Free Book—Statistical Thinking: A Simulation Approach to Modeling Uncertainty

(cross-posted from Citizen Statistician)


Catalyst Press has just released the second edition of the book Statistical Thinking: A Simulation Approach to Modeling Uncertainty. The material in the book is based on work related to the NSF-funded CATALST Project (DUE-0814433). It makes exclusive use of simulation to carry out inferential analyses. The material also builds on best practices and materials developed in statistics education, research and theory from cognitive science, as well as materials and methods that are successfully achieving parallel goals in other disciplines (e.g., mathematics and engineering education).

The materials in the book help students:

• Build a foundation for statistical thinking through immersion in real world problems and data
• Develop an appreciation for the use of data as evidence
• Use simulation to address questions involving statistical inference including randomization tests and bootstrap intervals
• Model and simulate data using TinkerPlots™ software

Why a cook on a statistics book? It is symbolic of a metaphor introduced by Alan Schoenfeld (1998) that posits many introductory (statistics) classes teach students how to follow “recipes”, but not how to really “cook.” That is, even if students leave a class able to perform routine procedures and tests, they do not have the big picture of the statistical process that will allow them to solve unfamiliar problems and to articulate and apply their understanding. Someone who knows how to cook knows the essential things to look for and focus on, and how to make adjustments on the fly. The materials in this book were intended to help teach students to “cook” (i.e., do statistics and think statistically).

The book is licensed under Creative Commons and is freely available on gitHub. If physical copies of the book are preferred, those are available for $45 at CreateSpace (or Amazon) in full color. All royalties from the book are donated to the Educational Psychology department at the University of Minnesota.

Catalysts at the 2013 Advanced Placement Statistics Reading

N. Parker, Laura Ziegler, Robin Lock (of St. Lawrence University), and Elizabeth Fry at the Advanced Placement Statistics Reading in Kansas City, Missouri

Every year, statistics teachers congregate to grade the Advanced Placement Statistics Exam, the final assessment given to high school students who completed the Advanced Placement Statistics course. This year, three of our Ph.D. students, N. Parker, Laura Ziegler, and Elizabeth Fry made it down to Kansas City for the reading, June 11–17.

Laura was a table leader, and N. was an "acorn"—the affectionate name given to first-time readers. AP Statistics gets bigger and bigger every year, with about 630 readers grading nearly 171,000 exams!  In fact, this year there were enough exams that the AP readers conquered the "million question challenge":  by grading more than a million responses.

We look forward to the day when enough students are taking AP Statistics that we face a two million question challenge!

Change: Catalysts at the 2013 US Conference on Teaching Statistics

Many of University of Minnesota's statistics education group sallied forth to wet, warm North Carolina to share and learn with statistics educators around the country at the US Conference on Teaching Statistics (USCOTS) 2013! The conference theme this year, "Change", is very dear to our group, and throughout the conference, we presented some of what we've learned about rebooting statistics education to serve students better. Along the way, we learned from the wide variety of perspectives and insights on the discipline from statisticians, education researchers, and teachers.

Right before the conference, we led two fully enrolled workshops:

Bob delMas (second from left), along with Ph.D. students Laura Ziegler, N. Parker, and Laura Le, taught a workshop on UMN's CATALST curriculum, which exclusively uses simulation and resampling methods to teach a post-secondary introductory statistics course.  

Michelle Everson (right), with Master's student Ethan Brown, Ph.D. student Rebekah Isaak, and Master's student Anelise Sabbag, discussed practical tips and tricks for teaching a dynamic, engaging online statistics course.

Did we stop there? Of course not. The conference opened that night with a series of 5-minute presentations, including one by Bob delMas about his wizardly journey to improve statistics education.

Bob led a breakout session on Friday on evaluating new curriculum, using materials developed by the eATLAS project, along with Laura Le, Anelise Sabbag, and Elizabeth Fry.

Michelle, the perennial evangelist of online statistics education, participated in two more breakout sessions—one on time-management in online statistics courses, and another on the flipped classroom, as well as leading a lunch discussion group on planning the 2014 electronic Conference on Teaching Statistics (eCOTS).

Liz, N., and Ethan, who've been working with Joan Garfield to improve Wikipedia's coverage of statistics education, led another lunch discussion table to gather feedback and new collaborators on what should be included there.

The University of Minnesota's Catalysts for Change were inspired and motivated by this year's USCOTS, including the plenary speeches from Macalester College's Daniel Kaplan and Nicholas Horton (soon to be at Amherst College), North Carolina State University's Hollylynne Stohl Lee, Harvard University's Xiao-Li Meng, and University of Auckland's Chris Wild, and many more.  The slides of these speeches can be downloaded from the conference website.

Here's all the Catalysts who could make it, smiling in the energizing glow of the shared passion for excellence in statistics education!

The Journal of Statistics Education shines out in new directions

(Photo source: Chandra X-ray Observatory, Smithsonian Institution)

Michelle Everson's hard work as the new editor of the Journal of Statistics Education has borne fruit! The March issue is hot off the presses and freely available online. The issue includes new research on faculty views of statistics, a presentation of a delicious active learning exercise using M&M's, and a new regular feature on research for K-12 education by Tim Jacobbe of the University of Florida.

Michelle is also bringing her social media experience to help spread JSE's beautiful words to new realms. You can catch up with JSE on its facebook page and follow its Twitter feed, @JStatEd. The JSE team is also planning a series of webinars on CAUSEweb starting in June to give readers a chance to interact with the authors of recent JSE features.

You can read all about the JSE team's plans on the JSE page and read the new issue here.

Building the Logic of Statistical Inference on Day 1: The CATALST iPod Shuffle Activity

How random is the iPod shuffle? Your students can investigate.

 
What does it mean for a process to be "random"? The CATALST introductory statistics course engages students in this question in the very first activity, written up in the latest issue of Teaching Statistics by U of M's Laura Ziegler and Joan Garfield.

As Rob Gould points out, students have extensive prior experience with data and randomness. They do not enter the introductory statistics classroom as so many blank slates!

This situation presents both challenges and opportunities: we've heard from many students that it seems like some artists play more frequently than others on the Apple iPod's "shuffle" mode, which plays all songs in a supposedly random order.

Apple even ran an ad campaign in 2005 for the iPod Shuffle device with the slogan "Life is random":

But how random is it? Laura and Joan describe how the iPod shuffle activity elicits and refines student's prior conceptions of randomness. Students first examine 25 randomly generated playlists of 20 songs from a library of 80 songs. They discuss what rules they would use to flag a playlist as non-random. For instance, many students think that a playlist that has more than 5 songs by the same artist should be flagged.

We then give them five more playlists and give them an opportunity to refine their rules based on the additional information. Oftentimes, their rules will incorrectly flag one of these additional playlists and students may want to rethink their rules.

Finally, they get a chance to apply their rules to three playlists to make a decision about whether they have enough evidence to decide these playlists aren't random.

The process of the CATALST iPod Shuffle activity

Laura and Joan regard the full-class discussion, however, as quite crucial. Here is where students can hear the variety of different rules and face the logic and perception of what it means to be random. Students make all sorts of decisions that provide opportunities for rich conversations about the nature of chance: some students can provide convincing arguments that their rules are useful even when they incorrectly flag a playlist known to be random, while others are quick to say that their rules "prove" that the 3 final playlists were generated randomly.

This in-class activity is distributed in the Unit 1 Materials (zip) (Unit-01 > Student-Activities > 01-iPod-Shuffle.doc) on the CATALST materials page. The article also describes a follow-up homework assignment where students actually create a computer model of the process in TinkerPlots. This assignment is not publicly distributed, but interested teachers can contact the first author of the paper to find out more.

The publication is timely, because here at the U of M our students are just finishing up this first activity! It's a great way to get students started on the path to statistical thinking, and we always have fun hearing the creative things that students come up with.

Presenting a radical introductory course at the 2013 Joint Mathematical Meetings

Standing: outgoing SIGMAA chair Andy Zieffler; seated: Robin Lock, Kari Lock Morgan, Laura Ziegler, Elizabeth Fry, Rachel Dunwell, Allan Rossman, Soma Roy

Elizabeth Fry and Laura Ziegler, PhD students in the University of Minnesota's statistics education program, didn't even slow down after finishing their projects and exams this fall. They powered on during winter break to present the innovative CATALST introductory statistics course at the Joint Mathematical Meetings in sunny San Diego, California.

CATALST represents a sharp break from many statistics education traditions. Elizabeth and Laura described its radical content, pedagogy, technology, and assessments as part of a panel discussion on randomization methods in the introductory course:

CATALST course materials can be downloaded from the CATALST website. Development was funded by NSF DUE-0814433, and the full project team can be viewed here.

What's so radical about CATALST? The course joins the new wave of randomization-based curricula, spurred on by statistic education luminary George Cobb: "Randomization-based inference makes a direct connection between data production and the logic of inference that deserves to be at the core of every introductory course." (from The Introductory Statistics Course: A Ptolemaic Curriculum?)

Laura and Elizabeth presented CATALST as a part of a panel discussion on randomization curricula organized by the Statistics Education SIGMAA group. This was one of U of M Senior Lecturer Andy Zieffler's final duties as the 2012 chair of the SIGMAA. Rachel Dunwell of Rhodes College started by talking about how they used to teach a traditional curriculum, and now they're doing simulations with Fathom; Allan Rossman and Soma Roy of California Polytechnic State University talked about their randomization course; and Kari Lock Morgan and Robin Lock talked about their new book and online StatKey software.

CATALST's pedagogy is also radical. The curriculum moves students through a range of activities that they work on in groups. Instructors deliver support with "just-in-time" statistics instruction that's driven by the activities. These activites are made possible by allowing students to directly model probabilities in TinkerPlots. Elizabeth and Laura's presentation discusses an activity, "Matching Dogs to Owners", where students create simulation models of a messy situation that would be difficult to solve analytically.

These radical techniques call for radical assessment that is based on the actual goals of the course. The assessments, known as GOALS and MOST and part of the e-ATLAS project for the Evaluation and Assessment of Teaching and Learning About Statistics, measure conceptual understanding rather than the procedural knowledge of how to compute t-statistics and correlations.

Elizabeth Fry with her poster on the e-ATLAS evaluation and assessment project.

Want to know more? U of M's Laura Ziegler and Joan Garfield wrote an article about the first activity in the course in the latest issue of Teaching Statistics! We'll be taking a closer look at this article in a forthcoming post.

Cliff Konold Demonstrates Data Games, Discusses Research at UMN

"I don't think that we've really demonstrated that we can teach the fundamental ideas at any level. It'd sure be nice to do that!"

Cliff Konold, Director of the Scientific Reasoning Research Institute (SRRI) and Research Associate Professor at the University of Massachusetts Amherst, graced us with his presence on Friday, November 30. He is a major voice in the statistics education research community, and our CATALST course makes extensive use of the software he helped design, TinkerPlots™, for learning introductory statistics using simulation, randomization, and the bootstrap.

Cliff the Researcher

Cliff started out the day, however, wearing his researcher hat. Students in Joan Garfield's statistics education research seminar asked him about his evolution as a researcher, accompanied by a dotplot ("headplot"?) of all his first-author papers, as reported by his publications page at UMass:

Over the years, Cliff has used his head extensively for research purposes

Cliff's research has ranged from close studies of how people perceive randomness to informal inference and data analysis. He said his most proud accomplishment as a researcher is his 2002 Journal for Research in Mathematics Education article with fellow UMass researcher Alexander Pollatsek, "Data analysis as the search for signals in noisy processes", which explores why students are not comprehending the usefulness of measures of center. They argue that ideas of stochastic processes, rather than samples and populations, should be more emphasized in statistics instruction.

Cliff's papers getting all mixed up in TinkerPlots™.

Students Elizabeth Fry and Ethan Brown then decided to turn Cliff's creation against him. They put a selection of his papers into a TinkerPlots™ mixer—a simulated device for random sampling—and shuffled them to pick two papers to discuss with him. The first was a 1997 paper that Ruma Falk was the lead author on, "Making Sense of Randomness: Implicit Encoding as a Basis for Judgment" in Psychological Review. Cliff thought of this as some of the tightest research that came out of SRRI and described what a pleasure it was to have Ruma Falk there visiting and collaborating. The next paper which popped out of the mixer, "Understanding probability and statistical inference through resampling" from 1994, sparked reminiscences of getting deeply lost in Perugia, Italy at the first meeting of the International Conference on Teaching Statistics, where he presented the paper.

Cliff the Software Designer

For the afternoon, Cliff put on his software designer hat to show us his latest project with KCP Technologies, Inc., Data Games, a series of activities where students have to successfully analyze game data to improve their strategy. He's a co-PI on this project with Bill Finzer (see the full team here).

But his researcher hat was still on, poking out from below the software designer hat! Cliff discussed how we typically introduce students to univariate data by discussing natural objects or events such as people's heights. He argues, however, that this is actually a very difficult context to think about measures of center and variability, because there is no concrete thing that the "average person's height" represents.

Instead, he proposes that we can more easily teach these concepts using repeated measures settings. He designed an activity where different students measure the teacher's head; in this case, the center of the distribution is the actual person's head, and the variability is the student's errors in measurement (rounding issues, where exactly they hold the measuring tape, and so on).

Cliff uses not only his own head, but Professor Joan Garfield's as well.

Another promising setting is a production processes: in this settings, the center is the target of the process, and the variability is a combination of measurement error and production errors, which again can be named and pointed to.

But how can these be efficiently brought into the classroom? Having students do a production process or repeated measures takes quite a lot of time to collect the data. This is where the Data Games project comes in.

Ship Odyssey teaches students how to use rats for statistical inference.

Ship Odyssey gives students a chance to engage with repeated measures in a fanciful simulated environment. As intrepid treasure hunters on the high seas of yesteryear, gamers can send down highly skilled rats who find a treasure and then swim up. But they don't swim precisely straight up—they may get tossed to and fro, introducing variability. Students learn how to send down enough rats to get a good estimate of the center of the rat-measures distribution. When they send down their hook, they either see that they've collected a pile of sludge or they hear the satisfying cha-ching of successfully getting the treasure.

We had a great time seeing Cliff and hearing about his research, and we can't wait to see how Data Games develops. In the meantime, our challenge is to not let playing Ship Odyssey distract us from our end of semester work!