论如何将实例结合在线性代数教学中

作为数学基础课程,线性代数抽象、概念与定理多,学生学习过程中不容易理解.因此,将实例应用在线性代数中,能够使得学生的兴趣提升,从而实现教学目标.介绍了线性代数的应用,通过Euler四面体体积问题的求解,对实例应用在线性代数教学中进行了探讨.通过实例表明,线性代数对于矩阵可逆性判断、矩阵逆的求解、矩阵乘法等问题的求解都非常有利的.     

"有理数的乘法"教学设计

教学目标知识技能:通过实例,了解有理数乘法的意义,会根据有理数乘法进行乘法运算。数学思考:1.能正确进行有理数乘法运算。2.用数形结合的思想方法得出有理数乘法法则。解决问题:能运用有理数乘法解决实际问题。情感态度:通过师生互动,学生反应讨论探究,让学生充分参与到数学学习中来。重点:了解有理数乘法的意义,会根据有理数乘法法则进行有理数的乘法运算。难点:乘法中符号的确定。教学方法:自主探究、合作交流、自主练习、归纳反思(四步四课型单元教学法)。教学过程:活动一:复习旧知,引入课题,培养学生提出问题力。我们已经熟悉正数及0…     

小学数学二年级乘法教学思考

根据课程标准的要求,小学二年级乘法是教学的重点之一。为了有效地实现乘法教学,让学生理解乘法的含义,熟记乘法口诀,并且能够熟练运用乘法快速计算和解决实际生活中的问题,教师需要积极探索乘法教学的多样化形式,让学生感受到学习乘法的乐趣和价值,激发其数学学习兴趣。     

负数的本质与有理数乘法法则：从数学的角度解析“负负得正＂

一、有理数乘法法则需要数学证明有理数乘法法则是初中数学的重要内容,“负负得正”是其中的难点．研究表明,虽然学生都能准确记忆有理数乘法法则,并能依据法则进行计算,然而绝大多数学生都不能举出实例来验证法则,更没有学生能够解释法则背后的数学道理”．这也就是说,学生仅仅掌握了有理数乘法的算法,且只能遵循算法进行机械计算,并没有真正理解其中的算理．     

“生活中的乘法“课堂实录及教学反思

教学目标: 一、从生活实际引入乘法的认识,激发学生学习数学的兴趣和学好数学的自信心。二、在参与数学活动的过程中,初步认识乘法。三、会读写乘法算式,能说出乘法各部分的名称。     

一次成功的教学设计

又到了教学《用两步计算解决实际问题》这一课了。这部分内容教学要求学生进一步理解乘法运算的意义,体会乘法运算的实际价值,积累用两步计算解决实际问题的经验,进一步学会数学思考,增强数学应用意识。     

创设有效活动 建构数学概念——“乘法的初步认识”教学实践与思考

数学概念是数学知识的基本要素,也是数学基础知识中最基础的内容。对数学概念的理解和掌握,关系到学生解决实际问题能力的培养和对学习数学的兴趣。本文结合“乘法的初步认识”一课,浅谈教师如何创设有效的学习活动,引导学生体验、建构乘法这一数学概念。     

浅谈高等数学及工程数学在高职工程测量专业中的应用

高等数学及工程数学可以实际应用于高职测量工程专业中。如全微分与误差传播定律、矩阵乘法与直角坐标系的旋转、正态分布与测量误差等。     

“乘法分配律”例题呈现的教材比较研究

"乘法分配律"是小学数学运算定律中的重点内容,又是小学数学运算律中的难点。在教学"乘法分配律"时,教材往往会提供一个贴近学生生活实际的例题,引导学生通过解决问题,分析算理,继而建立乘法分配律的运算模型。新课程背景下的小学数学教材呈现的例题主要有哪些?各个版本教材提     

“7的乘法口诀”教学设计与设计意图

<正>教学目标:1.引导学生联系生活中的实际问题,借助加法计算的和编出7的乘法口诀;通过珠心算帮助学生记忆7的乘法口诀,学会用7的乘法口诀口算相应乘法算式的得数。2.使学生主动参与编制口诀的过程,具有自主、独立的探究意识,增强学习数学的信心,初步体会数学的应用价值。     

矩阵乘积的精彩——贯穿于《线性代数》始终的矩阵乘积的教学方法探讨

探讨了在《线性代数》教学过程中关于矩阵乘积的问题。首先是矩阵乘法引入时要注意的问题,其次是在矩阵分块以后探讨矩阵乘积的规律,然后是用内积的观点来看待矩阵的乘积。这样从多个侧面引导学生去理解矩阵的乘积可以开阔他们的视野,提高他们分析问题和解决问题的能力。     

Application of CAE in Teaching Vibration Engineering

CAE has enabled vibrational problems, which were regarded as intractable 20 years ago, to be solvable by students using computational support. The paper describes a problem set to final year undergraduates which concerns the torsional vibrational response of a three degrees of freedom system which is subjected simultaneously to three different arbitrarily varying torques. The solution involves the use of standard library routines for matrix multiplication and eigensolutions, a Runge-Kutta routine to solve a second order differential equation and general competence in writing software.     

Teaching the partial products algorithm with the concrete representational abstract sequence and the strategic instruction model

Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning provides the foundation for advanced mathematics and algebraic reasoning. For students who struggle in mathematics, instruction in multiplication algorithms should ensure conceptual understanding so that students have a foundation for success in advanced mathematics. The concrete representational abstract (CRA) sequence addresses conceptual understanding and the strategic instruction model (SIM) supports procedural knowledge. The current pilot study combined these methods to teach elementary students the partial products algorithm. Twelve students in grades four and five participated in the study, receiving instruction from teachers in their school during an intervention period. Within a pre-experimental design, using pre- and postintervention data, students showed a significant change in performance. The article will describe and show how teachers implemented the CRA-SIM interventions and discuss implications for practice.     

Visualizing Matrix Multiplication

Efficient visualizations of computational algorithms are important tools for students, educators, and researchers. In this article, we point out an innovative visualization technique for matrix multiplication. This method differs from the standard, formal approach by using block matrices to make computations more visual. We find this method a helpful alternative for introducing matrix multiplication.     

Assessing Development in Numeracy of Students from Different Socio-Economic Areas: A Rasch Analysis of Three Fundamental Tasks

Development in the ability of 11-year-olds to solve numerical problems of addition, multiplication, and proportion was analysed by means of three Rasch models of change. The students, who had participated in a New Zealand numeracy project in 2002, comprised two groups that differed in socio-economic status: 1,274 students came from low socio-economic areas, and 564 students came from high socio-economic areas. The Rasch analysis showed that students from low socio-economic areas found all three tasks difficult, although they made some progress during the course of the year. Their development was consistent with a model in which each student underwent their own specific development. The development of students from high socio-economic areas was best described as stemming from two latent classes, one of which made substantial and uniform progress and the other of which made no progress. The cumulative nature of the tasks meant that failure on addition propagated to failure on multiplication and proportional reasoning.     

Excel在矩阵行列式中的应用．

Excel作为一款表格软件。具有强大的数据处理和分析功能．通过具体实例的操作,介绍Excel在计算行列式、求逆矩阵、解决矩阵乘法运算以及求线性方程组解的方面的应用,利用Excel可以避免繁琐的手算过程,提高运算的速度和解题的准确性．     

数域F上形如A＝（a11）的1×1矩阵的特殊约定及理论论证

本文从矩阵乘法运算出发,约定数域上形如FA=(a11的×矩阵在进行矩阵乘法运算或)11作为矩阵乘法运算结果时相当于数域中的一个数,Fa11,并对此约定进行理论论证,从而使矩阵乘法运算法则更加完备,并使得空间解析几何中推广的一般维向量空间中的向量的数性积,高等代数中的矩阵n乘法运算与欧式空间中内积定义完整有机联系起来。     

Strategic development of multiplication problem solving: Patterns of students' strategy choices

Low mathematics achievement is a persistent problem in the United States, and multiplication is a fundamental area in which many students manifest learning difficulties. This study examined the strategic developmental levels of multiplication problem solving among 121 elementary school students in Grades 3 through 5. A latent class analysis modeling was used to identify three valid groups representing different patterns of strategy choices for each of three types of multiplication problems. Findings indicated intra-group variability for problem-solving accuracy, for frequency of using different strategies, and for accuracy of executing direct retrieval/algorithm (DR/AG) strategies. Students demonstrated relative consistency in their strategy choices for solving the three problem types. Students who used DR/AG strategies most frequently showed the highest problem-solving accuracy and the highest accuracy of executing the DR/AG strategies. Students who most frequently relied on incorrect operations or who indicated they did not know how to solve problems demonstrated the lowest problem-solving accuracy among the three groups; the number of students in this group increased with problem difficulty levels. Implications are discussed in terms of identifying students' strategic developmental levels and providing differentiated instruction based on the identified levels.     

矩阵的秩教学方法新探

结合多年教学实践,从例题出发引入矩阵的秩的概念,并给出了一些常用的结论及常见错误分析;自然地引出了线性方程组的解的理论和矩阵乘法的消去律;总结了适合非数学类专业学生特点的教学方法,提高了他们的理解能力。     

Solving arithmetic word problems. An analysis of Spanish textbooks / Resolución de problemas aritméticos verbales. Un análisis de los libros de texto españoles

This study analyses whether the primary school mathematics textbooks from two Spanish publishers show a varied instructional diet of addition and multiplication problems at different levels of complexity. To do so, it analyses the problems in all the primary grades by the publishers Santillana and SM according to two levels of complexity: (a) procedural (number of steps needed to solve the problem); and (b) semantic/mathematical (addition or multiplication structures, with their different subtypes). The results show that: (a) these problems are so simple that the books themselves cannot be regarded as a sufficient tool to teach students to solve the more complex problems; and (b) if we compare them with previous studies, the design of the problems has hardly changed in 10 years. These results show that the variety of problems in books should be expanded both procedurally and semantically/mathematically, and teachers should be given assistance to compensate for these shortcomings when using these textbooks in class.