基于专业特点的概率论与数理统计课程教学方法探讨由刀豆文库小编整理，希望给你工作、学习、生活带来方便，猜你可能喜欢“概率论与数理统计课程”。
概率论与数理统计是研究和揭示随机现象统计规律性的一门数学学科，是大学理工科、经管专业的一门重要公共基础课.概率论与数理统计的建模方法和数学知识可以应用到金融、工程、生物、民航等各个专业领域，成为许多重要专业课的基础.长期以来，在我国概率论与数理统计课的课堂教学中，专业知识与概率统计知识联系不紧密，造成知识上的断裂.这种情况，导致一些学生认为“概率甚至数学无用论”，学习兴趣降低，而在一些涉及概率与数理统计知识的一些专业问题时，专业老师还需重新回顾概率知识.概率论与数理统计是应用性很强的学科，其生命力和发展动力在于它与其他应用学科的密切联系，隔断这种联系概率论与数理统计就成了无源之水.因此在教学实践中，如何加强数学基础课与专业之间的联系，培养学生用数学基础知识解决实际问题以及专业问题的能力，是目前概率论与数理统计课程以及高等数学、线性代数等数学基础课面临的一大问题.为此，针对不同专业的学生，结合各个专业的特点，调整教学内容，设计与学生所学专业相关的概率统计模型、实例和考核方式，一方面可以激发学生对概率与数理统计课的兴趣，提高学生运用数学知识解决实际应用问题的能力，另一方面有利于学生对专业课的进一步理解和掌握.为了加强概率论与数理统计课与专业课的联系，我们从以下几个方面进行探索研究.1.因材施教，针对不同专业调整课程教学内容
在保持概率统计经典内容的前提下，针对不同专业的学生适当调整教材内容，综合考虑学生的专业方向，侧重概念、建模思想、方法和现实背景在专业等方面的应用.针对工科和经济类专业的学生，改变传统的“重推理、重计算，轻应用”的思想，弱化一些概率论定理的证明过程，加强对定理和定义的理解和运用.例如关于分布函数的性质，可以删除证明过程，而强调其性质的应用.对于数学期望和方差，为加深学生对其定义的理解和应用，介绍概念来源的背景，引入其在投资及其风险的应用，为经济类专业后续的收益和风险等专业知识打好基础.对于各种常见的分布，基于学生的专业特点，介绍在各种专业背景下各类事件的分布，为学生进一步的专业课学习做好基础.如针对保险类学生，在讲解泊松定理和泊松分布时，结合保险知识，引导学生理解保险事件的发生服从泊松分布.在数理统计部分，考虑某些专业有专业的统计课程，可以强调各种检验和估计的前提条件，引导学生对各种检验的原理进行理解，为以后的专业统计课打下基础.同时针对没有专业统计课的学生，适当增加统计实验课的内容，引进SPSS、SAS等统计软件的内容，引导学生会运用统计软件做假设检验及曲线拟合等，为以后的专业课打下基础.2.设计与专业相关的案例教学
概率论与数理统计是从实际生产中产生的一门应用型学科，来源于实际又服务于实际.因此，在课堂上采取案例教学法，引导学生利用已学的概率统计知识解决实际问题，提高学生的综合能力.针对不同的专业，设计不同的案例，将专业知识和概率知识结合起来，培养学生的建模思想和处理问题能力，有助于学生更好地学习专业课.如在讲授大数定理时，大多数学生感觉内容枯燥无味，为此，我们针对保险专业的学生，结合保险学的专业知识，设计以下问题：（1）保险公司在设计保单时，根据每年的生死率而计算保单持有人的保费，根据大数定理，保险公司的生死率是如何得到的？（2）若某保险公司根据生死率设计了某保单，销售时仅卖出了50份保单，作为产品经理应作出什么决策，并说明理由.上述问题的设计，可以帮助学生更好地理解频率以概率收敛于概率，当保险公司销售的保单数量没有达到足够的数量时，此时实际的生死率与保单设计时利用的生死率将会有较大差别，保险公司此时合理的决策应修改保费的计算或者与保单持有人终止合同.3.融入数学建模思想，用数学基础知识解决专业问题
数学家李大潜指出：如果数学建模的精神不能融合进数学类主干课程，仍然孤立于原有数学主干课程体系之外，数学精神是不能得到充分体现和认可的.在概率论与数理统计的课程中，模型化方法贯穿整个课程中，如在全概公式和贝叶斯公式的各类计算题中，我们需要首先建立数学模型，将问题描述问各个事件的关系，从而利用已有的概率公式计算.但是，面对一些稍微复杂的问题时，大多数学生还是不会建立数学模型，不会将专业知识和数学知识结合起来解决专业理论中的一些实际问题，造成知识上的断裂，缺乏实际应用能力.因此，在教学实践中，融入数学建模思想，结合各专业的特点，引导学生用概率论与数理统计、高等数学等数学知识来解决一些实际的专业问题.如针对经济类专业，结合经济理论中诸如需求、供给、生产、投资、消费等实际经济问题，引导学生根据所研究的问题与经济理论，找出经济变量间的因果关系及相互间的联系，找出自变量和随机因素，建立经济数学模型.从而，收集经济变量的统计资料，利用概率论与数理统计的方法对参数进行估计，并对估计的参数进行假设检验，从而解决实际的专业问题.4.考核方式
考核方式和考核内容是教学过程中的指挥棒，不同的考核方式和考核内容会引导学生在平时的学习情况的不同.传统的考核方式是采用期末闭卷考试，按照固定的内容和格式出题，侧重对各种概念和公式的考核，试卷内容上也是侧重概率的计算，这样的考核方式和考核内容引导学生在平时学习中死记硬背概念和公式，而不注重所学知识的应用，重视概率的计算而轻视统计的应用.这导致学生对概率论与数理统计的知识掌握的片面化，在实际生活中不能将知识综合应用.为此，我们有必要对概率论与数理统计课程的考核方式和内容进行改革.一方面，考核方式改变传统的期末闭卷考试，而采用闭卷考试和开卷考试相结合的考核方式.闭卷考试改变传统的重计算的传统，侧重对概率论与数理统计的基本知识点、基本运算和基本理论进行考核.开卷考试侧重对知识点的综合应用情况进行考核，结合各专业的特点，考查学生数学建模思想和解决问题的能力.结束语：综上所述，在实际的教学实践中，结合学生的专业特点，加强概率论与数理统计与专业的联系，利用各专业的特点设计案例，解决实际专业问题，可以激发学生学习概率论与数理统计的学习兴趣，培养学生的实际解决问题能力，有助于专业课程的深刻学习.Probability and mathematical statistics is the study and reveal the random phenomena statistical regularity of a mathematical discipline, is an important public university in science and engineering, management, profeional basic course.Modeling method of probability and mathematical statistics and mathematics knowledge can be applied to finance, engineering, biology, civil aviation, and other profeional fields, as the foundation of many important profeional course.In China for a long time, probability theory and mathematical statistics course of claroom teaching, the profeional knowledge and probability and statistics knowledge does not close, cause the fracture on the knowledge.This kind of situation, lead to some students think that “probability and mathematical usele theory”, learning interest, and in some profeional iues related with the knowledge of probability and mathematical statistics, the profeional teachers still need to review the knowledge of probability.Probability and mathematical statistics is applied very strong discipline, its vitality and development power is that it closely connected with other application subject, partition the connection probability and mathematical statistics is a madraa reflected.So in teaching practice, how to strengthen the connection between the mathematical basic courses and profeional, to cultivate students with basic knowledge of mathematics to solve practical problems and the profeional ability, is the theory of probability and mathematical statistics course as well as advanced mathematics, linear algebra and mathematical basic course facing a big problem.For this, according to different students, combining with the characteristics of various profeional and adjust the teaching content, design related to your major students of probability and statistics model, instance and the inspection way, on the one hand, can stimulate students interest in probability and mathematical statistics course, improve students' ability to apply the mathematics knowledge to solve practical problems, on the other hand is helpful for students to further understand and master course.In order to strengthen the probability and mathematical statistics course and specialized course, we study on exploration from the following several aspects.1.According to their aptitude, for different profeional courses teaching content adjustment In keeping the claic content under the premise of probability and statistics, according to different students adjust the teaching material content, considering the student's profeional direction, focusing on the concept, the modeling ideas, methods and practical background in profeional applications.In view of the students majoring in engineering and economic, to change the traditional heavy reasoning, calculating and light “applied” thoughts, reduced some probability theorem proof proce, and to strengthen the understanding and using of theorem and definition.For example on the nature of the distribution function can delete the proof proce, and emphasizes the nature of the application.The mathematical expectation and variance, and to deepen students' understanding of the definition and application, introduced the background of the concept of source, the introduction of its application in investment and risk, such as economic cla profeional returns and risk of subsequent profeional knowledge.For a variety of common distribution, based on the profeional characteristics of student, is introduced in a variety of profeional background, the distribution of all kinds of events for the students to further completes the basis of profeional course learning.Students such as for insurance, in the interpretation of the poion theorem and poion distribution, combined with insurance knowledge, guide the student to understand the insurance event obeying poion distribution.In mathematical statistics section, consider some of the major profeional statistics course, stre can be all kinds of test and estimate the premise condition, guide students to understand the principle of all kinds of inspection, to lay the foundation for later profeional statistics cla.At the same time, in view of the students without profeional statistics course, appropriately increased statistical experiment content, the introduction of statistical software such as SPSS, SAS, content, guides the student to utilize the statistical software to do hypothesis test and curve fitting, etc., and lays the foundation for later profeional course.2.Design and profeional related case teaching Probability and mathematical statistics of actual production to produce an applied subject, from the practical and serve the actual.Therefore, take the case teaching in cla, guide students to learn and use have been knowledge of probability and statistics to solve practical problems, improve the students' comprehensive ability.According to different specialty, design different case, combine profeional knowledge and probability knowledge, cultivate the students' modeling thought and ability to deal with the problem, help students to better learn profeional cla.As in the teaching of large number theorem, most students feel dull content, to that end, we against insurance major, combining the profeional knowledge of the insurance, design the following questions:(1)the insurance company in the design policy, according to the annual death rate and calculate the policyholder premiums, according to the law of large Numbers, the death rate of insurance company is how to get?(2)if a certain insurance company according to the life and death rate of the design policy, sales sold only 50 insurance policy, as a product manager www.daodoc.com www.daodoc.com shall make what decisions, and explain the reasons.The problem of design, can help students better understand the frequency in probability, convergence in probability while the number of insurance company sales policy is not enough, the number of the actual life and death rate and policy design utilization rate there will be a larger difference between life and death, insurance company the reasonable decision should modify the premium calculation or with policy holders to terminate the contract.3.Blend in mathematical modeling thought, use mathematics knowledge to solve major problems Mathematician daqian li pointed out: if the spirit of mathematical modeling can't fusion into the main course of mathematics, remain isolated from the original backbone mathematics curriculum system, the mathematical spirit cannot be fully reflect and recognition.In probability theory and mathematical statistics course, throughout the course of modeling method, such as in the whole formula and bayes formula of computation problem, we need to first establish mathematical model and described the problem ask the relationship between various events, so as to make use of the existing probability formula.However, in the face of some slightly more complicated problem, most of the students will not establish mathematical model, not combine profeional knowledge and mathematics knowledge to solve some practical problems in the theory of profeional knowledge on the rupture, the lack of practical ability.In teaching practice, therefore, integrated into the mathematical modeling thought, based on the profeional characteristic, guides the student to use probability and mathematical statistics, such as higher mathematics mathematics knowledge to solve some practical profeional problem.As for economy cla specialty, combined with economic theory, such as demand, supply, production, investment, consumption and other practical economic problems, guides the student according to the research question and economic theory, and find out the causal relationship between economic variables and the relationship between each other, find out the independent variables and random factors, economic mathematics model is set up.Thus, collecting statistical data of economic variables, using probability theory and mathematical statistics method is used to estimate the parameters, and to estimate the parameters of hypothesis test, so as to solve the actual profeional problem.4.The appraisal way Aement method and aement is the baton in the proce of teaching content, different ways of aement and examination content will guide students in the usual learning situation is different.The traditional check method is to use comparative economics final exam, according to the fixed content and format, the questions focus on the appraisal of various concepts and formulas, the examination paper content is also focuses on the calculation of probability, this way of evaluation and examination content guide students rote learning concepts and formulas in the study at ordinary times, and not pay attention to the application of knowledge, attach importance to the calculation of probability and despise the application of statistics.This leads to the student to the knowledge of probability and mathematical statistics one-sided, in real life can't be integrated application of knowledge.Therefore, it is neceary for us to check method and contents of the theory of probability and mathematical statistics course reform.On the one hand, the examination way to change the traditional request for final exam, and adopts the comparative economics test and the way of combined examination of an open-book exam.Request for change the traditional heavy computation of the traditional exam, focusing on the basic knowledge of probability theory and mathematical statistics,www.daodoc.com to examine the basic operation and basic theory.An open-book exam focuses on the knowledge of comprehensive application of the inspection, according to the characteristics of the various profeional test students' ability of mathematical modeling thought and solve the problem.Conclusion: to sum up, in the actual teaching practice, combined with the profeional characteristics of student, strengthen the contact with the profeional theory of probability and mathematical statistics, advantage of the characteristics of various profeional design case, to solve practical profeional problem, can stimulate the learning interest of the student to study the theory of probability and mathematical statistics, cultivate the students' practical ability to solve problems, help to profeional course of profound learning.
