**1. Introduction**

As instructors, we are assigned classrooms. We can make requests if we have enough seniority, but even then, there are no guarantees. We all want to get through to our students, and we all want the best environment for doing so. At one time, that environment was the porch of a Greek market where the Stoics met. Later, a one-room schoolhouse gave most students all the education they would receive, while higher education evolved from students gathering in their professor's office to listen and talk with them. Eventually, when the office could no longer accommodate the increased number of students, classrooms were built, giving students a place to sit, listen, and take notes. Figure 1 depicts such a traditional classroom.

Before the days of the printing press, books were generally unavailable. Those that possessed them would read them to those that did not have them (or could not read). As these "lecturers" achieved a reputation, it became necessary (and profitable) to extend their reach as far as possible. This was achieved by following the model of the Greek theatron, the stadium-like seating around the stage. Figure 2 illustrates how this model of conveying a lecture to an audience has persisted over a millennium despite books and a wide range of instructional technology being widely available and affordable.

**Citation:** Swart, W.; MacLeod, K. Evaluating Learning Space Designs for Flipped and Collaborative Learning: A Transactional Distance Approach. *Educ. Sci.* **2021**, *11*, 292. https://doi.org/10.3390/ educsci11060292

Academic Editors: Sandra Raquel Gonçalves Fernandes, Marta Abelha and Ana Teresa Ferreira-Oliveira

Received: 7 May 2021 Accepted: 9 June 2021 Published: 12 June 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Figure 1.** A traditional classroom.

**Figure 2.** Tiered classrooms then and now.

Stadium-like classrooms are great for lecturing, but lecturing is not necessarily good for learning. An article in BBC NEWS [1] asked whether lectures should not be obsolete by now, quoting research showing that students remember as little as 10% of their lecture just days afterward and referencing a Harvard study that found, on average, attendance at lectures falls from 79% at the start of the term to 43% at the end.

Prince [2] found that problem-based learning (PBL) can be superior to traditional lecture-based learning. Bishop and Verleger [3] report similar results for the flipped classroom, a particular type of PBL, which they define as an educational technique that consists of two parts: interactive group learning activities mediated by the instructor in the classroom and direct computer-based individual instruction outside the classroom.

Selingo [4] proclaimed flipped learning as the future of higher education. This proclamation appears to have been a prophesy considering the exponential growth of research about the flipped classroom, shown in Figure 3 from Talbot [5]. This explosion in knowledge about flipped learning has encouraged its adoption in the classroom. According to the Flipped Learning Global Initiative, by 2017, approximately 16% of U.S. teachers were flipping their classes, 35% wanted training on how to flip their classes, and 46% of principals wanted new teachers who knew how to flip a class [6]. As can be expected, adoption in the classroom has created a market for flipped products (software, hardware and services) which was valued at \$971 in 2018 and is forecasted to grow to \$1.9 Billion by 2024—a compound annual growth rate of 15.5% [7].

**Figure 3.** Published research on flipped learning (# of peer-reviewed articles).

Based on the theory that a new type of learning will require a new setting, in 2013, the then Dean of our College of Business initiated a remodeling program to convert existing classrooms to specifically support PBL, at a cost of approximately US \$190,000 per classroom. The rooms are showpieces, with a very large (120") screen at the front and from 5 to 8 group stations around the room, each consisting of tables (on wheels) with seating for six, a computer with internet access, and a large (90") screen, where the students can project their work in process. Simultaneously, to encourage faculty to consider PBL, the Dean solicited proposals from the faculty for implementing it in their classes.

The authors proposal to implement flipped learning in a required undergraduate course in the Bachelor of Science in Business Administration (BSBA) program in the PBL classroom was accepted. With their course scheduled in the new PBL room, when they asked the Dean what he expected to see in the class, the response was "I do not want to see lecturing. I want to see student working in teams collaborating with each other, sweating to solve a complex problem." His vision aligned directly with the flipped classroom. Figure 4 shows a flipped class in action in one of the PBL classrooms.

**Figure 4.** A flipped class in action in a PBL room.

The authors experienced success teaching their course as a flipped class in the PBL classroom. The average final grades increased by approximately 15 points and the range between the highest and lowest average final grade in the class decreased by over 45 points [8]. Consequently, they adopted flipped learning in all their classes. Due to the limited number of PBL classrooms, however, their classes could not always be scheduled in PBL rooms, so they have taught their classes in the PBL rooms when fortunate enough to have been assigned to one and in flat or stadium classrooms when less fortunate. When not in a PBL room, they improvised to adapt the classroom to help, not interfere, with the collaborative work required of their students. For the flat classroom, this was simply to have the students drag desks together in groups of four to six and to share their work on their laptops. For the stadium classroom, the desktops and chairs are fastened to the floor, so the groups sat together, either strung out along one row or in two rows, with the students in front turning around to talk to the ones behind, again sharing work on the laptops.

Regardless of the classroom type assigned, all classes were flipped in the manner described in Swart [9]. The school's Learning Management System contained the lecture material (notes and videos) the students read and watched outside of class. During class, the lecture material is applied to an assigned problem or task, upon completion of which an individual quiz assesses how well the material was mastered. The instructor, instead of lecturing, moves from group to group, answering questions and providing guidance. Swart [9] has shown that student outcomes and satisfaction are better with the flipped paradigm. We had not observed any change in grades, however, regardless of the type of classroom assigned. This led us to the overarching research question of what benefits in student learning are obtained from the monies that are being spent on creating PBL rooms?

In the next subsections, we will review pertinent literature to our research covering both learning spaces and transactional distances. The latter provides the theoretical foundations for the scale of transactional distance, which will be our measurement tool for the research.

#### *1.1. Learning Spaces*

Problem-based, or active learning, classrooms designed to facilitate collaborative work are becoming more common [10–12]. Some research [13,14] has shown that students do not like collaborative learning, while others [8,15] have found no difference or improved student performance in collaborative settings. Student preference for entertaining and interactive learning environments was noted by Leverett et al. [16]. Enhancements to learning spaces has been a topic for numerous authors [17–20]. In [13], the authors noted the need for inquiry into the relationship between active learning classrooms and student attitudes toward collaborative learning.

Discussion of learning spaces goes back before any talk of collaborative learning. By 1979, Weinstein [21] found enough research to provide a review concerning the physical environment of schools. The 2006 book *Learning Spaces* [22] provides a series of articles discussing how to "reconceptualize learning spaces to facilitate active, social, and experiential learning." Clinton and Wilson [23] note that classrooms were designed to facilitate lectures, but Peberdy [24] notes many institutions are redesigning classrooms to facilitate active learning, despite the substantial costs. While students indicate that collaborative learning classrooms help their concentration [25], Cleveland and Fisher [26] call for better understanding of student opinions of their learning spaces. Clinton and Wilson [23] provide a small study using their own survey of student perceptions of their course taught in both a traditional setting and a collaborative setting, concluding that "students perceived active-learning classrooms as better suited for collaborative learning than traditional classrooms ... ". Swart [9] found that student performance and satisfaction improved in flipped classes in the PBL classrooms compared to lecture-based classes in traditional classrooms.

#### *1.2. Transactional Distance*

The theory of transactional distance was developed by Michael G. Moore [27] and is one of the seminal theories governing distance education. It constituted a paradigm shift in that it viewed "distance" as a social and communications gap, a space of potential misunderstandings between the instructor and learners. He proposed that transactional distance is a function of two sets of variables, dialogue (interaction) and structure (course design). High structure and low dialogue yield high transactional distance and vice versa.

Zhang [28] updated Moore's theory to include online learning. She posited that transactional distance (TD) represented the barriers existing between students and their full engagement with the learning environment. She defined it as a multidimensional construct consisting of: transactional distance between student and student (TDSS), transactional distance between student and teacher (TDST), transactional distance between student and content (TDSC), and transactional distance between student and the instructional TECHnology used for teaching/learning (TDSTECH). She then postulated that these constructs resulted in three learning outcomes: student SATISFACTION with learning, PROGRESS toward achieving learning goals, and whether LEARNING has occurred in the class.

Zhang operationalized the above concepts by breaking down each construct into multiple elements, resulting in 31 questions plus the three outcomes, shown in Appendix A. Each element is associated with a five-point Likert scale (1 = Untrue, 5 = True). The resulting questionnaire, referred to as the scale of transactional distance, was subjected to structural equation modelling techniques including exploratory and confirmatory factor analysis, confirming goodness of fit and validation of the scale [28].

Figure 5 summarizes the content of the scale of transactional distance, detailed in Appendix A. Student engagement is obtained from the responses to the element questions under TDSI, TDSC, TDSS, and TDSTECH, while outcomes are measured from the responses for LEARNING, GOALS, and SATISFACTION. All the responses are recorded on the same survey.

**Figure 5.** Content of the scale of transactional distance.

#### *1.3. Research Hypotheses*

Swart [9] achieved a 15 point (out of 100) increase in final average grade when changing from a lecture to a flipped format. However, the authors did not find a difference in grades when the flipped course was taught in either a stadium, flat of PBL classroom. Grades are important to students. However, as instructors, Schwab et al. [29] note that we are more interested in student learning. While we already knew that student grades in our flipped classes were not impacted by classroom type, we did want to find out whether classroom type impacted student engagement, which is "highly correlated with many desirable learning and personal developmental outcomes of college", according to Axelson and Flick [30]. Thus, from the data obtained from administering the scale of transactional distance survey, we tested the following four research hypotheses:

#### Research Hypothesis 1

**Hypothesis H10.** *Student engagement and outcomes in a flat classroom = student engagement and outcomes in a PBL classroom.*

**Hypothesis H1a.** *Student engagement and outcomes in a flat classroom* = *student engagement and outcomes in a PBL classroom.*

*Independent-samples t-tests will be used to test these hypotheses. SPSS 27 will provide the results for both engagement and outcome, hence the reason for including both in the hypothesis.*

#### Research Hypothesis 2

**Hypothesis H20.** *Student engagement and outcomes in a PBL classroom = student engagement and outcomes in a stadium classroom.*

**Hypothesis H2a.** *Student engagement and outcomes in a PBL classroom* = *student engagement and outcomes in a stadium classroom.*

*Independent-samples* t*-tests will be used to test these hypotheses. SPSS 27 will provide the results for both engagement and outcome, hence the reason for including both in the hypothesis.*

#### Research Hypothesis 3

**Hypothesis H30.** *Student engagement and outcomes in a stadium classroom = student engagement and outcomes in a flat classroom.*

**Hypothesis H3a.** *Student engagement and outcomes in a stadium classroom* = *student engagement and outcomes in a flat classroom.*

*Independent-samples* t*-tests will be used to test these hypotheses. SPSS 27 will provide the results for both engagement and outcome, hence the reason for including both in the hypothesis.*

#### Research Hypothesis 4

**Hypothesis H40.** *Student engagement and classroom type are unique significant predictors of outcomes.*

**Hypothesis H4a.** *Student engagement and classroom type are NOT unique significant predictors of outcomes.*

*Stepwise multiple regression will be used to test Research Hypothesis 4.*

Hypotheses 1–3 refer to results obtained after the fact, when PBL rooms were already built. We envision the possibility of using the scale of transactional distance to evaluate alternate PBL room design using user focus groups. Focus groups could be presented with renderings of actual design alternatives, including virtual reality representations of the physical PBL room design alternatives. They could then fill out the scale of transactional distance survey indicating how they would respond to the questions for each design alternative. The results could then be entered into a robust regression model to predict student outcomes for each design alternative.

#### **2. Materials and Methods**

The data was gathered over a five-semester period (Fall 2017–Spring 2019) in a required undergraduate class in the Bachelor of Business Administration (BSBA) program. The instructor was the same for all classes and taught the class in a flipped format as described in [9]. The classes were scheduled in either a PBL classroom, a flat classroom, or a stadium classroom, based on availability and administration priorities.

The scale of transactional distance survey was used to collect student engagement and outcome data. Student engagement data was obtained from the transactional distance questions, while outcomes data was obtained from Zhang's three outcome questions. Table 1 indicates the total enrollments in each of the classroom types during the five semesters as well as the response rates obtained.

**Table 1.** Enrollment and response information by classroom type.


#### **3. Results**

Several researchers have shown that the three outcome measures are significantly correlated [24,31,32]. We obtained the bivariate correlations to determine whether this was the case for our data as well. The results are presented in Table 2.


**Table 2.** Bivariate correlations for Zhang's learning outcomes.

\*\*: Correlation is significant at the 0.01 level (2-tailed).

The bivariate correlations shown in Table 2 are statistically significant (*p* < 0.001) and their Pearson Correlation Coefficients are 0.695 or higher. As done in several other studies [23,24,30], we have elected SATISFACTION as the representative outcome in the rest of our analyses.

Table 3 exhibits the group statistics for the data obtained from the scale of transactional distance surveys.


**Table 3.** Group statistics for the scale of transactional distance data.

Figure 6 shows a radar graph comparing the means of the engagement factors and the outcome variable SATISFACTION for the three types of classrooms tested. The vertical axis shows the outcome variable SATISFACTION and each of the other four axes represent an engagement factor. The Likert scale in the scale of transactional distance was defined so that the greater the transactional distance, the better the engagement and outcomes. Although opposite to the traditional definition that a "big" distance is bad, we found that respondents were less confused filling out a survey in which big was associated with better. Thus, it appears as though the data indicates that the stadium classroom is not as good as either of the other two on all student engagement factors or outcome. To draw any conclusions from this data, we must test the statistical significance of the differences shown on the radar diagram.

**Figure 6.** Radar diagram of mean SATISFACTION and engagement factors by classroom type.
