ISSN 1069-1898

 An International Journal on the Teaching and Learning of Statistics

## JSE Volume 14, Number 1 Abstracts

#### Dor Abrahamson, Ruth M. Janusz, Uri Wilensky There Once Was a 9-Block ...- A Middle-School Design for Probability and Statistics

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..

Key Words: Computers; Education; Mathematics; Sample; Statistics.

#### Michael D. Larsen Advice for New and Student Lecturers on Probability and Statistics

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.

Key Words: Active learning; Contrasts; Problem Solving; Statistical Reasoning; Student Participation; Teaching Methods.

#### Jürgen Symanzik and Natascha Vukasinovic Teaching an Introductory Statistics Course with CyberStats, an Electronic Textbook

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.

Key Words: Computer; Interactivity; Statistical Concepts; Undergraduate Course; Web-enhanced Course.

#### Dirk Tempelaar, Wim Gijselaers, and Sybrand Schim van der Loeff Puzzles in Statistical Reasoning

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.

Key Words: Assessment; Attitudes toward statistics; Learning approaches; Statistical reasoning assessment.

#### Hrissoula Zacharopoulou Two Learning Activities for a Large Introductory Statistics Class

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.

Key Words: In-class simulation; Peer teaching; Sampling distribution.

Datasets and Stories

#### Mary C. Meyer Wider Shoes for Wider Feet?

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.

Key Words:

#### Thomas L. Moore Paradoxes in Film Ratings

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.

Key Words: Controlling for a variable; Non-transitivity of positive correlation; Simpson’s paradox.