Introduction

The field of statistics has always held a special place in my heart. When discussing programs of study with students, colleagues, friends, and family members, each individual is able to recall a story related to an introductory statistics course, working with data, or exploring data literacy. These stories often begin with comments about the relationship between mathematics and statistics and a fear of delving into computations and calculations. Yet, in many cases, these conversations expose revelations about the interdisciplinary nature of statistics and how it requires a synthesis of skills to interpret the meaning of data. The ubiquitous nature of statistics courses in post-secondary programs—regardless of discipline—drew me to the SoTL in such environments. More specifically, I focused on how introductory statistics courses could be offered in online spaces. I wondered:

• How do instructors design and facilitate courses that are often meant to be an entry point for students to the world of data literacy and research?
• How do instructors weave together pedagogy, content, and technology in a virtual setting?
• How do instructors approach challenges in online spaces?

Technology in Online Statistics Classes

Gould (2010) argues that statistics and technology are inseparable. While there are various definitions of what technology means in the context of statistics education (e.g., statistical programming languages, databases, data access and manipulation, visualization tools, and simulations), it has become clear that there is a need to meaningfully utilize technology within statistics courses (Nolan & Lang, 2010).

Before an instructor incorporates technology into a statistics course, students should be provided with concrete examples of how the tool is being used and the underlying mechanisms of the tool. Garfield et al. (2015) note that without such examples, students may lack statistical understanding of particular concepts or they may not believe the results produced by the tool. They explain:

The thought is that software tools allow students to be directly involved with “building up” the sampling distribution and allowing them to focus on the process involved and therefore on key ideas, rather than simply being presented with the formal end result. (Garfield et al., 2015, p. 335)

Furthermore, it is important for instructors to ensure that technology is scaffolded in their classes to ensure that students have a foundation on which to build their technological understanding.

In order to incorporate technology into statistics courses, many questions must be considered, including how students will engage with statistical technology throughout the course and once the course is finished. To help meet the diverse needs of students with regard to statistical technology, McNamara (2015) suggests that the technological tools used in statistics courses should have multiple entry points. As noted by Gould et al. (2017), technological tools in statistics should “strive to provide easy entry for new users while still allowing the flexibility to build extensions onto the system, support a cycle of exploratory and confirmatory analysis, promote interactivity, and make it simple to publish and reproduce analysis” (p. 465). Furthermore, students should be able to use the technology as novices and have the opportunity to explore the technology more thoroughly as they become more experienced users.

Building on previous literature that has focused on student retention, completion, and achievement in online statistics courses, this research explores how instructors design, develop, and facilitate online undergraduate introductory statistics courses. With specific reference to teaching statistics, Tishkovskaya and Lancaster (2010) call for an educational reform: “leading statistics educators formulated difficulties in learning statistics, raising issues of concern in statistical education, and urged a reform of statistics instruction and curriculum based on strong synergies among content, pedagogy, and technology” (p. 1). This study, then, aims to investigate the following research questions:

1. How is technology used in online introductory statistics courses?
2. What types of technology are used in online introductory statistics courses?

Methodology

The approach used to conduct this research was a case study using a qualitative empirical methodology. This approach was selected because it allowed me to develop an in-depth understanding of a particular experience (Creswell, 2013; Yeo et al., 2023). Further, Merriam (2009) and Mill et al. (2010) assert that a case study approach is appropriate when the objective of the study is to construct both meaning and understanding. Within the case study, two types of data were collected and examined: semi-structured interviews and course materials (e.g., course syllabus, assignments).

Data Collection

Participants in this research included four instructors (James, John, Lyla, and Greg) who have taught an introductory statistics course online to undergraduate students at a specific university in southern Ontario. The bounded constraints of the case study included the location, the level and type of course being taught (introductory statistics), and the modality of the course (online).

Multiple sources were used to gather evidence during this study. The first data type was semi-structured interviews. Interview questions were organized into subsections, including background questions and questions that aligned with the technology, pedagogy, and content knowledge (TPACK; Mishra & Koehler, 2006) framework. All interviews were recorded and transcribed. Once the interviews were transcribed, a copy of the transcript was shared with the interviewee (member checking) to ensure the information was accurately captured (Birt et al., 2016).

In addition to conducting interviews, course content was examined. The primary document that was investigated in each course was the syllabus. As with the interviews, the TPACK model was used as a lens to explore the experience of teaching statistics online. The purpose of using course content as evidence was to capture the experience of teaching an online statistics course more holistically. Further, evidence presented during interviews was compared and contrasted to how the online course was facilitated.

Data Analysis

Data analysis happened as data was being collected to help guide the follow-up semi-structured interviews (Creswell, 2015). Data was transcribed and coded as interviews proceeded. This allowed me to conduct a constant comparison analysis of all data as it was collected (Leech & Onwuegbuzie, 2011). The purpose of concurrently collecting and analyzing data was to explore the experience until saturation was reached and inform adjustments that should be made to the data gathering (e.g., interview questions, course content analysis).

Determining when a sufficient amount of evidence was collected included considering the themes that emerged within the data. Data was coded in the NVivo 12 software using a combination of deductive and inductive coding informed by the TPACK model.

Lessons Learned About the Relationship Between Online Statistics Courses and Technology

While James, John, Lyla, and Greg used technology in ways that support their learners and teaching philosophies, there are some common themes among how the instructors incorporate technology in their courses. Specifically, the conversations about the use of technology in their online statistics courses centred around multimodal representation, communication, and the mechanics of calculations.

Multimodal Representation

The instructors used both synchronous and asynchronous delivery modes for their courses. James facilitated his course completely asynchronously. His rationale for using this approach was to allow students to progress through the course at their own pace. While he provided them with due dates for evaluation pieces and a recommended schedule, students were responsible for learning the material. This follows his teaching philosophy of treating students like adults and giving them autonomy with their learning. Meanwhile, John, Greg, and Lyla used asynchronous elements in their courses to catch up on material and to provide additional content for optional exploration.

Greg, John, and Lyla all incorporated live, synchronous class time in their courses. Both John and Greg received positive feedback from students for hosting live classes. They credited this success partially due to how they purposefully used asynchronous and synchronous elements in their courses. Greg described how live classes helped mimic the live theatre atmosphere of teaching on campus. Further, he felt that taking this approach to teaching allowed for more authentic learning to take place. He specifically used the example of wanting to be able to work through a problem with students in live-time and follow their directions, rather than using pre-designed slides and revealing the answer immediately. In accordance with Mills and Raju (2011), Greg and John found that facilitating synchronous conversations supported learner-instructor interactions.

Because Lyla designed her course following a flipped-classroom model, she reserved synchronous class time for activities and discussions. She developed videos for students to watch before class and had tasks designed for in-class discussion. When she implemented this teaching approach in her online course, she faced resistance from students. She explained that students felt double the workload, since they had to attend a synchronous class and review content outside of class. Given that her course was a first-year course, students may have resisted this model in part due to motivation and ability to self-direct learning. Farmus et al. (2020) explain that the success of a flipped-classroom model relies on the idea that “students are motivated enough to ‘self-pace’ their lecture viewing” (p. 316). Lyla noted that, if she were to offer the course online again, she would either use a purely asynchronous model or synchronous model to avoid student confusion and frustration.

Regardless of whether they facilitated their course using a synchronous or asynchronous approach, each of the participants underscored the importance of recording their material and making content available for students to access at their own convenience. John felt that teaching online lends itself well to allowing students to review content at their own pace. In agreement with Conrad and Openo (2018), Greg, Lyla, and James also noted that the benefit of online learning is that students can access content at their own convenience. Moreover, the participants leveraged the online learning environment to ensure students could access and review learning resources as they pleased.

In addition to discussing their selection of course modality, the participants highlighted the use of various mediums to present statistical concepts. Employing their knowledge of pedagogy and technology, James, Lyla, and John designed short videos for students that focused on specific concepts. Each of these instructors noted that they limited the length of the videos, since they wanted to be concise and keep the students’ attention. James believed it was essential to give students choice with regard to how they engage with material—whether that be reading text or watching videos. Each of the instructors also used additional resources, such as textbooks (Lyla, John, and Greg) or self-authored resources (James), to provide students with alternative explanations of concepts.

Finally, the instructors integrated scenarios in their class that replicated evaluation situations. For example, John and Lyla would review prior tests and exams so that students had an idea of what types of questions to expect. They felt students appreciated these review sessions, since they were able to better understand what was expected on assessment pieces. Similarly, Lyla would ask interactive questions during her live lectures using a program called Top Hat. She believed these questions provided students with an opportunity to engage in low-stakes assessments so they could build their confidence when faced with statistical concepts. Greg also designed lectures so that students could respond to questions that were similar to the assignment questions. He felt that giving students the opportunity to guide solutions helped to clarify misconceptions and helped them to develop their communication and statistical thinking skills.

Communication

The participants drew on both their pedagogical knowledge and technological knowledge to facilitate communication channels using technology between themselves and their students as well as among students. Lyla, Greg, and John used Zoom to host their live synchronous lectures as well as their office hours. Though Mills and Raju (2011) suggest that delivering a course synchronously can support learner-instructor interactions, the participants discussed the challenges of offering synchronous courses with large enrollment numbers. They pointed out that it was difficult to note body language and visual cues that students understood the material, since students did not always have their cameras on and it was impossible to see everyone on one screen.

With regard to communicating with students, the participants identified technology as a way to provide students with feedback. Due to the large class sizes, the instructors found it difficult to provide personalized feedback. Though James, Greg, and John used Crowdmark for handwritten assignments, there were limited TA resources to provide individualized instruction. The challenge of providing students with unique feedback on major assignments is in line with comments made by Conrad and Openo (2018) and Figueroa-Cañas and Sancho-Vinuesa (2018). Moreover, the instructors explained that they use class time as an opportunity to provide general feedback, answer commonly asked questions, and clarify misconceptions. That being said, the participants often made use of auto-generated feedback for tasks graded electronically, such as quizzes in the LMS, Maple TA assignments, and online tests.

To provide opportunities for more personalized feedback and one-on-one learning experiences, many of the participants offered virtual office hours. However, that required students to take initiative and seek out feedback and additional help. The participants felt that virtual office hours were used very infrequently and less than during on-campus learning. Nevertheless, the instructors highlighted the satisfaction students had when they did choose to attend virtual office hours. For example, Lyla discussed how students would sometimes attend virtual office hours in small groups and ask a variety of questions.

An additional form of technology that instructors used to interact with students was email. Though Mills and Raju (2011) suggest that email can be an advantage to online learning, Greg and James pointed out that it was easy to get overwhelmed by the number of emails they received from students. The participants noted that students were more likely to email them questions than post them to the discussion board. Moreover, the participants used a variety of technology to communicate with students, keeping with the theme of multiple means of expression and action (CAST 2018; Chen et al., 2018).

Technology also served as an outlet for students to communicate with one another. Though many of the instructors incorporated discussion boards in their course, they found that they were not used frequently. As previous research has pointed out, instructors need to purposefully integrate discussion boards in a way that is related to the structure and the design of their courses (Boothe et al., 2018; Dell et al., 2015; Juan et al., 2011). Instructors who taught synchronously used breakout rooms to allow students to collaborate and communicate with one another. John expressed how he hoped that this would help students socialize with one another. Likewise, Lyla integrated small tasks in her course that students could complete while in the breakout rooms. She also integrated Top Hat questions to get a quick snapshot of student engagement and content comprehension.

While learner-learner interactions were not often observed on discussion boards or within the classes, the participants noted that students were using social media platforms and other outlets to communicate with one another. Moreover, while previous literature has identified that communication and collaboration among learners supports motivation, connectedness, and engagement (Boothe et al., 2018; Conrad & Openo, 2018; Juan et al., 2011; Sun et al., 2018), the participants felt that such interactions were happening beyond the tools used in their courses.

Mechanics of Calculations

According to the participants, much time was spent determining how to display statistical syntax online. James, Lyla, Greg, and John noted that their approaches stemmed from a desire to mimic the look and feel of teaching statistics in person, thus synthesizing both their pedagogical knowledge and technological knowledge. James explained that when he first started teaching introductory statistics online, he looked for software that he could use to record himself writing that captured the essence of writing on a chalkboard. Similarly, John, Lyla, and Greg created a space where they could teach synchronously in a manner similar to teaching in class. To make the videos, Lyla would record teaching using a whiteboard and document camera. She noted that filming ahead of the class allowed her to make edits and adjustments to the videos.

While teaching synchronously, both Lyla and John used document cameras connected to their laptops so that they could write and display statistical concepts. Greg primarily set up his teaching space to teach while writing on a whiteboard. The instructors highlighted the importance of both verbally explaining and visually displaying statistics content. The challenges the participants faced with regard to typing and displaying mathematical syntax (such as Lyla’s attempt to use Microsoft Word for lessons) give credence to the arguments made by Trenholm et al. (2019) about the additional layer of complexity that instructors encounter while teaching introductory statistics courses online. Interestingly, as James acquired more experience teaching statistics online, he shifted away from handwritten videos towards high-quality videos with typed up notes. He pointed out that this was due to wanting his videos to be clearer as he felt his handwriting was not particularly neat.

There was some variation regarding the use of statistical software in introductory statistics courses. Keeping in mind their audience as well as their content knowledge and technological knowledge, the instructors selected software and calculation methods to best meet the needs of their learners. They were purposeful in how they integrated statistical software, as they were aware of how technical issues could negatively impact student motivation and efficacy (Eichelberger & Leong, 2019). For example, Greg and James used R in their courses. They felt it was important to provide students with programming skills to visualize and analyze large data sets. James and Greg identified programming skills as a way for students to take ownership of their learning and to build their technological skillset. They explained that one of the reasons that they use R in their courses is because R is free, even if you are not a student. Furthermore, students can use the tool beyond the scope of their courses. They also noted that R is well-supported from a technical support standpoint and that students can take it upon themselves if they want to learn more about how to use the software.

Meanwhile, Lyla and John do not have students use software in their introductory statistics courses. In previous years, when John had more TA support, he had students use Microsoft Excel to conduct statistical calculations. He noted that, as a compromise, he used Maple TA in his introductory course to have students practice typing statistical syntax. Lyla expressed the importance of students conducting calculations using calculators in her class. Her hope was for students to develop a strong foundational understanding of what was happening in each calculation. Moreover, she used small datasets in her course to ensure the computations were manageable. John and Lyla explained that their students may not take statistics courses beyond their introductory course; therefore, they wanted to distinguish between statistical calculations and programming. John and Lyla mentioned that students are expected to use statistical software (e.g., R, SPSS, MATLAB) in upper-level statistics courses within their faculties.

Implications and Recommendations

It is clear that James, John, Lyla, and Greg took many factors into consideration when determining how to use educational technology in their online introductory statistics courses. They asked themselves questions about their students, the learning management system, and how they could adapt their teaching practices based on feedback and available support. A primary observation made by the instructors was the value of providing students with flexibility regarding assessments and content access in online spaces. When they transitioned to teaching online, they highlighted the importance of reshaping their courses to include multiple assessment opportunities to help students stay on track while learning from a distance. They also believed it was essential to provide students with continuous access to content so that they could engage with content at their own pace.

The instructors also noted the importance of using technology that accurately presented statistics syntax and provided students with the chance to practice writing statistics syntax and explaining the implications of statistical results. Though James, John, Lyla, and Greg used varying tools, each instructor emphasized the need to incorporate handwritten statistical syntax both as an instructor and as practice for students.

In order to successfully facilitate an online introductory statistics course, the instructors felt they needed opportunities to learn to teach statistics online in formal settings (e.g., professional development, webinars) and informal settings (e.g., discussions among colleagues). In some cases, this could include an online space where instructors can try new content, pedagogy, and technology. In other cases, this may involve providing instructors with lead time so that they can prepare and experiment with different tools, integrate opportunities for co-teaching, or share resources among instructors so that they do not have to start planning from scratch.

The findings from this study have many implications for various individuals within post-secondary settings, including instructors, teaching support units, academic leadership teams, and educational software developers. These recommendations include the following:

• Incorporation of opportunities for co-teaching between faculty and graduate students. While graduate students often have the chance to work as teaching assistants, it is less common for them to partake in teaching undergraduate courses. Allowing for instructors and graduate students to co-teach courses supports knowledge sharing in the domains of pedagogy and technology.
• Educational software developers may consider designing learning management systems that integrate social media tools and communication platforms (e.g., Discord, Slack) to support learner-learner interactions and learner engagement.
• Academic planning units may consider providing instructors with lead time for their courses. When changing the modality of introductory statistics from on-campus to online, establishing some lead time would allow instructors time to explore technology for course delivery, determine how to present statistical syntax, and investigate how to assess learners from a distance.
• Multiple assessment pieces should be used to allow students to build statistics efficacy and demonstrate their understanding. Assessments should draw on real data and consist of frequent, low-stakes evaluation, assignments that promote statistical communication and dissemination skills, and peer-collaboration.
• Regardless of online course modality (i.e., synchronous or asynchronous), instructors should leverage the flexibility of online learning and ensure that content is available to learners so they may access and review content at their own pace. This may include recording and posting live lectures and posting course content at the beginning of the term.
• Formal professional development workshops provided by teaching support units should include specific examples of how to integrate specific pedagogical and technological approaches in online courses. They may consider having other instructors demonstrate examples of how they use alternative forms of assessment, technology, or course modality.

Conclusion

Online introductory statistics courses provide learners with flexible options for pursuing their studies. Instructors can provide students with agency and autonomy of their learning by presenting statistical concepts using real data, recognizing the value and experiences each learner brings to the class, acknowledging the challenging nature of statistics, and incorporating multiple ways for students to demonstrate their understanding. These approaches combined with using technology to communicate with learners and facilitate online courses help create an authentic learning environment. These strategies help address the complex nature of interweaving synchronous and asynchronous discourse in online spaces as identified by Greg:

There is no place for live theatre if everything has to look like an Avengers movie. You have got the two or three hours of super slick, massively prepared things; live theatre is a different business… But you have to treat them as to what is your value in a live lecture? I think that is one of the things – how can you capture more of that in an online course when you are thinking of an online course? (Interview, December 8, 2021)

Online facilitation of introductory statistics courses has the ability to empower learners by giving them the chance to play, rewind, and interact with educators at their own pace.

The interviews with the participants revealed that educators are receptive to using technology to enhance communication and demonstrate statistical computations in online spaces. Likewise, they are invested in using innovative teaching approaches—such as assignments, participation, in-class tasks, and group work—to help students better understand statistical concepts. As educational technology continues to evolve, the reflections shared by these instructors act as a reminder to pause and reflect on how our teaching practices may continue to change and adapt to support our students.

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