*3.3. Testing Research Hypotheses 3*

Figure 9 shows pictures of the actual stadium and flat classrooms used by our students when they completed the scale of transactional distance survey.

**Figure 9.** Pictures of flat and stadium classrooms used in this research.

The results of analyzing that data with an independent-samples *t*-test are given in Table 6. The result of Levene's Test for Equality of Variances indicated that equality of variances could not be assumed for any of the factors or the outcome data. Thus, the significance levels of the tests for these all these had to be obtained from the "Equal variances not assumed" rows of the table.

The results of the *t*-tests indicated that there was a significant difference between the transactional distance between student and student in the two rooms (*p* < 0.017) as well as between SATISFACTION between the two rooms (*p* < 0.029). There also was a marginal statistical difference in TDST between the two rooms. Thus, H20 is not supported for TDSS and SATISFACTION nor for TDST at a significance level of 0.094.


**Table 6.** Independent-samples *t*-test for flat vs. stadium classrooms.

#### *3.4. Research Hypothesis 4*

Stepwise multiple regression was used to test Research Hypothesis 4. The dependent variable was SATISFACTION, and the independent variables were TDSS, TDSC, TDST, TD-STECH, STADIUM and FLAT. The last two are indicator variables to account for classroom type. Note that PBL is the base case so that when the two indicator variables are zero, the data correspond to teaching in a PBL room.

Table 7 exhibits the results of the stepwise multiple regression. The robust regression equation is given by:

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

**Table 7.** Stepwise multiple regression results with SATISFACTION as the dependent variable.


Note: \* *p* < 0.000; \*\* *p* < 0.006.

The predictor variables are significant as indicated by the note at the bottom of the table. The regression equation accounts for 59.4% of the variance and is significant. The VIF values give no indication of multicollinearity. Classroom type is not a significant predictor of SATISFACTION and, because of their significant bivariate correlations with each other, neither are LEARNING or PROGRESS. Thus, H40 is not supported.

#### **4. Discussion**

Table 8 summarizes the significant results from testing research hypotheses 1–3 and indicates how the three classroom types that were used for flipped learning compared in terms of student engagement (measured by the four transactional distance factors) and outcomes.


**Table 8.** Summary significance levels for hypotheses tests.

Note: *p* > 0.1000 is indicated by "-".

To make sense of this data, we have copied the measurements on the TDSS, TDST, and satisfaction axes, showing the actual transactional distance scores, from the radar graph (Figure 5) and shown them in Figure 10. TDSC (student-to-content) and TDSTECH (studentto-technology) were not included in Figure 10 since they had no significant differences for any of the comparisons. For TDSC, this was not surprising since the content is delivered identically, via the LMS, to all students who must learn it outside of class, as required for flipped classes. We were surprised that the additional technology (TDSTECH) of the PBL room seems not to have mattered to the students: file-sharing is just easy on their portable computing devices, no matter what the classroom type.

**Figure 10.** Comparison of classroom layouts.

Regarding Figure 10, beginning with SATISFACTION, both the flat and the PBL rooms were statistically different from the stadium room. On the graph, the PBL and flat bars both extend to the right, which is why they have no significant differences between them, while both show significant differences from the stadium classroom. If this were a lecture-based class, this result would have been surprising, since a stadium (or tiered) classroom is designed for lecturing. As previously noted, a stadium classroom is not likely the best design for a "flipped" class, and this appears to be reflected in the SATIFACTION data. The fixed desktops and chairs were simply awkward for the students working in

groups and equally awkward for the instructor when trying to squeeze between the rows to work with the groups, explaining details of the material or helping them get back on track to solve the problem. That kind of interaction is exactly what the PBL classroom was designed to facilitate, so it is rather surprising that the flat classroom garnered just as good SATISFACTION numbers. Provided the students were able to work together effectively, they appear to be equally satisfied whether in the high-tech PBL room or simply rearranging the desks in a flat classroom. As noted earlier, the scale of transactional distance has three auto-correlated outcomes represented by SATISFACTION, so similar result would have been obtained if LEARNING or PROGRESS had been used instead.

Considering student engagement with other students, both PBL and flat classrooms had statistically better (0.002 for PBL and 0.017 for flat) results for student-to-student (TDSS) interactions than the stadium classroom. Again, this can be attributed to the classes being flipped. In flipped classes, class time is devoted to interactive group learning, requiring real time, face-to-face communication. The tiered classroom simply does not meet the needs of the students, presenting a barrier to their ability to interact with one another, as shown in the transactional distance of the PBL and flat TDSS (4.313 and 4.134, respectively) scores from the stadium TDSS score (3.688). More surprising was the lack of significant difference between the PBL and flat classrooms. It would seem that the technology and pod arrangement were not as important as simply the ability to see one another (when the desks were rearranged into groups) and the ability to share files on their laptops. With the focus of the classroom time on solving a problem, the special advantages of the PBL room may have been lost in the student's concentration on the work to be done.

The final statistically different result was for the engagement of students with the instructor (TDST), where the flat classroom is significantly greater (*p* < 0.094) than the stadium classroom. Flipped classes require that the instructor be a learning coach and consultant to teams and individuals. This requires the instructor to move from one group to another. Such movement is easier in the flat room because the instructor can walk from one team to another without physical barriers. In a stadium room student teams are at various levels and it is awkward for the instructor to move from one level to the next because it requires exiting one row, moving to a different tier, and then moving across the row where the team requiring attention is located. Further, the instructor is either standing before a group of six students spread out in a row or standing in the middle of the group split between two rows. In either setting, approximately half of the group would have a difficult time seeing what the instructor was demonstrating.

Given that flat classrooms were statistically superior to stadium classrooms on the TDST score, it was almost unbelievable that the PBL classrooms were not. In both cases, the instructor stands at one edge of the group, so it would seem, at first glance, that the two were identical, but the students perceived a difference. Somehow, the physical barriers of the stadium layout equate to other barriers in the PBL layout, perhaps that the students face a wall (screen) in the PBL room rather than the instructor. In the PBL rooms, the groups are located along the walls, with an open area in the center of the room. In a flat classroom, the students invariably grouped the desks toward the center of the room rather than along the walls, so the instructor could literally turn around and be talking to another group. For that matter, it was not unusual for one group to "listen in" while the instructor was talking to a near-by group, thus gaining information before the instructor addressed that group. Perhaps it was simply the informality of the hastily rearranged flat classroom that made the students more comfortable, but clearly the PBL rooms gained no advantage over the flat classrooms in terms of students interacting to solve a problem.

The most unexpected result of our research is that there was no significant difference in student engagement or outcomes between the PBL and flat rooms. An entire book was devoted to reconceptualizing learning spaces to facilitate active, social, and experiential learning [16] and many institutions are redesigning classrooms to facilitate active learning despite substantial costs [14]. Yet, we found no evidence beyond this research that anyone has made such a decision based on data that proves that the investment in such classrooms can be justified in terms of improving student engagement or outcomes. Our results indicate that providing students with the ability to rearrange a flat classroom to face each other provided similar engagement and satisfaction as an expensive classroom reconfiguration. In short, while the technology (and luxury) of PBL classrooms is impressive to donors, visitors, and prospective students and their parents, students in this study find that they can do just as well without it.

Another indirect measure of student satisfaction is their willingness to recommend the course to other students. That question was included in the questionnaire and Table 9 shows both the number of students and percentage for the three classrooms. These results reflected our statistical results. Similar percentage of students would recommend the class taught in the PBL and flat classrooms to their friends while a much lower numerical percentage would recommend the same course taught in the stadium room to their friends.


**Table 9.** Responses to "Would you recommend this class to another student?"

With the decline in on-campus enrollments [33], campuses are under pressure to use every possible marketing strategy to attract students [34]. Undoubtedly, therefore, impressive physical facilities, including classrooms, will continue to be built. Ideally, such classrooms will not only involve form, but also function. Thus, the question becomes one of how to predict student satisfaction for a classroom *before* it is built, so that the investment decision can include costs as well as benefits/drawbacks to students. Research Hypothesis 4 was developed to answer this question and provided the robust prediction equation developed earlier:
