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.
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
Key Words: Active learning; Contrasts; Problem Solving; Statistical Reasoning; Student
Participation; Teaching Methods.
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;
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
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
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.
Key Words: Controlling for a variable; Non-transitivity of positive correlation; Simpson’s paradox.