概率方法在其它问题中的应用

在实施概率论的教学过程中,启发引导学生运用概率论的方法去解决其它问题,从而寻求数学问题新的解法,其目的可加深学生对概率知识的理解、掌握,从而激发学生的创造力。     

概率统计在信息社会中的教育价值

基于对信息化社会中概率统计教育重要性的认识,重点从四个方面论述了概率统计的教育价值：（1）概率统计的随机观念有助于人们认识和理解随机现象;（2）概率统计的学习有助于学生对数学的整体理解;（3）概率统计的数学方法有助于提高公民处理信息的能力;（4）概率统计的思想方法有助于培养学生的科学观念.     

Providing ability to probability: Reducing cognitive load through worked‐out examples

Undergraduate students tend to struggle with probability in their introductory statistics course. Probability problem solving requires several steps. First, students must make sense of the probability scenario, then determine the appropriate probability rules, and finally, execute the procedures to solve the problem. With no previous exposure to probability, this presents too great a cognitive load for many students. Using worked‐out problems then transitioning to partially worked‐out problems in an introductory statistics course at a large university helped students succeed at solving probability problems. The worked‐out problems included writing prompts to encourage self‐explanation of students' thinking through studying the worked‐out examples. This paper explains the use of these instructional principles and their implementation in an introductory statistics course for non‐STEM majors, resulting in higher student achievement and understanding.     

对初中生学习概率定义的思考

了解概率的意义,已成为我国初中数学的教学内容之一,不同的初中数学教材对概率定义的处理方式有所不同.在概率论的历史上,概率的定义经过了古典概率、几何概率、概率的频率定义以及概率的公理化定义.初中生学习概率的意义时,可以将古典概率作为起点,然后引申到几何概率,最后上升到更具有一般性的概率的频率定义。     

“辨误”在概率论教学中的应用

对学生在概率论学习中若干常见错误进行辨析,旨在帮助学生正确掌握有关概念、结论及其之间的关系,加深对概率论的思想和方法的认识,同时也为概率论教学提供参考。     

Using camels to teach probability and expected value

There is much debate about the place of probability in an introductory statistics course. While students may or may not use probability distributions in their post‐collegiate lives, they will likely be faced with day‐to‐day decisions that require a probabilistic assessment of risk and reward. This paper describes an innovative way to teach students in an introductory statistics course how to reason about probability and expected value through the board game Camel Up. The in‐class activities described here can be scaled to fit the needs and abilities of the students in a wide range of introductory statistics courses at a variety of levels.     

Demarches de resolution et de simulation face au probleme de la ruine d'un joueur

Prior to large experimentations on the teaching of probability theory, it appeared useful to observe some students working for a fairly long time. This observation should make more precise the difficulties of an important aspect when solving probability problems: the modelling aspect. Does systematic use of simulation produce miracles as it is sometimes said? Are the students naturally sensitive to a frequentist approach of probability theory? This paper contains some results on these questions, for example we pointed out for some students an obstacle to the frequentist approach. The results permit to conceive how using simulation for teaching could contribute to an improvement of students' approach to probability.     

Malawian Students’ Meanings For Probability Vocabulary

The paper discusses findings of a study that investigated Malawian students' meanings for some probability vocabulary. The study explores the meanings that, prior to instruction, students assign to some words that are commonly used in teaching probability. The aim is to have some insight into the meanings that students bring to the classroom. The sample for the study consisted of 154 students in their first year of secondary school education and whose first language was Chichewa. The paper demonstrates that many of the students' preconceived meanings for probability vocabulary were distant from established conventional probability meanings. In addition, there was a wide range of meanings associated with each of the words. An attempt is made to analyse the students' meanings and to explain their possible sources, some of which are rooted in the students' first language. The paper highlights the importance of having an awareness of students' preconceived meanings, and also stresses the importance of language in learning probability.     

Misconceptions of probability: An experiment with a small-group,activity-based,model building approach to introductory probability at the college level

Summary The day-by-day observations made by the experimenter during one of the activity-based classes indicate that college students can learn to discover some elementary probability models and formulas for themselves while working on probability experiments in small groups. Furthermore, the effects of sample size upon measures of central tendency and variability can be learned by students working on activities such as those developed for the experimental course in this study. Making guesses for the probability of events and checking guesses with a hand-held calculator seems to help college students to be more cautious about probability estimates, and helps to make them aware about some of their own misconceptions about probability. Small-group problem solving, keeping a log of all class work and activities, and investigating the misuses of statistics all appeared to have a positive effect upon college students' attitudes towards mathematics, as indicated in the questionnaires filled out by the subjects in the experimental sections.The present results of this study support the hypotheses of Kahneman and Tversky [10, 12] which claimed that combinatorially naive college students rely upon availability and representativeness to estimate the likelihood of events. Kahneman and Tversky were skeptical about the possibility of helping students to overcome their reliance upon availability and representativeness. The results on the posttest in this study suggest that the manner in which college students learn probability makes a difference in their ability to overcome misconceptions that arise from availability and representativeness. Mere exposure to probability concepts is not sufficient to overcome certain misconceptions of probability. Fischbein [9] notes that the synthesis between the necessary and the possible-which is the basis of probabilistic thinking-does not in fact take place spontaneously .... He claims that science education emphasizes only the deterministic aspect, and neglects the study of uncertainty. Thus peoples' intuition of probabilistic thinking is distorted by science education's emphasis on the necessary, and neglect of the possible. This experiment suggests that the course methodology and the teaching model used in an elementary probability course can help develop peoples' intuition for probabilistic thinking. A course in which students carry out experiments, work through activities to build their own probability models, and discover counting principles for themselves can help students to overcome their misconceptions about probability, and can help restore the synthesis between the necessary and the possible which is essential to probabilistic thinking.     

基于认知理论的中学概率教学策略研究

概率是学生素质的重要组成部分.中学概率教学可遵循以下原则:认识不确定现象,初步体验事件发生的可能性大小;体会概率的意义,了解频率与概率的关系;通过实例进一步丰富对概率的认识,发展随机观念;强调归纳的思维方法;引导学生认真审题,确定合理的解题策略;引导学生一题多解,让学生感受求解概率问题方法的灵活性与多样性;引导学生开展课题研究,增强学生学概率用概率的创新意识与能力.     

Probability With Less Pain

The teaching of probability theory has been steadily declining in introductory statistics courses as students have difficulty with handling the rules of probability. In this article, we give a data‐driven approach, based on two‐way tables, which helps students to become familiar with using the usual rules but without the formal structure.     

工科《概率论》复习设计

工科<概率论与数理统计>课程中的概率论部分可以看成是围绕概率计算而展开的,本文主要讨论如何进行概率论部分的复习,使学生更容易掌握概率论的知识体系.     

概率论中一个易产生歧义解的问题的分析

经济数学基础课程的概率论部分的学习中，学生对概率定义的理解有一定的难度，对使用定义求解概率问题常常出错，本文通过概率定义的总结及进一步理解和对易产生歧义解的问题进行分析，以期达到理解定义、解决问题的目的。     

The effects of exemptions to Florida's test-based promotion policy: Who is retained?: Who benefits academically?

We evaluate the impact of Florida's test-based promotion policy on the probability that low-performing students are retained using data on the universe of third-grade students in the state of Florida from 2001 to 2004. We also examine the effect of formal exemptions to the policy on student proficiency in reading two years later. In an evaluation of retention for third-grade students over time with a logit model we find that Florida's policy has increased the probability that minority students are retained to a greater extent than white students. Contrary to previous research, this differential retention occurs after controlling for student academic proficiency. However, in an evaluation of the academic performance of students who were in the first class subject to the retention policy, we find that retained students outperform students who received an exemption from the policy in reading two years after baseline, indicating that on average exemptions have not been granted to those individuals who would benefit from promotion.     

体育锻炼对中专学生抑郁状态与应对方式之影响

采用自评抑郁量表（SDS）、简单应对方式问卷、体育锻炼调查问卷来探讨体育锻炼对中专学生应对方式与抑郁状态的影响,结果显示：高体育锻炼次数的学生比低体育锻炼次数的学生在遇到困难时采取积极应对方式的概率高,低体育锻炼次数的学生比高体育锻炼次数的学生在遇到困难时采取消极应对方式的概率高;中专学生的抑郁状态对其应对方式也存在影响,抑郁组的学生遇到打击时,采取积极应对方式的次数比非抑郁组的学生少,而采取消极应对方式的次数比非抑郁组的学生多。     

Students’ expectations about earnings and employment and the experience of recent university graduates: Evidence from Cyprus

The employability of university graduates constitutes a major policy concern in both developed and developing nations. In this context, the present study uses self-reported data to compare the earnings and employment expectations of university students, and the realised earnings and employment paths of recent graduates. The sample consisted of 476 individuals (243 students and 233 graduates of the University of Cyprus). The analysis points to both differences and similarities in the effect of different variables on (a) the probability of employment for graduates and the probability of expected employment for students, and (b) the conditional salary of graduates and the conditional expected salary of students. The completion of postgraduate studies, the area of family residence and the department of study are the key factors affecting the graduates’ employment probability, while the students’ probability of expected employment is determined differently, namely by characteristics such as secondary education performance and studies in the business administration department. Gender and family income are among the main determinants of both the graduates’ actual earnings and the students’ expected earnings, with women earning or expecting to earn less than men, and graduates/students with higher family incomes earning or anticipating to earn more than their lower income counterparts. The findings are compared to those of similar studies in other countries.     

基于OBE理念的“概率论与数理统计”课程教学模式的思考与实践

本文提出了基于OBE理念的"概率论与数理统计"课程探究式教学模式,以人为本,尊重学生的实际需求,以OBE为目标,结合专业需要,建立概率论与数理统计的新的教学方法和教学体系,调整教学内容,采取混合教学方法,构建多样化的考核体系,在实际教学活动中落实OBE的思想理念。     

用“做数学”理念探究“随机事件及其概率”

生活中的随机现象无处不在,概率问题到处可见.几何画板的动画演示可以让学生体会概率的理论性和频率的可变性,澄清生活中的错误认识,联系"实验"、"问题"与"生活",学到"好玩的"、"有用的"的数学,培养学生实验法探究知识的能力.     

Active learning? not with my syllabus!

We describe an approach to teaching probability that minimizes the amount of class time spent on the topic while also providing a meaningful (dice‐rolling) activity to get students engaged. The activity, which has a surprising outcome, illustrates the basic ideas of informal probability and how probability is used in statistical inference.     

成就动机与学生学习

成就动机与学习成绩有正相关 ,激发学生的学习动机是提高学习成绩的前提条件之一 ;学习动机与成功概率密切相关 ,布置适合学生实际的学习任务 ,让学生以适度的“成功率意识”去从事学习 ,可激发学习动机。