Laplace逆变换得到物理空间内的温度和含湿量.在此基础上利用有限元分析方法得到混凝土湿热耦合收缩变形.该方法克服了其他求解过程中特征值复杂、耦合困难及准确性差的问题,并有效解决了现有有限元软件难以处理湿度应力及变形的难题.以Hundt试验为算例的数值计算表明,模拟结果与试验数据具有良好的相关性. 相似文献
20.
推导了两光滑平板间干气密封微尺度流动场的非线性雷诺方程,应用PH线性化方法、迭代法对非线性雷诺方程近似求解,得到气膜压力的近似解析式;利用极坐标下的流线方程,通过Maple程序求解压力方程和流线方程得到流线,此流线就是符合条件的拟合曲线。对拟合曲线槽干气密封气膜刚度进行计算与测试,并与螺旋槽进行比较。研究结果表明：在相同工况下,拟合曲线槽干气密封气膜刚度比螺旋槽大,且气膜刚度比螺旋槽稳定,这在工程实践中具有重要意义和应用价值。 相似文献