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Case Study of Interactive Statistics in an Online Class

Case Study of Interactive Statistics in an Online Class

I’m really proud of this latest study involving our Interactive Statistics (I am a co-author with Michael Sullivan) by Sam Bazzi at Henry Ford College. I saw Sam present his results at ICTCM and was really impressed. I encourage you to check out his case study.

Read the Study Here

This reinforces the fact that there is not a better product to use in an online statistics course: students persisted at higher rates and their test scores improved as the semester progressed. Sam took a lot of time and effort to set this course up, and according to his students it really paid off.

How It Works

The overall idea behind Interactive Statistics is for students to read a little, watch a little, and do a little as they make their way through the section.

  • Concepts are presented through text and video, and reinforced through applets.
  • Each example has 3 associated video solutions: by hand, by StatCrunch, and by calculator.
  • Examples are followed by exercises that students complete. Scores are incorporated into the student’s grade book immediately.

My Online Class

My online students do an IRA (Interactive Reading Assignment) for each section to learn the material, then follow up with a traditional homework assignment. In addition to the guided notebook that is available inside Interactive Statistics, I provide my students with Pointers for each section, and Guides for each IRA and HW assignment – check them out on my website here. The IRA can replace the “lecture” that traditional students get. My students come to campus for an in-person midterm exam and final exam.

Not Just For Online Classes

I use Interactive Statistics for my face-to-face classes as well. I use it to flip my classroom.

  • Students complete the IRA for the section before it is discussed in class.
  • Most classes begin with a Learning Catalytics session to determine the level of understanding and to identify any misconceptions.
  • Many classes incorporate collaborative engaging problem solving during the class session.
  • I no longer “lecture” – we have a student driven discussion instead.

This has allowed me to develop inferential intuition through simulations early in the semester, and incorporate alternative randomization tests and nonparametric tests later in the semester. I feel like my students have a greater understanding of statistics, and I am having more fun in the classroom than ever.

Any Questions?

If you’d like to talk about how to use Interactive Statistics in your class, or how to flip your statistics class, please leave a comment or reach out to me on Twitter or through the contact page on my web site.


Flipping a Two Hour Class – Intro Stats

Flipping a Two Hour Class – Intro Stats

This semester I am teaching a short term Intro Stats class, and I have found it more challenging to flip this class. The class meets 4 days a week for 2 hours a day. This can be difficult because I typically have two main concepts to cover, and students have trouble preparing for a second topic until they get a chance to work on the first concept in class. I will share some of the strategies I have used.

The Best Days

I have found that the best days are those which I have a concept that can extend to the entire two hours. For example, today I covered the two mean test using independent samples. We started by having a discussion about comparing the two mean test to the paired difference test that we covered yesterday. Students then worked through a few tests in their groups. Once I felt they had the two mean test under control I pivoted to the nonparametric Mann Whitney test, the test we use when the necessary conditions for the two mean test are not met. I was able to introduce this concept with a brief 10 minute mini-lecture, and followed up with another group activity with four tests to work through – some two mean & some Mann Whitney. Students got a chance to learn when to use each technique, and I felt confident that they understood both tests.

Making it Work

I have had to be flexible with my traditional approach. For example, I often cover binomial probabilities on one day and follow up with Poisson probabilities the next day. I think asking students to work on a Flip assignment on Poisson probabilities before we discuss binomial probabilities is a tall order.
First Day
So, for the first day students worked a Flip assignment on binomial probabilities before class, and in class the first hour was devoted to a Learning Catalytics assignment and a problem solving session. At that point I could have given a short 20 minute lecture on Poisson probabilities followed by more problem solving. Instead, we spent the second hour on a project introducing the concept of a one proportion test using the binomial distribution. (That is 4 chapters before we formally cover hypothesis testing.)
Second Day
For the second day, students worked on a Flip assignment on Poisson probabilities before class. We spent the first hour doing a team-based Learning Catalytics session followed by some problem solving with the Poisson distribution. For the second hour students did more problem solving on a mixture of general discrete probability distributions, the binomial distribution, and the Poisson distribution.

In a typical class that meets an hour per day this might have taken 3 days, but it took 4 hours of in-class time. This has happened a lot, and I have had to be real careful in terms of how I plan the schedule for this class. Switching from unit exams to a midterm/final approach has bought me a few days. I have learned to be more efficient with other topics.

Stacking Concepts

There are some pairs of topics that can be handled with two flip assignments on the same night. For example, sampling and sampling techniques are covered in two sections in our textbook and I typically spend two days on this material. I was able to give a combined flip assignment on sampling. In class we worked on a Learning Catalytics assignment, followed by an activity in which students got to experiment with the various methods.

Other places where this worked included qualitative and quantitative graphs, and measures of central tendency and dispersion.

Mid-Class Flip

One strategy I did not employ, but holds great promise, is using a mid-class flip assignment. The idea is that I could give students a flip assignment on one topic and begin the class with a group activity, then follow up with a 15-20 minute flip activity for that day’s second topic.

If technology is not available, that flip assignment could be as simple as a guided reading assignment. An open-ended problem solving assignment from the next section could be given. In a smart classroom, videos could be played for the entire class. There are many options.

Once that mid-class flip assignment is done the class could move on to a group activity or a Learning Catalytics assessment.


I feel I will be better prepared for the next time I flip a 2-hour class. I think the real key is to stop doing things the way I have always done them and really leverage the advantages of the flipped classroom.

I have also flipped my elementary algebra classes this semester, and will share about those in a later blog.

If you have any questions, please leave a comment or reach out to me on Twitter or through the contact page on my web site.


Using IF-AT as Part of Exam Review

Using IF-AT as Part of Exam Review

blog if-at image

One of the highlights of the recent ICTCM conference was Eric Mazur’s keynote address about “Assessment For Learning.” He mentioned an assessment technique known as IF-AT (Immediate Feedback Assessment Technique) that reminded me a great deal of the review strategy I have been using in my intermediate algebra course. (Here’s a blog on that review strategy.) I thought it was a great idea to try, so immediately postponed my elementary algebra exams on systems of two linear equations in two unknowns by one day to give this a try. I added a second review day so I can introduce this strategy to my students over a two day period.

The idea is that students work on a series of problems individually. After half of the class period has ended, students submit their individual work and form groups of four students. They then discuss their answers as a team and submit a team answer to the first problem. If they get it right the first time they get full credit. If they get it wrong they can select a second answer to submit for 1/2 credit. They can even try it a third time if needed for 1/4 credit. I saw a video where the problems were in a  multiple choice format with 4 possible answers, and the teams were given a scratch off card. A star was displayed on the right answer – if students see the star they know they are right, if they see a blank space that counts as an incorrect attempt.

You can see a step-by-step demonstration of how the IF-AT works
on this web page posted by Epstein Educational Enterprises.

I am going to use a Learning Catalytics Team-Based Assessment to put my spin on this process. On day 1, students will work individually on 8 problems for 30 minutes. Some problems will be conceptual, some will be systems to solve, and there will be two word problems. They will submit their answers as they work. I will then launch the team portion of the assessment. Students will form their own groups of 4, with one person responsible for entering their team answers. I have decided to give teams only two attempts on each problem. A correct answer on the first attempt will receive full credit and a correct answer on the second attempt will receive half credit.

The individual portion will make up half of the score, with the team portion making up the other half of the score. I will be counting the score as an in-class activity in my flipped classroom model. I expect students to take a little time to get used to working with Learning Catalytics, so I have tried to select problems that they will be able to answer in the given time limit. I expect day 2 of the review will be smoother. My students work so well together, and I expect to see their bonding pay off in this review.

Later this week I will let you know how it goes.

Do you have any experience using IF-AT in the classroom? Do you use it for testing? I’m curious how you address students who have testing accommodations through the testing office. Let me know by leaving a comment, reaching me through the contact page on my website, or reaching out to me on Twitter (@georgewoodbury).


Flipping Elementary Algebra

Flipping Elementary Algebra


This semester I am teaching two sections of elementary algebra using a flipped classroom model. The approach is different than the way I have flipped my statistics course, but has been very effective. I am relying heavily on MyMathLab outside the classroom.

For each section that we cover …

  • Students complete a “Flip” assignment before the material is discussed in class.
    The assignment contains conceptual videos that introduce each topic as well as videos of examples where problems are worked out.
    After students finish the videos, there are a handful of problems that they have to work through, and all of the learning aids (except “Show Example” are available. Students can try each problem as many times as they would like.
  • The “lecture” period is intended to involve active learning.
    Some days begin with a class driven recap of what they learned in the Flip assignment. I count on students to drive this discussion, stepping in only when I have something to clarify or add. I mostly ask questions and wait for students to respond.
    Most days involve group work or collaborative learning. Some days students turn in their assignments. Other days we go over answers as we go, or I ask students to share their answers and strategies at the board.
    Every day is different, and I am looking for my students to be as agile in their learning as I am in my teaching.
  • After class, students take a 5 question “Reflect” quiz that focuses on the problems that I feel are most important.
    The results on the student’s first Reflect quiz attempt load a personalized HW assignment, containing 3 exercises associated with each problem on the quiz. If a student gets a problem correct on the first quiz attempt, they get instant credit on the personalized HW for the 3 associated problems.
    Students use the personalized HW for self remediation, then they can go back and take the quiz again as many times as they would like to.

One question many have about flipping the classroom is “What do you do if students arrive unprepared?” In my experience, having the Flip assignments due for a grade motivates students to do them. Also, because they hear their classmates participating in the discussions and contributing during “lecture they feel more compelled to be prepared themselves. I have seen some of my students in the tutorial center in the morning before class starts trying to get some help to make sure they understand the material, and that can only lead to good things.

I am happy with the way things are going, and I am progressing towards less discussion at the beginning of class as my students become stronger. It gives me (& my embedded tutor) more opportunities to walk around during class and talk to students one-on-one, clarifying as we go.

The classes just took the exam on Chapter 3 (Graphing lines, equations of lines), and 61 out of 71 students passed the exam. The mean score in each class was in the high 80s, with median scores of 92 and 93 in the two classes. This test was very similar to the test I gave last semester, but the results are much stronger. On to systems of equations …

Are you flipping your classroom? I’d love to hear what you are doing. Interested in trying this approach? Please leave a comment on this blog, contact me through the contact page on my website, or reach out to me on Twitter (@georgewoodbury).

I am a mathematics instructor at College of the Sequoias in Visalia, CA, as well as the author of algebra and statistics textbooks with Pearson.

Flipped Classroom Materials for Statistics

Flipped Classroom Materials for Statistics

Last semester I flipped my Statistics classroom, and was really happy with the results. I have put together some pages explaining exactly how I flipped the classroom, with links/descriptions of documents that I used along with a calendar showing how I we covered the material.

You can find it all at

I will be adding more to the site as I make my way through a second semester of flipping that classroom – this time in a short-term (8 week) semester.

– George

Building an Early Inferential Approach into the Calendar

Building an Early Inferential Approach into the Calendar

I have had a few questions about how I am managing to work all of these early inferential projects into my Intro Stats course.

1) Switching from Chapter Exams to a Midterm and a Final

In the first 7 chapters of our textbook I used to give 4 exams. That means that I would use 4 days for exams and approximately 6 days for review. I have 4 days built into my calendar for review (2 days) and the midterm exam (2 days). That is a net gain of 6 days in the first half of the course.

I have 8 project days scheduled in the first half of the course so that only puts me two days behind, but I have been able to avoid spending more than one day on any section so there are unofficial gains there.

I have checked in with two colleagues and I am one day behind one of them and even with the other.

In the second half of the course I will apply the days saved from chapter tests to cover alternatives to the traditional hypothesis tests, including simulations and non-parametric tests.

2) I Will Not Have To Introduce Hypothesis Testing in the Second Half of the Course

I typically spend 4 days to cover the first hypothesis test (the 1-proportion test), but I should be able to jump right in and cover that test in one day.

My Calendar for Weeks 1-5

Here is the schedule I have followed to this point. I have put the project days in bold.

Date Topic
15-Aug Day 1 Syllabus etc.
16-Aug 1.1 Intro to Stats
17-Aug 1.2 Observational Studies, Experiments
18-Aug 1.3/1.4 Sampling Techniques
22-Aug 1.6 Experimental Design
23-Aug 2.1 Qualitative Graphs
24-Aug Project 1: Simulation for 1-Proportion
25-Aug Project 2: Randomization Test for 2-Proportions
29-Aug 2.2 Quantitative Graphs
30-Aug 3.1 Measures of Center
31-Aug Project 3: Bootstrap Method for Estimating a Mean or Median
1-Sep Project 4: Using Simulation for a Population Mean
5-Sep holiday
6-Sep Project 5: Using Bootstrap Method for a Paired Difference Test
7-Sep 3.2 Measures of Dispersion
8-Sep 3.4 Quartiles
12-Sep 3.5 5-Number Summary and Boxplots
13-Sep Project 6: Randomization Test for Two Means
14-Sep 4.1 Correlation
15-Sep Project 7: Hypothesis Test for Correlation


Comparing Two Samples (Quantitative)

Comparing Two Samples (Quantitative)

My students are wrapping up the part of the course where we cover descriptive statistics. I gave them two sets of data (test scores from two different versions of the same exam) and they spent the day in class computing sample statistics and creating graphs for each sample. Their overall goal was to analyze their results and determine whether there was a significant difference between the two versions or not.

Download a pdf of this activity

Students compared measures of central tendency and the 5-number summaries and I asked them to share their observations. They went on to compute measures of dispersion and then we talked about whether the dispersion of each sample was similar. Finally they created histograms, pie charts, and boxplots and we discussed what they felt the graphs were telling them.

We had another great opportunity to discuss the fact that a perceived difference may not be significant unless we can determine whether the observed difference (the means were 4.8 points apart) would be unusual through some sort of repeated sampling.

This leads into our sixth project of the semester where we will use the randomization test for two means to determine whether the observed difference was significant. We will use StatCrunch for this test, although there are many other tools out there that can be used. My students will then move on to apply this test to two sets of data they collected. I will blog about the outcomes of that project in my next post.

Book Review: Teaching with Classroom Response Systems by Derek Bruff

Book Review: Teaching with Classroom Response Systems by Derek Bruff

Just finished reading this book by Derek Bruff (@derekbruff on Twitter), so I thought I’d share what I wrote on Goodreads. (By the way, if you’d like to be reading buddies, here’s my Goodreads profile page.)

Here goes …


Although some of the technology has really changed since this book was published, I would strongly recommend this book to anyone who plans to incorporate classroom response systems into their teaching. Bruff clearly lays out the pros and cons of different strategies of incorporation, grading schemes, question types, revealing correct answers, …

He does a great job introducing Peer Instruction, and I have been using that strategy in my classroom with great success. I feel that more of my students understand more of the material at this point of the semester than in previous semesters. (I am moving on to Mazur’s Peer Instruction book to go into greater depth on the strategy.)

I also love the concept of Agile Teaching. I love the uncertainty of not knowing which way the class will go, while remaining confident that I can adapt to what I am seeing from my students. I am teaching the same class back-to-back, and have had to focus on different topics with each class. It’s a lot of fun, and it fits in with my belief that we teach our students instead of teaching the material. I now walk into class each day thinking “I Am An Agile Teacher” and I feel so empowered. I should probably put that on a t-shirt.

Note: I am using Learning Catalytics as my classroom response system in my Intro Stats classes, and I am about to start using Plickers in my Elementary Algebra classes.

Learning Catalytics for Turning In Class Assignments

Learning Catalytics for Turning In Class Assignments

Last night my intro statistics students worked through an Interactive Reading Assignment for measures of central tendency. In class today they will be working with four data sets and computing various measures of central tendency. To collect their work I will run through a Learning Catalytics module asking them for certain specific answers.

My plan is for students to work individually while consulting with each other. If they have different results it will be a great opportunity to check each others data entry and computational processes.

Learning Catalytics ability to collect numerical responses is definitely an advantage over the clickers of old that only allowed multiple choice answers. It also does a great job of evaluating numerical answers – it treats all of these as equivalent: 0.6, 0.60, .6, 3/5, 9/15, …

I sometimes use Learning Catalytics in this fashion to collect some written homework. I assign a handful of problems the night before, then collect certain answers at the very beginning of class. I also mix in some interpretation questions or conceptual questions that were not asked in the homework. Sometimes I follow up with a new similar problem to make sure they can do it in class. It’s very efficient and flexible for collecting some “by hand” problems.

Day 2 of Flipped Classroom/Peer Instruction in Statistics

Day 2 of Flipped Classroom/Peer Instruction in Statistics

OK, this was a good day. No. It was a great day!

I cut down the review of the home content to 10 minutes, and was happy to see so many students participating in the student-driven review by offering their own explanations and definitions. Students know to come to class prepared and looking to participate. I can see where this could turn into a situation where only a handful of students participate though, and will seek to eliminate this pre-review and jump more quickly into the Peer Instruction portion of the class.

I also cut down the number of questions I asked by half. We did not feel so rushed, and it gave more time for deeper discussion. I guess one of my weaknesses is trying to cram too much into my class sessions (and exams too). I will constantly ask myself if I have too many questions, and if can I make due with fewer.

After making our way through a series of experiments where students had to determine the explanatory and response variables I stopped the class to make sure my students understood why I am using the approach. I asked them how confident they were about knowing the difference between an observational study and a designed experiment as well as how confident they were in their ability to identify explanatory and response variables. They were highly confident. Then I asked them if they would have felt as confident learning the material in the opposite order – with me giving the definitions and some examples followed by them cementing their understanding working at home. I saw the lights come on for many students. They understood that their learning was much greater in this system, and I think I have a great deal of buy-in from them now.

Tomorrow we turn our attention to an activity involving sampling techniques instead of a Learning Catalytics assessment. Although we won’t be using our “clickers” I will try to encourage the same level of discussion that I witnessed today.