By Brandi Falley and Ryan Sides

While the topics and depth covered in Elementary Statistics varies by school, it is still often a difficult course for the majority of students. Statistics is not a traditional math course where pattern recognition can aid in solving problems, and students are often forced to use logic and critical thinking with little background training. In facing this problem at a mid-sized, Hispanic serving institution in the south, we discussed various options to increase student success including eliminating the most missed exam questions from previous semesters, decreasing the amount of content, and adding more practice problems. One option that was discussed but never implemented due to the implementation cost (in terms of time) was “flipping” the course—providing students with lecture videos and using class time for deeper questions and more practice.

Then the pandemic happened.

As many were forced to do, we had a sudden need to improve our online version of the course due to the fact that all sections were now online. Pre-pandemic, with only a few online sections, it was easier to provide paper exams in-person for local students and work with proctors for distance learners. That obviously wouldn’t fly with the students now scattered across the country and in much larger numbers; we needed a better testing system. We already operated our homework on the free platform MyOpenMath, in which we had created our own questions and assignments, in addition to using some from the bank of questions provided. Therefore, creating exams there didn’t require a large learning curve. It also offered several nice benefits. First, we used a random number generator in the programming which allowed each student to have an exam with different answers. Second, pools of questions can be formed such that students are asked n questions from the group, allowing some variability among exams. Third, in the spirit of combining the previous two ideas, some questions have a random component to them that switches what’s asked from one thing to another. An example of this is when a scenario is laid out for a problem and students have a one-in-four chance of being asked to identify the sample, the population, the statistic, or the parameter.

As the summer of 2020 rolled along and it became clearer that some form of in-person learning would take place in the 2020-2021 academic year, we returned to the idea that we toyed with for some time previously: a flipped classroom. We still had lingering concerns that we may need to switch back to 100% online at any moment, depending on the status of COVID-19, so this was a great solution. This teaching method would allow us to easily transition to 100% online, if necessary. We wondered, would it allow us to maximize our time with the students and create better outcomes? We decided to give it a try.

The first question to decide was how many days per week we’d meet with the students. With social distancing the norm at that part of the pandemic, meeting with them just one of the two usual weekly meetings became the easy solution: breaking them into one group that met on the earlier day of the week and another that met on the later. However, even as things have returned to somewhat normal in the classroom, we’ve stuck with one meeting per week. Obviously, students would gain more by meeting more frequently, but since we ask them to watch a full week’s worth of lecture videos and complete the usual homework, it seems fair to give them a little bit of the “allotted” class time back for those purposes.

Because we now had extra classroom time usually reserved for traditional lecturing, we created one worksheet to accompany each week of material. While there have been a few iterations each semester based on student feedback, each class usually proceeds in the following manner:

• First, we spend 20-30 minutes highlighting the key ideas from that week’s lecture videos. Because students need to hear things multiple times, hitting the high points again is a logical starting point in trying to make sure they capture the most important pieces of that week’s material.

• Then we work the first page of the worksheet, a set of example problems, with the students similar to how an instructor would typically do an example problem during a traditional lecture. Even though the students have seen examples from the lecture videos, they’re still usually on some unsure footing at this point. Walking them through another problem or two and asking them questions about why certain choices were made tends to help solidify the material some.

• The second page of the worksheet tends to be conceptual questions—symbols, true/false, or multiple choice. The third page is more practice problems, sometimes with previous material thrown in so that they remain sharp overall. We let the students work at their own pace and in groups on these last two pages, and we recap answers at the end of class if time permits or post the key online if it doesn’t.

We quickly learned from the feedback of numerous students that we should have heeded the advice to keep videos short. We broke our 40-80 minute videos into 10-20 minute chunks by section, topic or type (new material versus example problems). Making this change rounded out an overhaul of the course that we believe provides the students a better overall experience.

In addition to the worksheet, we have also implemented the use of review materials. One week before each exam, we ask students to write a One-Minute Paper and answer three questions to help us learn where students are struggling. (This idea came from the Association of College and University Educators’ ideas for Checking Student Understanding.) The first question involves pinpointing something the student has learned that may have surprised them or that they struggled with and finally understood. The second question asks students what is still lingering in their minds, and the third question asks students if there is anything they didn’t understand or if they have any other comments. We gather this information (it can be anonymous), and we create a list of topics to discuss on “review day.” Then, on review day, we dive a little deeper into the areas where we know our students are struggling. This offers a way for our quiet students to express their areas of concern and for us to address those concerns prior to each exam. This idea also extends to a purely asynchronous online course with the topics to be covered being presented via a recorded video.

The One Minute Papers have offered us additional insights about our students’ understanding. One student wrote: “Everything is understandable in the course. The hardest part is finding the clues to make sure that you are using the correct formulas or thinking about the correct concepts.” Another student wrote that the “most important thing I’ve learned is to take your time.” Often we glean valuable information as to other tips the instructor might want to pass along to students or small changes that can be made to the course that can provide a better experience.

For those thinking about flipping the classroom, do it! Elementary Statistics is not a typical math class so learning from a traditional lecture style may not appeal to most students. Change it up. Bring in new activities, new worksheets, and new conversations, and allow students to approach the class in a non-traditional way.

Brandi Falley is an Associate Professor and the Lead for the Division of Mathematics at Texas Woman’s University. Outside of teaching, her interests include playing soccer and enjoying the outdoors.

Ryan Sides is an Assistant Professor in the Division of Mathematics at Texas Woman’s University. His other research areas include Bayesian statistics and sports modeling (including the use of predictive probabilities in sports gambling).