Teaching

  • This article presents a sequence of explorations and responses to student questions ( Why not use perpendicular deviations? Why not minimize the sum of the vertical deviations? Why not minimize the sum of the absolute deviations? Why minimize the sum of the squared deviations?) about the rationale for the commonly used tool of line of best fit. A noncalculus-based motivation is more feasible than is often assumed for each aspect of the least-squares criterion "minimize the sum of the squares of the vertical deviations between the fitted line and the observed data points."

  • Spreadsheets are used to explore the lottery, addressing common misconceptions about various lottery "strategies" and probabilities and providing real-world applications of topics such as discrete probability distributions, combinatorics, sampling, simulation and expected value. Additional pedagogical issues are also discussed. Examples discussed include the probability that an integer appearing in consecutive drawings, the probability that a single 6-ball drawing includes at least two consecutive integers, the probability that exactly one person wins the jackpot, and the probability that a frequent player eventually wins the jackpot.

  • With the growth in the availability of inexpensive computing the emphasis in teaching introductory statistics must shift from the mechanics of performing statistical procedure n a calculator or by hand to the interpretation of results easily obtained by computer. Textbooks in statistics provide ample instruction on using technology to perform statistical analysis but provide little in the way of hands on activity or simulation to teach abstract concepts. Many sites on the World Wide Web have Java applets that allow users to simulate sampling but these are subject to change both in how they work and where they are located which makes planning instruction with these programs difficult. Several software programs have been specially developed to allow for simulation of sampling distribution but some colleges may be unwilling or unable to purchase or support such specialized packages. In spite of lacking the graphics of commercial packages and web-based simulations, simulation exercises in Excel have the advantage of utilizing a program that is available and supported on most campuses.<br>In this paper I describe two exercises which use repeated simulated sampling in Microsoft Excel to teach about sampling distributions, particularly the Central Limit Theorem and the interpretation of confidence intervals. First, I will give a brief overview of the key concepts in the Central Limit Theorem and confidence interval estimation, describe the difficulties students have in learning these concepts and describe the potential of simulation to add clarity to these concepts. Next, I will describe how Excel is used to simulate sampling in my courses. Next I will describe the assignments I use in my classes to teach Central Limit Theorem and confidence interval estimation. Finally I will discuss possible exercises in repeated simulated sampling to teach other concepts in statistical inference as well as ways in which the effectiveness of these simulations in promotion g student learning can be formally evaluated.

  • Explores the need to teach undergraduate sociology majors about statistical methods. Identifies student based obstacles to the learning of statistics. Offers an instructional model that includes (1) warm up sessions; (2) organizational models; (3) application exercises; (4) pattern recognition; and (5) sociological meaning. Recommends the model as a basic design for the introductory statistics course.

  • The teaching of mathematics is not confined to a single approach. Because of the increasing diversity of knowledge and the quantitative data involved, students must make sense of the numerical data they are constantly facing. Seventeen people offer their ideas on how to teach numbers to students. Some espouse relating science teaching to mathematics. Otheres propose math education in relation to the work place. The value of logical thinking and analysis is also upheld as essential to the learning of numbers.

  • Teachers can use variety of strategies to instruct students in stat literacy. One such stratedy is using articles that contatin statistics which display commonly held beliefs. These encourage students to seek weaknesses and di ** strengths of factual information. Using essay questions that appear to have a answer are another means to engage students in statistical learning.<br>University students are best taught statistical literacy through a general education course. The first step is to explore an issue that has been taken for granted and is incontrovertible in the students' minds, such as the safety and effectiveness of immunizations. Students begin by evaluating an article with a negative slant on immunizations and by examining their own preconceived ideas. Students then receive a comment sheet in which the teacher responds generally to their arguments, provides factual support for their beliefs, and mentions some of the strengths of the article. Students are then asked to consider how a study can be designed to examine a particular question and to discuss why such a definitive study cannot actually be performed. An example of how the student discussion can be translated to a consideration of immunizations for Hepatitis B is presented.

  • This paper describes a number of generally accessible web-based tools the authors<br>developed over the last couple of years and used in several statistics courses, ranging<br>from the introductory statistics course to a specialized design of experiments course. The first set of tools (VESTAC) illustrates statistical concepts, the second one (VIRTEX)<br>consists of virtual experiments. We discuss some of our experiences with regard to the<br>development and maintenance of these tools and their use in ex cathedra teaching<br>sessions, in guided practice sessions and in student projects. Finally we discuss a third<br>type of tools: distance experiments.

  • Describes the WISE (Web Interface for Statistics Education) that was developed to enhance student learning and understanding of core statistical concepts relevant in higher education. Discusses the use of Web technology; the impact on teaching; barriers to computer-based learning; and impact on student learning.

  • The authors prepared a paper that described an example of a second course in applied regression analysis as part of the ASA Undergraduate Statistics Education Initiative (USEI) Symposium. They recommended that such a course include many practices that are not commonly integrated in a typical applied statistics course. Here the authors will give examples of such practices that they have used successfully (and can be effectively used in any introductory applied statistics course). Because data analysis must be the central theme of the course, examples of how the instructor and students can obtain interesting, real-world data will be given. These include novel activities to collect data in class, as well as web and text resources for data. The USEI paper strongly recommended that students should experience the entire data collection and analysis process. The USEI paper emphasized that active learning must be included in any such course. Activities that promote active learning such as the use of short talks to introduce concepts followed by class discussion and student presentations of examples will be given. Appropriate technology is an indispensable part of such a course. At a minimum this means that the course has suitable computational and conceptual software.

  • Descriptive statistics offer us several averages for a given set of variable numbers. Most elementary courses introduce the mean (i.e., arithmetic mean), the median and the mode.<br>On average, which is supposed to characterize a given distribution of values, is never identical with all the values (except for the trivial case). Each possible suggestion of an average involves some inaccuracy. The answer to the question "what is the best representation of the numbers?" depends on what is meant by "best representation". One could interpret this to mean that the average incurs the least possible "cost" in terms of differences between the average and the actual values. Each definition of the "cost" could be minimized by an appropriate average. Asking students to pay (symbolically) the costs of the errors incurred through use of different averages might introduce the averages via the idea of the least combined error.<br><br>The following procedure, which may be represented as a game in the classroom, has helped my students on both secondary school and college level.

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