Mixed, Augmented and Virtual, Reality Applied to the Teaching of Mathematics for Architects

applied sciences Article Mixed, Augmented and Virtual, Reality Applied to the Teaching of Mathematics for Architects Julio Cabero-Almenara 1,* , Julio Barroso-Osuna 1and Rosabel Martinez-Roig 2   Citation: Cabero-Almenara, J.; Barroso-Osuna, J.; Martinez-Roig, R. Mixed, Augmented and Virtual, Reality Applied to the Teaching of Mathematics for Architects. Appl. Sci. 2021,11, 7125. https://doi.org/ 10.3390/app11157125 Academic Editors: Maria Torres Vega and Michele Russo Received: 8 July 2021 Accepted: 30 July 2021 Published: 1 August 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/). 1Department of Didactics and Educational Organization, University of Seville, 41013 Seville, Spain; [email protected] 2Department of General Didactics and Specific Didactics, University of Alicante, 03690 Alicante, Spain; [email protected] *Correspondence: caber[email protected] Abstract: This paper examines the possibilities of Mixed Reality, the combination of two emerging technologies—Augmented Reality and Virtual Reality—in university education. For this purpose, an object was elaborated in Mixed Reality that underwent the evaluation of 44 first-year students from the degree in architecture who were enrolled in the subject “Mathematical Foundations for Architecture.” The instrument utilized was based on the TAM model, which analyzes the degree of acceptance of the technology used. The analysis of the responses provided by students supported the 23 hypotheses formulated in this study. It was found that MR significantly influences the perceived usefulness and ease of use. The results imply that MR utilization has positive effects on the mathematical teaching-learning processes in architecture from the students’ perception of their mastery of technology. It becomes necessary to offer support to those university teachers who promote the use of active MR-based methodologies in classrooms. Keywords: augmented reality; Virtual Reality; teaching 1. Mixed Reality Applied to Training Amongst the so-called emerging technologies that have recently been coming closer to the educational field, with true potential for training, “Augmented Reality” (AR) and “Virtual Reality” (VR) [ 1 , 2 ] stand out. They offer different possibilities for their implementation in training: fostering mobile, ubiquitous learning; removing unnecessary information that may prevent the observation of the significant one; enriching the information about reality to make its understanding easier; favoring the perception of the most relevant elements, offering faithfulness in the representation of objects; creating multimedia training scenarios, establishing active and interactive environments for learning; increasing students’ motivation; looking at objects from various points of view; adding value to the information supplied to students; and allowing the latter to become immersed in a totally controlled special training context. Despite this long list of possibilities associated with AR and VR, no unanimous consensus exists on their definition, which has to do with the rapid developments that have taken place within the context of these technologies. Different paths can be followed to distinguish AR from VR; one of them possibly being to place both of them along the realityvirtuality continuum, where AR would stand closer to the real context, while VR would be at one of the ends, with “Augmented Virtual Reality” or “Mixed Reality”—which brings together elements from AR and VR—positioned halfway between them. It is likewise possible to contrast AR and VR, and therefore we can say that, in AR, reality combines with informative elements located in technological devices so that a new reality can be attained, whereas VR places the subject within an immersive technological context that detaches the former from reality [ 3 ]. What AR pursues is to mix reality with the virtual sphere, or expressed differently, it enables the user to interact with the physical and digital worlds; Appl. Sci. 2021,11, 7125. https://doi.org/10.3390/app11157125 https://www.mdpi.com/journal/applsci Appl. Sci. 2021,11, 7125 2 of 16 instead, VR paves the way for users to access an alternative immersion world simulated by the computer in which different types of sensorial experiences take place and where subjects have the chance to interact with the environment as if they were inside it. In turn, the Tecnológico de Monterrey [ 4 ] recently performed a study that included a comparison between Augmented Reality (AR) (addition of virtual information to physical elements), Virtual Reality (VR) (immersion in a digital world), Mixed Reality (MR) (combination of AR and VR) and the Internet of Things (IoT) (objects with sensors or chips that interact in the real world) (Table 1). Table 1. Comparison between Augmented Reality (AR), Virtual Reality (VR), Mixed Reality (MR) and the Internet of Things (IoT). Criterion AR VR MR IoT User’s interaction with natural reality High The real world is an environment in which interaction occurs from the digital information that is added therein. Low Users isolate themselves from reality using a device to become immersed in a sensorial universe. Medium The real world serves as a stage which projects the Virtual Reality in which the user is immersed by means of a device. Low The user is a consumer of the information or performance of by things. Level of immersion in a digital experience Medium It depends on the digital density which is added to reality. High It implies a full immersion in a completely digitized parallel reality High The real world is replaced by a sensorial experience immersed in a virtual world. Low The user performs in a real environment, albeit having the chance to connect with the objects in the cloud. Emblematic device Apps in AR-equipped Smartphones Sensorial headphones Lenses which project digital information on a real environment Refrigerator able to provide information about the expiry date of food or to suggest recipes Representative enterprise in technology development Google Facebook Microsoft Cisco Development stage Right in the middle of an expansive exploration period In a readjustment period, after the initial bubble Right in the middle of an experimental revolution Immediate commercial boom What we are trying to highlight is that AR and VR propose different ways to interact with reality; whereas VR takes the subject to an unreal world and has as its aim for the subject to become immersed in it, AR adds information to the real world. When we talk about MR, both interaction options are found inside an object, which is the case at hand. Although educational experiences have been developed with AR to a greater extent than VR, amongst other reasons because the former does not require special devices to interact with objects, a diversity of experiences are actually beginning to appear, which combine them both so that they can be applied to different scientific fields: engineering and architecture [ 5 ]; language learning [ 6 ]; education sciences [ 7 ]; chemistry [ 8 ]; natural sciences [ 9 ]; biology [ 10 ]; geography [ 11 ]; medicine [ 12 – 14 ]; emergency protocol learning [ 15 ]; or physical activities [16]. Despite the scarcity of research studies devoted to the implementation of AR and VR in mathematics and in mathematical thinking, those carried out have turned out to be useful in a variety of ways: to prove their effectiveness for competence acquisition, as well as to improve performance and the attitudes towards mathematics learning [ 17 ] and to favor the acquisition of mathematical knowledge for students with limitations in that area [ 18 ]. From this perspective, Poot, Martin-Gonzalez and Menéndez-Dominguez [ 19 ] Appl. Sci. 2021,11, 7125 3 of 16 stressed their effectiveness when it comes to helping upper secondary education students to assimilate the contents related to Euclidean vectors and vector calculation [ 20 ], creating environments in AR where students are led to specific interfaces that make it easier for them to perform calculations and represent them graphically. Studies have likewise been carried out at various levels in geometry that serve to attest their effectiveness [ 21 ]. At the same time, evidence also exists for their usefulness for the development of visual-spatial ability [22] and for the acquisition of mathematical functions [23]. Such significant aspects have acquired relevance thanks to the possibilities in terms of freedom that these technologies offer from different spatial perspectives and interaction levels, since students can control the pace of their own learning and because of the chances that they provide for the three-dimensional graphic representation of geometric objects [ 24 ]. Furthermore, studies have shown that learners display a high level of acceptance regarding these technologies in addition to being greatly motivated when working with them [ 25 , 26 ], which results in students being more engaged with the contents that they must learn [27]. In short, these are technologies that provide the field of mathematics and its diverse areas with highly faithful representations alongside the possibility for the subject to interact with the object, even more so when AR and VR combine, which offers the student multiple perspectives. In this regard, our study has aimed to identify the factors that have an impact on the use of MR by university students through the utilization of the Technology Acceptance Model (TAM). To that end, we will firstly define the specific objectives sought with this study, subsequently offering a detailed description of the method used that will include the hypotheses posed. The results obtained will then be analyzed and presented so that we can finally discuss and draw conclusions about the most important findings based on those results. 2. Research Carried Out 2.1. Research Objectives The objectives set in this research are: (a) Ascertaining the degree of technological acceptance that the use of Mixed Reality (MR), Augmented Reality (AR) and Virtual Reality (VR) arouses amongst university architecture students in mathematics teaching. (b) Checking whether significant differences exist according to students’ gender in their perception of technical mastery regarding audiovisual resources, computer resources and the Internet. (c) Analyzing the extent to which students’ gender influenced their perceptions about MR as a training tool that could be used to teach architecture mathematics. (d) Verifying whether the degree of technological acceptance depends on the technical mastery expressed regarding audiovisual resources, computer resources and the Internet. 2.2. Information Collection Tools The instrument used to gather information consisted of two parts: one meant to analyze the degree of acceptance that technology aroused amongst students; and another one that enabled students to evaluate the objects in MR with which they interacted. In order to examine the degree of acceptance of MR, a decision was made to utilize the tool devised by Davis [ 28 ]—“Technology Acceptance Model”—TAM—which collects information from five dimensions: perceived usefulness (PU); perceived ease of use (PEU); perceived enjoyment (PE); attitude towards its use (AU); and intention to use it (IU). The theory about the degree of acceptance of a technology suggests that the potential predisposition for the use of any technology largely depends on the attitude towards it, which is in turn determined by the “perceived ease of use,” the “perceived usefulness” and the “perceived enjoyment” (Figure 1). The instrument included 14 Likert-type items (4 for PU, 3 for PEU, 3 for PE, 2 for AU, and 2 for IU), with seven response options ranging from “Extremely unlikely/I disagree” (1) to “Extremely likely/I agree” (7). The TAM model Appl. Sci. 2021,11, 7125 4 of 16 appeared to be quite consolidated in its application to AR when it was analyzed using the Structural Equation Model [29]. Appl. Sci. 2021, 11, x FOR PEER REVIEW 4 of 17 information from five dimensions: perceived usefulness (PU); perceived ease of use (PEU); perceived enjoyment (PE); attitude towards its use (AU); and intention to use it (IU). The theory about the degree of acceptance of a technology suggests that the potential predisposition for the use of any technology largely depends on the attitude towards it, which is in turn determined by the “perceived ease of use,” the “perceived usefulness” and the “perceived enjoyment” (Figure 1). The instrument included 14 Likert-type items (4 for PU, 3 for PEU, 3 for PE, 2 for AU, and 2 for IU), with seven response options ranging from “Extremely unlikely/I disagree” (1) to “Extremely likely/I agree” (7). The TAM model appeared to be quite consolidated in its application to AR when it was analyzed using the Structural Equation Model [29]. Figure 1. TAM model developed by Davis [28]. These variables may be simultaneously influenced by a series of external predictor variables, amongst which usually appear: type of user, gender, age, experience in the utilization of technology, level of education, professional qualification, or personal proneness towards innovation [30–32]. The Technology Acceptance Model has proved effective to ascertain people’s attitudes towards specific technologies, such as the future intention to utilize it, and has been applied to a variety of technologies: Augmented Reality [33,34], mobile devices used for online training [35], b-learning [36], engineering [37] or virtual training platforms [38]. The following predictor variables were identified for our research: gender; students’ perception about the quality of the MR object; and students’ perception about the technical mastery of audiovisual, computer and internet resources. This allowed us to build the model shown in Figure 2 below. Figure 1. TAM model developed by Davis [28]. These variables may be simultaneously influenced by a series of external predictor variables, amongst which usually appear: type of user, gender, age, experience in the utilization of technology, level of education, professional qualification, or personal proneness towards innovation [30–32]. The Technology Acceptance Model has proved effective to ascertain people’s attitudes towards specific technologies, such as the future intention to utilize it, and has been applied to a variety of technologies: Augmented Reality [ 33 , 34 ], mobile devices used for online training [35], b-learning [36], engineering [37] or virtual training platforms [38]. The following predictor variables were identified for our research: gender; students’ perception about the quality of the MR object; and students’ perception about the technical mastery of audiovisual, computer and internet resources. This allowed us to build the model shown in Figure 2below. Appl. Sci. 2021, 11, x FOR PEER REVIEW 5 of 17 Figure 2. Model based on the TAM developed by Davis [28] formulated for our research. (Translation: Gender//Quality//Internet technical mastery//Audiovisual technical mastery//Computer technical mastery; Perception about ease of use//Perceived self-efficacy//Perception about success; Attitude by use//Intention to use). This model enabled us to pose the following hypotheses for their statistical contrast: H1-H2-H3: The technical mastery of computers that the student claims to have impacts positively on the perception of success in relation to the use of MR, on the perceived self-efficacy regarding MR utilization, and on the perception of MR’s ease of use. H4-H5-H6: The technical mastery of audiovisual resources that the student claims to have impacts positively on the perception of success in relation to the use of MR, on the perceived self-efficacy regarding MR utilization, and on the perception of MR’s ease of use. H7-H8-H9: The technical mastery of the Internet that the student claims to have impacts positively on the perception of success in relation to the use of MR, on the perceived self-efficacy regarding MR utilization, and on the perception of MR’s ease of use. H10-H11-H12: The quality of the system produced in MR has a positive effect on the perception of success in relation to the use of MR, on the perceived self-efficacy regarding MR utilization, and on the perception of MR’s ease of use. H13-H14-H-15: The student’s gender has a positive effect on the perception of success in relation to the use of MR, on the perceived self-efficacy regarding MR utilization, and on the perception of MR’s ease of use. H16: The student’s perceived self-efficacy with regard to MR has a positive effect on the perception of success in relation to the use of MR. H17: The student’s perceived self-efficacy with regard to MR has a positive effect on the perception of MR’s ease of use. H18: The student’s perception about MR’s ease of use has a positive effect on the perception of success in relation to the use of MR. H19: The student’s perceived self-efficacy with regard to MR has a positive effect on the attitude towards MR utilization. H20: The student’s perception about MR’s ease of use has a positive effect on the attitude towards MR utilization. H21: The attitude towards MR utilization has a positive effect on the intention to use MR. H22: The student’s perception of success with MR has a positive effect on the intention to use MR and on the attitude towards MR utilization. H23: The student’s perception about MR’s ease of use has a positive effect on the intention to use MR. Figure 2. Model based on the TAM developed by Davis [ 28 ] formulated for our research. (Translation: Gender//Quality//Internet technical mastery//Audiovisual technical mastery//Computer technical mastery; Perception about ease of use//Perceived self-efficacy//Perception about success; Attitude by use//Intention to use). This model enabled us to pose the following hypotheses for their statistical contrast: Appl. Sci. 2021,11, 7125 5 of 16 H1-H2-H3: The technical mastery of computers that the student claims to have impacts positively on the perception of success in relation to the use of MR, on the perceived selfefficacy regarding MR utilization, and on the perception of MR’s ease of use. H4-H5-H6: The technical mastery of audiovisual resources that the student claims to have impacts positively on the perception of success in relation to the use of MR, on the perceived self-efficacy regarding MR utilization, and on the perception of MR’s ease of use. H7-H8-H9: The technical mastery of the Internet that the student claims to have impacts positively on the perception of success in relation to the use of MR, on the perceived self-efficacy regarding MR utilization, and on the perception of MR’s ease of use. H10-H11-H12: The quality of the system produced in MR has a positive effect on the perception of success in relation to the use of MR, on the perceived self-efficacy regarding MR utilization, and on the perception of MR’s ease of use. H13-H14-H15: The student’s gender has a positive effect on the perception of success in relation to the use of MR, on the perceived self-efficacy regarding MR utilization, and on the perception of MR’s ease of use. H16: The student’s perceived self-efficacy with regard to MR has a positive effect on the perception of success in relation to the use of MR. H17: The student’s perceived self-efficacy with regard to MR has a positive effect on the perception of MR’s ease of use. H18: The student’s perception about MR’s ease of use has a positive effect on the perception of success in relation to the use of MR. H19: The student’s perceived self-efficacy with regard to MR has a positive effect on the attitude towards MR utilization. H20: The student’s perception about MR’s ease of use has a positive effect on the attitude towards MR utilization. H21: The attitude towards MR utilization has a positive effect on the intention to use MR. H22: The student’s perception of success with MR has a positive effect on the intention to use MR and on the attitude towards MR utilization. H23: The student’s perception about MR’s ease of use has a positive effect on the intention to use MR. As for the way to evaluate the objects produced in MR, a decision was made to resort to a method already used to assess learning objects in an AR format [ 13 , 39 , 40 ]. With a Likert-type structure, it was made up of 11 items with six response options going from “Very positive/I strongly agree” [ 6 ] to “Very negative/I strongly disagree” (MN-1), which sought to collect information about two dimensions: technical and aesthetic aspects of the object produced in AR and VR (4 items); and user-friendliness (7 items). The reliability index was obtained for both tools using Cronbach’s Alpha, a procedure recommended for such instruments by O’Dwyer & Bernauer [ 41 ], reaching the values of 0.912 for that of TAM, and 0.943 for the one utilized to evaluate the objects. These values suggest high reliability levels in both tools. 2.3. The Sample The work was developed with 44 students (23 males—52.27% and 21 females—47.73%) enrolled in the subject “Mathematical Foundations for Architecture,” belonging to the first year of the Degree in Architecture taught at the “Escuela Técnica Superior de Arquitectura (Higher Technical School of Architecture)” at the University of Seville. Table 2shows the mean values and the standard deviations reached by learners, according to their gender, in the different technical mastery areas with respect to which they were asked to assign themselves a score. Appl. Sci. 2021,11, 7125 6 of 16 Table 2. Means and standard deviations. Technical Mastery Area Gender Mean S.D. Audiovisual resources Male 7.26 1.764 Female 6.90 2.095 Computer resources Male 7.48 1.855 Female 7.00 1.449 Internet Male 8.35 1.434 Female 7.62 1.717 Note that the sample used in our research was non-probabilistic and of a convenience or causal nature [ 42 ], and relies on easy access by researchers to the subjects who took part in the study. 2.4. The Material Produced The material produced in MR is called “Visualmat. Percepción del Espacio arquitectónico” (Visualmat. Perception of Architectural Space) and addresses how architectural space is perceived through a methodology based on analyzing the visibility graph and on interpreting some relative properties associated with the geometry of isovists. By means of MR, we intend students to be able to access the spaces illustrating the examples to which several figures refer. The building selected is the Chapel of the University of Seville, since the simplicity of its ground plan makes it possible to easily describe some of the indicators explained. The analysis of ground plan visibility begins from the point of view of a visitor entering the temple. The visibility graph is carried out using 3750 uniformly distributed locations (Figure 3). Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 17 Figure 3. Isovists in 2D and 3D and real image of the chapel from that area. The material produced incorporates AR and VR objects (Figure 4). Figure 3. Isovists in 2D and 3D and real image of the chapel from that area. The material produced incorporates AR and VR objects (Figure 4). Appl. Sci. 2021,11, 7125 7 of 16 Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 17 Figure 3. Isovists in 2D and 3D and real image of the chapel from that area. The material produced incorporates AR and VR objects (Figure 4). Figure 4. Augmented and Virtual Reality versions of the object: “Visualmat. Percepción del Espacio arquitectónico”. Attached to the material, we prepared a guide for students in which they were provided with explanations of the goals sought with the object produced in MR, the instructions to visualize figures with AR and VR, and descriptive information about the project (Figure 5). Both the guide and the object’s characteristics can be found on—and downloaded from—the following web address http://ra.sav.us.es/index.php?option= com_content&view=article&id=156:visualmat&catid=27&Itemid=123. The software programs listed in Table 3were utilized for its production. Table 3. Software programs used to produce the MR object. AUGMENTED REALITY SOFTWARE WHAT IT IS USED FOR Zappar Application launcher Sketahfab 3D launcher Android studio Java development environment. Apk export for Android. Autocard Image design–3D retouching Google sketah Up 3D retouching Adobe Photoshop Creation of equirectangular images. Graphics VIRTUAL REALITY Sketahfa 3D launcher Google Sketachfa 3D launcher Krpano Making reality via a video image website Google VR Making reality via a video image website Appl. Sci. 2021,11, 7125 8 of 16 Appl. Sci. 2021, 11, x FOR PEER REVIEW 8 of 17 Figure 4. Augmented and Virtual Reality versions of the object: “Visualmat. Percepción del Espacio arquitectónico”. Attached to the material, we prepared a guide for students in which they were provided with explanations of the goals sought with the object produced in MR, the instructions to visualize figures with AR and VR, and descriptive information about the project (Figure 5). Both the guide and the object’s characteristics can be found on—and downloaded from—the following web address http://ra.sav.us.es/index.php?option=com_con- tent&view=article&id=156:visualmat&catid=27&Itemid=123. Figure 5. Images of the accompanying guide. An experimental session was carried out with that material that consisted of different parts: description and presentation of the material for students, specification of the sites from where they had to download the corresponding app together with the instructions for use, description of the educational purposes sought with the object devised, interactions of students with the object, and completion of the evaluation instruments utilized. Appl. Sci. 2021,11, 7125 9 of 16 3. Results Achieved Here we show the mean scores and standard deviations obtained with both tools, starting with those reached with the TAM instrument. So that a correct interpretation is made, readers must bear in mind that the answer scale ranged between 1 (extremely unlikely/I disagree) and 7 (extremely likely/I agree). (Table 4). Table 4. Means and standard deviations obtained with TAM. MR m s.d. (1) Perceived usefulness (PU) 1.1. The use of this system could enhance my learning in the classroom. (PU1) 6.30 1.17 1.2. The use of this system during classes would make it easier for me to understand certain concepts. (PU2). 6.65 0.65 1.3. I think the system is useful when one is learning. (PU3) 6.38 1.16 1.4. The use of this system would improve my learning. 6.40 1.14 (2) Perceive ease of use (PEU) 2.1. In my opinion, the system is user-friendly. (PEU1) 5.23 1.16 2.2. Learning to use and operate the system was not a problem for me. (PEU2) 5.18 1.61 2.3. I found the explanations about how to use and operate the system clear and understandable. (PEU3) 5.72 1.41 (3) Perceived enjoyment (PE) 3.1. Utilizing the system was fun for me (PE1) 6.82 0.39 3.2. I enjoyed myself using the system (PE2) 6.58 0.81 3.3. In my view, the system allows you to learn while playing. (PE3) 6.63 0.70 (4) Attitude towards its use (AU) 4.1. Using the system makes learning become more interesting. (AU1) 6.62 0.55 4.2. In my opinion, using the system in the classroom is a good idea. (AU2) 6.31 0.89 (5) Intention to use it (IU) 5.1. I would like to use these systems in the future if I had the chance. (IU1) 6.65 0.71 5.2. I would like to use the system to learn both about the topics that were presented to me and about others (IU3). 6.63 0.62 Perceived usefulness (PU) 6.43 1.03 Perceived ease of use (PEU) 5.28 1.39 Perceived enjoyment (PE) 6.68 0.63 Attitude towards use (AU) 6.47 0.72 Intention to use (IU) 6.64 0.72 TAM GLOBAL VALUES 6.30 0.89 The analysis of the preceding table allows us to focus on two aspects: the degree of acceptance of MR technology can be regarded as very high and additionally quite uniform amongst all students, as shown by the low standard deviation values obtained. The high average value reached in the dimension “intention to use it” (6.64) also deserves to be stressed. Appl. Sci. 2021,11, 7125 16 of 16 47. Allcoat, D.; Hatchard, T.; Azmat, F.; Stansfield, K.; Watson, D.; von Mühlenen, A. 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