SATISFACTION = 0.601 ∗ TDSC + 0.452 ∗ TDSS + 0.285 ∗ TDST

It indicates that the classroom type is not a predictor of student satisfaction. What determines satisfaction is dictated by how well the classroom facilitates students learning the material (TDSC), by how well students can engage with each other in the classroom (TDSS), and by how well students can engage with the instructor in the classroom (TDSC). The fact that classroom type is not a predictor in the equation indicates that our data shows that neither classroom design has accomplished this any better than the others Thus, for this study, no classroom type is inherently better than another to produce student satisfaction (and the related outcomes).

We propose that the robust prediction model be used to evaluate alternate designs for future PBL room. Alternate PBL classroom design plans can be presented, one at a time, to a focus group consisting of classroom users. These alternate plans can be traditional plans and architectural renderings, but preferably they would consist of virtual reality models [25,35] that would allow users to experience the classroom as though it were already built. Based upon their experience and interaction with the PBL classroom design team, the focus groups members would be asked to complete the scale of transactional distance survey for each of the PBL design alternatives from which the TDSC, TDSS, and TDST could be calculated and used as input to the robust prediction model. This would yield a predicted measure of SATISFACTION for each design.

We recognize that many considerations must go into the selection of a best PBL classroom design. We posit that the impact of such a design on student engagement and satisfaction must be a primary consideration. Heretofore, it appears as though PBL rooms have been built on the presumption that they will improve student outcomes. This research presents a methodology that will allow the presumption to be tested before scarce resources are invested.

#### **5. Conclusions**

Our university, like several others, has invested hundreds of thousands of dollars in transforming traditional flat classrooms to PBL rooms and is currently gathering inputs on new technology and furniture requirements for consideration in the planning for the next generation of PBL rooms. Our results indicating that these expenditures may not have been necessary to achieve student engagement and outcome improvement are enlightening. However, as often is the case, aesthetics does not guarantee functionality.

We attribute some of our findings to the increased portability and capability of computing devices. Today's smart phones and tablets make it extremely easy for students to pass around their devices to classmates. When the first generation of PBL rooms were constructed, great attention was given to facilitating the sharing of information within and between groups. At the time, sharing of devices was cumbersome at best, hence relying on projecting information on large screens seemed the best alternative. Our results suggest that it may no longer be necessary to invest in multiple workstations, each having a networked PC and large screen for problem-based learning.

There is no doubt that the PBL rooms are a great marketing and advancement tool. Every open house conducted by our College and University conducts tours of campus and the PBL rooms have a great WOW! factor associated them. They impress students and parents and do influence and steer students to consider our university as their choice. These rooms are also a favorite stopping point for the Dean to extoll our commitment to student learning to potential donors. To that end, every door to the PBL room serves as a window and it is common to see the Dean showing a potential donor a PBL room in action. The challenge is to find problem-based learning rooms that will serve the dual purpose of showing our commitment to student learning while simultaneously delivering on that promise.

#### **6. Further Research**

This research was motivated by the growing number of institutions, including ours, that have or are contemplating investing in special purpose classrooms dedicated to collaborative learning. We have dubbed these as problem-based learning (PBL) rooms.

The investments required are substantial—our institution has spent US \$190,000 each to convert several traditional classrooms to PBL rooms. While the costs were clear, the benefits of doing so were, to the best of our knowledge, intuitive. It was assumed that outfitting classrooms with tables and chairs on wheels would facilitate collaboration and that networked computers with large display screens would facilitate student interaction with each other as they collaborated on solving problems.

While the above reasoning appealed to almost everyone's intuition, there was no data to support the intuition. Did PBL rooms do a better job of engaging students and did they lead to better outcomes than other types of classrooms that might already be available?

We measured student engagement and outcomes in three different types of classrooms: stadium, flat and PBL. The same course was taught by the same instructor using flipped learning. Flipped learning required collaboration when the course met in a classroom. We used the scale of transactional distance to measure student engagement and outcomes in each of the classroom. Our results indicated that there was no significant difference in student engagement and outcome between the PBL rooms and the flat classrooms. Hence, from a student perspective, the investment in PBL rooms was not justifiable since students taking the course in traditional flat rooms were just as engaged and had similar outcomes.

Our results were for a specific type of pedagogy (flipped) and a specific business course, Business Analytics, a quantitative course requiring students to use computer models to solve problems. Thus, the results may not be transferrable to other types of collaborative learning or other types of disciplines. Research is required for alternative disciplines and collaboration modes to determine whether our results can be generalized.

However, our methodology is not dependent on subject matter or collaboration mode. It can be used to determine student engagement and outcomes in any subject, collaboration

mode and/or classroom type. We tested the methodology on a specific flipped course in existent classrooms. Our results did make sense in identifying the stadium room as yielding the least student satisfaction and outcomes amongst the three types of classroom tested. This result that was confirmed by the much smaller number of students that would recommend the course to their friend when taught in a stadium room than if were taught in a PBL or flat classroom.

The purpose of our research was to provide a quantitative measure of student engagement and outcomes to decision makers *before* a decision was made to invest in a specific PBL room design. Our research has developed a tool that can compare actual classrooms based on student engagement and outcomes. Research is required on whether stakeholders confronted at the planning stage with several alternate classroom designs can evaluate such designs, preferably as virtual reality models, by completing the scale of transactional distance for each in order to provide decision makers with a measure of how each design would generate student engagement and outcomes and use this as part of their design selection criteria.

**Author Contributions:** Each author has contributed equally to all aspects of this research. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Study ID: UMCIRB 18-000457 Date Approved 3/9/2018 Does not expire.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data presented in this study are available upon request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.

**Research Ethics:** Study ID: UMCIRB 18-000457. Date approved 3 September 2018. Does not expire.

#### **Appendix A**

**Table A1.** Scale of Transactional Distance.



#### **Table A1.** *Cont*.

#### **References**

