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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).


ICTCM 2017 

ICTCM 2017 

Had a great time at ICTCM 2017 in Chicago. And I learned a lot. Between Maria Andersen’s opening day keynote and Eric Mazur’s Saturday sessions I feel that I am making good progress in some areas, but there is still room for improvement. My “lecture time” is very active and engaging, but I feel like I need to turn it up a bit and allow my students more time to experiment and discover. I need to use assessment FOR learning. 

I heard from many instructors who are using our (Sullivan/Woodbury) Interactive Statistics and having great success. It gives students more responsibility for learning, and has changed the ways that the class is taught. We have quite an ambitious plan for 2.0, and cannot wait to share the details. 

Finally, it was great to catch up with so many friends and well respected colleagues. I learn so much from you all and you motivate me to be my best. I am thankful to have such a terrific personal learning network. 

Next week I will summarize the sessions I attended and the trends I noticed. 

– George 

Learning Catalytics- #ICTCM17

Learning Catalytics- #ICTCM17

This Saturday I will be speaking at ICTCM about how I use Learning Catalytics in my Statistics and Algebra courses. 

Collecting Homework 

I started slowly in my Statistics courses, using Learning Catalytics to collect “written” homework. I often give written assignments to supplement MyStatLab exercises, and Learning Catalytics allows me to collect certain problems or parts of certain problems. The answers are automatically graded and scores are transferred to my grade book in MyStatLab. This strategy encourages students to do the homework and to be on time. Students, if you wish, can have conversations about their strategies or answers. As the results come in I can address common errors or misconceptions. 

Reviewing for Exams

I found Learning Catalytics to be helpful for reviewing for exams. For example, while reviewing for an inferential exam I can post a problem and ask students to tell me which hypothesis test is the appropriate one to use. The same can be done for reviews on probability distributions, descriptive statistics, … I can ask conceptual questions or problems requiring calculations. 

I can use these results to get a real time read on how my students are doing with their preparation, and determine which concepts to address in detail. 

Flipping the Classroom/Peer Instruction

Here is where the real classroom power lies. When I flipped my Statistics class, I used Learning Catalytics to make the class sessions more interactive and engaging. I post a question and ask students to submit an answer. Then I either ask students to explain their answers to the class, discuss their answers in small groups, or I offer some insights of my own. At that point I allow students to change their answers if they wish. 

This approach has turned my class into a conversation with my students, or a conversation among my students, which is more effective than the traditional “top down” lecture.  

If you have any questions or comments about Learning Catalytics, flipped classrooms, Interactive Statistics, or anything else in this blog, please leave me a comment or reach out to me on Twitter @georgewoodbury. 

ICTCM here I come …

A Student Shares a Great Observation

A Student Shares a Great Observation

Today in my elementary algebra class we were reviewing solving systems of equations by addition or substitution. We were going over a system where students were having trouble determining what number to multiply each equation by in the system 12x+23y=47<br> 14x+31y=59 in order to eliminate the variable x. We had been discussing that the goal is to find the LCM of 12 and 14, but I told them that on exam day they could always fall back on multiplying each equation by the coefficient of x in the other equation (while making sure that produced one positive coefficient and one negative coefficient).


I then showed the class that they could find the LCM by finding the prime factorization of 12 and 14, gathering the results in a Venn diagram. Multiplying 6 by 2 by 7, the LCM is 84.

systems_vennI finally showed them where the Venn diagram tells us that we can multiply 12 by 7 to get 84, and 14 by -6 to get -84.

One of my students pointed out to me (and the entire class) how he came to decide that he could multiply the two equations by 7 and -6. He started with 14 and -12, then divided both of those by their common factor of 2.


I loved the original thought, and repeated what he said to the entire class. I saw a lot of heads shaking in approval, and my students have a new strategy to use when the LCM does not jump out at them. It was a great day in elementary algebra!

Do you have a story about a student discovery to share? I’d love to hear from you through the contact page on my website, posting a comment, or by 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.

Embedded Tutor FTW!

Embedded Tutor FTW!


Thanks to the Transformation Grant, our college has begun to provide embedded tutors for developmental math and English classes. I have a tutor in each of my Math 200 (Elementary Algebra) classes. My tutors walk around throughout the class session, helping students and answering questions. I have had great results, and I am happy to say that my students feel that having a tutor in the classroom is very beneficial. Many developmental math students are much more comfortable asking questions in a one-on-one fashion, rather than stopping a lecture to ask a question in front of the whole class. I also have my tutors grading some of the in-class group work assignments.

Today we were reviewing for the test on graphing linear equations and inequalities in two variables. I was going over one of the problems that students had worked on (finding the equation of a line that meets given conditions) when one of my students stood up and told the entire class that he noticed that many students found m and b, but neglected to write the equation. It was a great example of feedback provided at an important time, and I am sure that students will benefit from that tomorrow.

I am so proud that the tutor felt comfortable enough to make that observation. I feel that the embedded tutor has increased the sense of community in our classrooms, and look forward to encouraging more instructors to take advantage of this opportunity.

Do you have classroom tutors? Are there any successes you want to share? Words of warning? I’d love to hear from you through the contact page on my website, posting a comment, or by reaching out to me on Twitter (@georgewoodbury).


New Algebra Review Strategy

New Algebra Review Strategy


This semester I am teaching a short term intermediate algebra class. I taught this last year, and I taught a chapter each week followed by a week to review for the midterm. I repeated the same schedule for the final. This semester I have changed the schedule and have had great success. After I finish covering each chapter, I devote a day to reviewing that chapter immediately.

I bring in an old copy of a chapter exam, and the review takes place in 3 parts.

  • I give the students 30 minutes to work the exam on their own. I do not allow them to use notes or any other reference materials.
    30 minutes might seem a little short, but I do write my (1-hour) exams to be on the short side, and most students can get through a majority of the problems in 30 minutes.
    I then have the students identify each problem as a 1 (I have this under control), 2 (I need a little help), or 3 (I need a lot of help).
  • Once students have rated each problem I have them pair up and try to help each other. Many times students who have a problem marked as a 3 can find a student who has it marked as a 1 who can hep them to understand the problem. If the pair of students struggle with the same problem, they can refer to their notes to try to make sense of the problem.
    After another 30 minutes I have the pairs rate each problem again.
  • The third part of the review involves me. I ask students to tell me which problems are still giving them trouble. We have done this for 4 chapters, and each time we narrow it down to 3 or 4 problems that several students are struggling with.
    I work through each problem, asking for students in the class to lead the discussion. What did you try? What is important to remember here? I also offer my advice.

My students have found this very rewarding. One of the strengths of this approach is encouraging students to use retrieval practice. So many times I have heard students say that they thought they had it under control only to have things fall apart on the exam, but if they had put themselves in a test situation without test consequences they may have realized that they were not as prepared as they thought they were.

Another strength of this approach is that students get a chance to turn to each other for help. Often the advice of a classmate will be more helpful to a student than just watching me solve a problem again.

After the midterm I asked my students if they would rather review after each chapter or save all of the review days until the end of the semester, right before the final exam. They overwhelmingly voted to continue with the same review process.

I’d highly recommend giving this a try in your class. Do you have a class that only meets for one hour a day? Try having the students work through the problems, both alone and then in pairs on one day. Then have a debriefing session the next day where you can address their questions.

How do you structure your review sessions? I’d love to hear what you do. Please leave a comment!

– George

I am a mathematics instructor at College of the Sequoias, and an Algebra/Statistics author with Pearson. Follow me on Twitter (@georgewoodbury) or reach out to me through the contact page on my website.

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