Teaching

  • ProbLab is a probability-and-statistics unit developed at the Center for Connected Learning and Computer-Based Modeling, Northwestern University. Students analyze the combinatorial space of the 9-block, a 3-by-3 grid of squares, in which each square can be either green or blue. All 512 possible 9-blocks are constructed and assembled in a ?bar chart? poster according to the number of green squares in each, resulting in a narrow and very tall display. This combinations tower is the same shape as the normal distribution received when 9-blocks are generated randomly in computer-based simulated probability experiments. The resemblance between the display and the distribution is key to student insight into relations between theoretical and empirical probability and between determinism and randomness. The 9-block also functions as a sampling format in a computer-based statistics activity, where students sample from a ?population? of squares and then input and pool their guesses as to the greenness of the population. We report on an implementation of the design in two Grade 6 classrooms, focusing on student inventions and learning as well as emergent classroom socio-mathematical behaviors in the combinations-tower activity. We propose an application of the 9-block framework that affords insight into the Central Limit Theorem in science.

  • Lecture is a common presentation style that gives instructors a lot of control over topics and time allocation, but can limit active student participation and learning. This article presents some ideas to increase the level of student involvement in lecture. The examples and suggestions are based on the author?s experience as a senior lecturer for four years observing and mentoring graduate student instructors. The ideas can be used to modify or augment current plans and preparations to increase student participation. The ideas and examples will be useful as enhancements to current efforts to teach probability and statistics. Most suggestions will not take much class time and can be integrated smoothly into current preparations.

  • In the Fall 2001 semester, we taught a ?Web-enhanced? version of the undergraduate course ?Statistical Methods? (STAT 2000) at Utah State University. The course used the electronic textbook CyberStats in addition to ?face-to-face? teaching. This paper gives insight in our experiences in teaching this course. We describe the main features of CyberStats, the course content and the teaching techniques used in class, students' reactions and performance, and some specific problems encountered during the course. We compare this Web-enhanced course with other similar textbook-based courses and report instructors' and students' opinions. We finish with a general discussion of advantages and disadvantages of a Web-enhanced statistics course.

  • The Statistical Reasoning Assessment or SRA is one of the first objective instruments developed to assess students? statistical reasoning. Published in 1998 (Garfield, 1998a), it became widely available after the Garfield (2003) publication. Empirical studies applying the SRA by Garfield and co-authors brought forward two intriguing puzzles: the ?gender puzzle?, and the puzzle of ?non-existing relations with course performances?. Moreover, those studies find a, much less puzzling, country-effect. The present study aims to address those three empirical findings. Findings in this study suggest that both puzzles may be at least partly understood in terms of differences in effort students invest in studying: students with strong effort-based learning approaches tend to have lower correct reasoning scores, and higher misconception scores, than students with different learning approaches. In distinction with earlier studies, we administered the SRA at the start of our course. Therefore measured reasoning abilities, correct as well as incorrect, are to be interpreted unequivocally as preconceptions independent of any instruction in our course. Implications of the empirical findings for statistics education are discussed.

  • In a very large Introductory Statistics class, i.e. in a class of more than 300 students, instructors may hesitate to apply active learning techniques, discouraged by the volume of extra work. In this paper two such activities are presented that evoke student involvement in the learning process. The first is group peer teaching and the second is an in-class simulation of random sampling from the discrete Uniform Distribution to demonstrate the Central Limit Theorem. They are both easy to implement in a very large class and improve learning.

  • From a very young age, shoes for boys tend to be wider than shoes for girls. Is this because boys have wider feet, or because it is assumed that girls are willing to sacrifice comfort for fashion, even in elementary school? To assess the former, a statistician measures kids? feet.

  • I selected a simple random sample of 100 movies from the Movie and Video Guide (1996), by Leonard Maltin. My intent was to obtain some basic information on the population of roughly 19,000 movies through a small sample. In exploring the data, I discovered that it exhibited two paradoxes about a three-variable relationship: (1) A non-transitivity paradox for positive correlation, and (2) Simpson?s paradox. Giving concrete examples of these two paradoxes in an introductory course gives to students a sense of the nuances involved in describing associations in observational studies.

  • This paper describes an interactive activity developed for illustrating hypothesis tests on the mean for paired or matched samples. The activity is extended to illustrate assessing normality, the Wilcoxon signed rank test, Kaplan-Meier survival functions, two-way analysis of variance, and the randomized block design.

  • This article explores the uses of a simulation model (the two bucket story)?implemented by a stand-alone computer program, or an Excel workbook (both on the web)?that can be used for deriving bootstrap confidence intervals, and simulating various probability distributions. The strengths of the model are its generality, the fact that it provides a powerful approach that can be fully understood with very little technical background, and the fact that it encourages an active approach to statistics?the user can see the method being acted out either physically, or in imagination, or by a computer. The article argues that this model and other similar models provide an alternative to conventional approaches to deriving probabilities and making statistical inferences. These simulation approaches have a number of advantages compared with conventional approaches: their generality and robustness; the amount of technical background knowledge is much reduced; and, because the methods are essentially sequences of physical actions, it is likely to be easier to understand their interpretation and limitations.

  • This paper describes a project with the goal of exposing both elementary school and undergraduate students to the concepts associated with the experimental method, from the formulation of a researchable question to the analysis and interpretation of the results. Under the guidance of their university mentors, fourth and fifth grade students formulated a research question, designed an experiment to answer that inquiry, recorded the appropriate measurements, calculated the necessary statistics, created visual displays of their results, and interpreted their findings at a student-centered Numeracy Conference.

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