*Article* **Online Education and the COVID-19 Outbreak: A Case Study of Online Teaching during Lockdown**

**Nastaran Peimani 1,\* and Hesam Kamalipour <sup>2</sup>**


**Abstract:** The COVID-19 pandemic has become a critical challenge for the higher education sector. Exploring the capacity of this sector to adapt in the state of uncertainty has become more significant than ever. In this paper, we critically reflect on our experience of teaching urban design research methods online during the early COVID-19 lockdown in the UK. This is an exploratory case study with a qualitative approach with an aim to inform resilient practices of teaching in the face of public health emergencies. Drawing on the experience of teaching the Research Methods and Techniques subject during lockdown, we discuss the rapid transition from face-to-face to online teaching and point to the challenges and opportunities in relation to the learning and teaching activities, assessment and feedback, and digital platforms. This paper concludes by outlining some key considerations to inform the development of more adaptive and resilient approaches to online teaching in the context of unprecedented global health crises such as the COVID-19 pandemic. We argue that it is critical to move beyond fixed pedagogical frameworks to harness the productive capacities of adaptive teaching.

**Keywords:** online teaching; urban design; higher education; pandemic; COVID-19; public health; technology; EdTech; research methods

#### **1. Introduction**

The COVID-19 pandemic has become a critical challenge across many sectors, including higher education. Exploring the capacity of the higher education sector to adapt in the state of uncertainty and manage the emerging situations associated with the pressing challenge of the coronavirus outbreak and subsequent lockdowns has become more critical than ever. There is an emerging body of knowledge exploring the impacts of the COVID-19 pandemic on higher education [1–8]. Many universities across different countries have experienced an unprecedented transition from face-to-face to various forms of online education and remote learning amid the COVID-19 outbreak and subsequent lockdowns as discussed in case studies in China [9], India [10], Bulgaria [11], Pakistan [12], and Germany [13], among others. Reflecting on the early experiences of managing the conditions of uncertainty and emergency can pave the way for developing more nuanced approaches to learning, teaching, and assessment (LTA), and for enhancing the resilience of the higher education sector in the face of public health crises.

In this paper, we focus on a case study of teaching urban design research methods right in the middle of the early COVID-19 outbreak in the UK (March 2020) by drawing on the experience of teaching the Research Methods and Techniques (RMT) subject during lockdown. RMT is an intensive subject in the MA Urban Design (MA UD) programme at Cardiff University. The MA UD students take this subject before dissertation. While the RMT subject used to be delivered mostly face-to-face, it has been inevitably and rapidly adapted for online mode of delivery during the early lockdown period. This rapid transition from face-to-face to online teaching delivery is further discussed in this paper with the aim to outline some key considerations for online education in the face of unprecedented

**Citation:** Peimani, N.; Kamalipour, H. Online Education and the COVID-19 Outbreak: A Case Study of Online Teaching during Lockdown. *Educ. Sci.* **2021**, *11*, 72. https:// doi.org/10.3390/educsci11020072

Academic Editor: Kelum Gamage

Received: 7 December 2020 Accepted: 6 February 2021 Published: 13 February 2021

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**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/).

public health emergencies. We argue that it is critical to move towards diversifying online teaching practices and developing adaptive approaches to sustain effective forms of online education and remote learning, particularly in response to unprecedented global challenges such as the COVID-19 pandemic.

This is an exploratory case study with a qualitative approach. The research questions that we seek to address are: How did the rapid transition from face-to-face to online teaching play out in the RMT subject delivery during the early COVID-19 lockdown in the UK? What were the key adaptations in this process? What were the challenges and opportunities associated with online mode of teaching delivery? How can learning from these rapid changes and adaptations during the early COVID-19 lockdown inform post-COVID-19 educational practices as well as measures to be taken in higher education against potential public health crises in the future? Following a concise review of relevant literature on online education and teaching during the COVID-19 pandemic, we discuss methods and case study analysis with a particular focus on the ways in which teaching urban design research methods played out during the early COVID-19 outbreak and the subsequent lockdown in the UK. The paper concludes by outlining some key considerations including primary challenges and opportunities to inform the development of more resilient and adaptive teaching frameworks in response to public health emergencies.

#### **2. Online Education and Teaching during the COVID-19 Pandemic**

#### *2.1. Higher Education and Online Mode of Delivery*

There is an evolving body of knowledge exploring the capacities and challenges of online education [14–18]. The constant and rapid evolution of information and communication technology has undoubtedly had profound impacts on the academic discourse and everyday practices of research, scholarship, and teaching. The use of up-to-date online technologies and the process of continuously evaluating them have also become integral to students' changing demands, particularly within their online educational contexts [19]. A substantial change has been "the speed and power of communications technology and the expanded capacity to send, receive, and use information" [20] (p. 57) along with the increased capacity to bridge time and space for educational purposes and goals [21]. As Prensky [22] (p. 1) puts it, "our students have changed radically. Today's students are no longer the people our educational system was designed to teach". Prensky views today's students as "digital natives" and their less digitally competent educators as "digital immigrants". It is important to note that digital natives have not only acquired a set of skills in using up-to-date technologies but also have developed new learning skills and styles using them. The induced learning styles may include "fluency in multiple media"; "learning based on collectively seeking, sieving, and synthesizing experiences"; "active learning based on experience"; "expression through non-linear, associational webs of representations rather than linear stories"; and "co-design of learning experiences personalized to individual needs and preferences" [23] (p. 10).

With the proliferation of online teaching in higher education, there is an increased need to discuss the challenges associated with this mode of delivery for both instructors and students alongside the related capacities. It has been argued that students taking online courses are less likely to participate in collaborative learning activities, discussions with others, and student–faculty interactions, compared to their counterparts in face-toface settings [14]. For Norton et al. [24], developing core professional qualities, including communication, interpersonal and practical skills among students, and sustaining student retention rates, along with training and support to effectively use online technologies and address technical issues and cyber security risks, are seen as major challenges for online education. Shuey [25] discusses challenges faced by instructors in higher education when adapting certain activities (e.g., continuous assessment and performance assessment) to the online setting without losing content knowledge or interactions between peers and/or instructors.

Despite the recent surge of interest in the introduction of research-based principles and instructional models for effective online teaching and learning [18,26], the remaining challenge to address "is not whether online courses will replace classrooms, but whether technology will drive the redesign of teaching and learning" [24] (p. 1). Public discourse on online education often makes a clear distinction between online and on-campus study, both of which are subject to change as a result of online technology. What matters is how emerging technology can be utilised to support teaching and learning activities regardless of the medium of delivery. Johnson et al. [27] (p. 9) highlight that "simply capitalising on new technology is not enough; the new models must use these tools and services to engage students on a deeper level." This accords with Hattie's [28] argument that effective teaching and learning strategies in higher education involve giving primacy to pedagogy over technology. To explore the potential benefits of learning with technology, it is also helpful to understand what technology this form of learning encompasses. As discussed by Norton et al. [24] (p. 21), such technologies vary between recorded lectures uploaded online and interactive digital subjects with adaptive learning platforms, in-built assessment, virtual simulations, and the like.

Online learning can act as a complementary approach to face-to-face training. This focuses attention on today's blended learning approaches, which typically include online lectures, discussions, forums, and interactive software with the capacity to connect students for synchronous learning activities. In other words, blended learning approaches and designs are among the most favoured course delivery models in higher education [29], typified by the "integration of thoroughly selected and complementary face-to-face and online approaches and technologies" most effective for meeting the learning outcomes of a course [30] (p. 148). A multifaceted approach is then required to enable effective blended teaching and learning [31]. The question here is to explore whether students favour blended learning design or other fully face-to-face or online options as their preference for course delivery models.

Technology inevitably will have impacts on students' choices between higher education providers. It is likely that competition will be most apparent between online universities and on-campus universities where the desire to blend technology and in-class teaching will be peaked [24]. This continues to have significant impacts on reimagining the future of universities and the academic community despite the widely held critique of higher education's digital transformation in the wake of rapid technological innovation and labour market transformation [32–34]. According to the findings from the ECAR Study of Undergraduate Students and Information Technology 2019, about 70% of students favour mostly or completely face-to-face learning environments [35]. This suggests that students continue to have a stronger preference for some forms of blended learning environments; they see in-class lectures as an opportunity to engage with teaching staff, peers, and course content, and they see technology as useful means to enable such engagement. The increased flexibility, integration of sophisticated multimedia, and ease of access have been among the most acknowledged advantages [29] (p. 12). While online tools and their effective application have been reported as increasingly useful to students' learning experiences, accessibility to stable internet connection is almost limited due to the low rate of Wi-Fi reliability in dormitories/campus housing and outdoor areas. The preferences (e.g., learning environments, technology experiences, and use in the classroom) might be considerably influenced by the changing landscape of the student demographics [35]. The 2019 EDUCAUSE Horizon Report cites the significant challenges that are more likely to impede technology adoption as "improving digital fluency", "increasing demand for digital learning experience and instructional design expertise", "the evolving roles of faculty with ed tech strategies", "advancing digital equity", and "rethinking the practice of teaching"—out of which, the first two are the most solvable [29] (pp. 13–19). Therefore, one can argue that rather than considering this report as the end of the discussion about the use of technology in students' learning experiences, it is important to pose the question

of how the meaning and use of these findings might change in the face of COVID-19 and emergency remote LTA.

#### *2.2. COVID-19 and Online Teaching*

The emergence and unprecedented spread of the COVID-19 as a global pandemic has been posing substantial challenges to the practices of everyday life. There has been a surge of interest to explore the dynamics of online education across different contexts amid the COVID-19 pandemic [36–40]. Many higher education institutions, particularly in the context of the global North, have inevitably made some urgent adjustments to LTA designs while coping with profound social suffering and significant economic hardship. To remain competitive within the emerging market conditions and to be adaptive to uncertainties and changing situations, academics as frontline providers of higher education did not cease all their programme deliveries although some LTA activities such as national and international field site visits and certain forms of assessment were suspended or adapted. The immediate impact of the outbreak left many higher educators with limited choices to address the condition of urgency by a headlong transition to digital interfaces [41]. It has also been reported that for many academics, the forced immersion into technology-enabled forms of LTA has become a disorienting and unusual experience shaped under the weight of panic and duress [42].

The rapid transition of higher education to online provision and the enforced digitalisation of pedagogical approaches in relation to LTA have engendered significant challenges for both the academic community and students. Gamage et al. [43] indicate the increased importance of the ways in which technological advancements enabling online delivery works otherwise to challenge academic integrity management and assessment security during the COVID-19 pandemic. A recent study derived from UK academics of various disciplines and positions identified an abundance of "afflictions", which overshadowed the potential "affordances" in the context of emergency online migration and online pedagogies [42]. These afflictions will continue to have undeniable impacts on "student recruitment", "countries' GDP made by international students", "local economies", "sustainability of universities within a global student marketplace," and "academic labour-market" [42]. While the majority of the survey respondents critically articulated the dark side of the rapid online migration, there were some—much fewer yet no less visible—who positively debated about its capacities and turned the tragedy of COVID-19 into an opportunity to deliberate its impacts on higher education. For these optimistic academics, the forced transition in the light of the coronavirus crisis could inform different forms of change that were long overdue. Besides, the technology advocates echoed how the enforced online migration has contributed to the professionalisation of academics as pedagogues, moving beyond "the tokenism of pedagogic credentialism" (i.e., outlining higher education "as a socially immersive and participatory learning experience") and further incentivising better practices [42] (pp. 631, 636). Such debates serve as the basis for diagnosing and exploring the impacts of emergency adoption and experimentation of online and other forms of technology-enabled LTA on the role of the academic community and the long-term future of higher education. This resonates with what other higher education commentators have previously argued as digital transformation [32–34]. Answers to many questions in this context are far from clear, yet the extent to which the higher education sector has the capacity to adapt in the context of emergency immersion into online/distance LTA and digital pedagogies remains a critical discourse and is a subject to further elucidation.

#### **3. Methods**

This is an exploratory research [44] (p. 64) with a qualitative approach focusing on a single case study [45]. We used the case study research design to "describe and diagnose" processes by observing their developments and contextual influences [46] (p. 98). The significance of case study has also been addressed in the context of education research as it can be adopted as an effective method to provide teachers with a range of experiences that can enable them to

become prepared and knowledgeable to manage different situations [47]. We selected the online teaching design model—what Power [48] (p. 509) called "blended online learning environment design model"—for the delivery of the RMT subject at Cardiff University as a critical response to the process of rapid transition from a face-to-face to a remote online mode of delivery during the early COVID-19 outbreak and subsequent restrictions in the UK. Access to the case study has been among the key selection criteria. We also used diagrammatic thinking as an abstraction with the capacity to unravel relationships between different elements/activities in the context of higher education. This paper was mostly written in May—July 2020 during the public health emergency related to the COVID-19 pandemic in the UK. In addition to scholarly publications, we also relied on emerging discussions in the digital media and news articles at the time.

The following limitations have also been identified in this study. Due to the suspension of face-to-face academic activities and rapid shift to remote online delivery during the early COVID-19 outbreak and subsequent lockdown in the UK, it was not possible to develop and collect comprehensive surveys from students and/or academic staff members at the time. In addition, subject evaluations were suspended for Spring semester subjects such as RMT. It is also beyond the scope of this paper to evaluate the process of learning, the associated institutional frameworks, or the related policy setting. Exploring the experiences of students is a limitation of this paper and remains a task for future research. The tight schedule of this study and the related subject delivery during the rapid period of transition to online teaching has also been among the key limitations.

#### **4. Context**

#### *4.1. The Early Lockdown in the UK and Transition to Online Education*

UK government announced a national lockdown in March 2020 [49] and fully suspended face-to-face teaching in higher education to contain the coronavirus. Consequently, universities across the nation including Cardiff university closed their campuses and took the steps necessary to rapidly move to remote and blended online methods of LTA during this period of disruption. Regardless of the difficulties imparted by government enforced movement constraints and social distancing measures, universities must have continued to ensure that necessary academic standards and high-quality student experience were maintained in accordance with the "safety net policy" and learning outcomes associated with each degree programme. In this paper, to reflect on the experience of teaching urban design research methods in the RMT subject, we carry out a comparative analysis of the pre- and post-adaptation of the subject design pertaining to digital transition to online platforms. We elaborate on the ways in which the RMT subject was adapted and redesigned when the COVID-19 outbreak led to the immediate closure of Cardiff University campuses and emergency migration of the teaching activities into online domains.

#### *4.2. Urban Design Education and Research Methods*

Urban design is an evolving field with critical links to a range of other disciplines including architecture, urban planning, geography, urban studies, social sciences, environmental psychology, and urban economics, among others. Addressing any research question in this field relies on a strong use of case studies, looking hard at cities [50] and adopting multiple methods and scales of analysis [51]. While engaging with specific research methods has been integral to some key contributions to the development of the knowledge base in the field of urban design [52–57], research methods have often remained underexplored, particularly in the context of urban design education. Learning urban design research methods can enable students to focus their inquiry by critically observing, analysing, exploring, and understanding cities.

There have been attempts to outline the capacity of certain methods in urban design education, such as urban mapping, digital parametric methods [58], and extensive geospatial databases such as GIS [59]. There has been less scholarly focus on developing pedagogical frameworks based on a more extensive range of urban design methods. This

paper focuses on teaching the RMT subject amid the COVID-19 outbreak and the subsequent lockdown in the UK. The primary aim of this subject is to introduce a range of research methods concerning critical questions in the field of urban design. It also seeks to enable students to deepen their methodological understanding and critical thinking in relation to those forms of urbanism that have remained underexplored [60–62] and to the ways in which urban places work at the intersections between spatiality and sociality [63], between the measurable and the non-measurable [64], and between urban morphology and streetlife intensity [65,66].

#### *4.3. Research Methods and Techniques Subject in MA Urban Design*

Figure 1 illustrates the position of the RMT subject within the broader context of the MA Urban Design (MA UD) programme at Cardiff University. The RMT subject typically starts in the last weeks of the Spring semester and ends before the Urban Design thesis—called Research-based Design Project (RbDP)—starting in summer. The MA UD programme is organised in three semesters from Autumn to Summer, and the main subjects include Urban Design Foundation, Urban Design Thinkers, Autumn Studio, Urban Development Debates, Spring Studio, Research Methods and Techniques, and Research-based Design Project. The programme also includes field study visit. Figure 1 illustrates the RMT subject in relation to other subjects in the MA UD. The RMT subject has been designed to support the MA UD students to prepare for their end-of-year dissertation subject.

**Figure 1.** The Research Methods and Techniques (RMT) subject in relation to other subjects in the MA Urban Design programme.

The RMT subject introduces students to various key methods and techniques for urban analysis and design through a mix of weekly lectures, reading seminars, and work-inprogress tutorials. The aim is to enable students to deepen their critical understanding and methodological approach in relation to a range of key topic areas and questions in urban design. The subject develops skills to draft a research proposal related to urban design and provides an understanding of alternative approaches to research in urban design. It also helps develop an ability to identify suitable methods to address the outlined research questions and provide an informed explanation for selecting a particular methodology to address the related research questions. Enabling a constructive alignment [67] between the subject material, teaching and learning activities, assessments, and intended learning outcomes has been a primary focus in developing the RMT subject.

#### **5. Case Study Analysis**

The RMT was among the subjects in the MA Urban Design programme that was hit the most in the time of the early outbreak in the UK. To become more amenable to online LTA, as illustrated in Figure 2, the entire subject was inevitably adapted and redesigned for online delivery under unprecedented pressures with limited substantial resources and increased demand for online teaching and learning. In what follows, we discuss the challenges and capacities of online teaching based on the experience of delivering the RMT subject during the lockdown with the aim to outline some key considerations for sustaining effective remote LTA in the face of uncertain, changing, and challenging situations such as the COVID-19 pandemic. The case study analysis section is structured in relation to the three themes of teaching and learning activities, assessment and feedback, and digital platforms with a focus on the conditions before and during the lockdown. The RMT subject delivery before and during the lockdown in the UK is comparatively summarised in Table 1 as well.

**Figure 2.** The emergency transition of the RMT subject from face-to-face to online learning, teaching and assessment (LTA) during the early COVID-19 outbreak in the UK.




**Table 1.** *Cont.*

#### *5.1. Learning and Teaching Activities*

Core lectures and guest lectures were the primary means for the face-to-face delivery of the academic content of the RMT subject. They presented the critical knowledge that students needed to develop their research proposals. A range of guest lectures were designed in a way that supervisors of the RbDP subject could deliver short presentations on their research themes and respond to students' questions. All face-to-face lecture material was uploaded online on a weekly basis. As an important component, face-toface reading seminars allowed students to individually discuss their reflections from the readings while interacting with their tutors and other students. These weekly RMT seminar readings were about empirical investigations that used or adopted those methodological approaches, methods, and techniques discussed earlier in that week's lectures. They also gave students the opportunity to understand other multiple ways of observing and analysing cities without reducing them to a single way of observing or analysing. Similar to seminars, face-to-face work-in-progress tutorials included a combination of group and individual activities. Encouraging discussion and enabling a critical understanding of the subject material and its relevance were among the effective teaching principles [68]. The weekly interactive tutorials provided the opportunity for students to critically discuss their ideas on how to develop their individual research proposals with their peers and tutors.

After the inevitable migration to online teaching and learning during the COVID-19 outbreak in the UK and the subsequent national lockdown, all the on-campus face-to-face lectures were replaced by a mix of synchronous and asynchronous online lectures (Figure 2). A part of the asynchronous online lectures included short lectures delivered by RbDP supervisors in the second week of the subject after the introductory lecture in the first week. All supervisors were expected to deliver a short presentation on their research themes in the RMT subject. These presentations were mostly recorded as PowerPoint presentations saved as narrated video files and made accessible via the Learning Central (LC) online platform—the Cardiff University's primary virtual learning and teaching environment. The advantage of making short presentations of supervisors available online was that it could allow students to engage with various research topics as well as each supervisor's broad research expertise in addressing different questions in relation to urban design thinking. The online material delivery rather than cessation of all such learning and teaching activities could also facilitate a better fit and informed alignment between supervisors' expertise and students' interests.

More asynchronous lecture material about research ethics, library resources, literature search, annotated bibliography, and referencing were made available using the LC online platform. The rest of the online lectures were synchronous, using Microsoft Teams as the primary online platform. As shown in Figure 2, reading seminars and work-in-progress tutorials were entirely replaced by online discussion sessions using the Microsoft Teams General interface. The Microsoft Teams has been quite effective in facilitating both synchronous online lectures and discussion sessions and enabling an engaging environment for a large cohort of students joining from multiple geographical locations and time-zones. It also facilitated both individual and group discussions, using different channels, conversations, scheduling, file sharing, and storage features.

#### *5.2. Assessment and Feedback*

Assessment in this subject includes both forms of summative and formative. Formative assessment allows tutors to gauge students' learning during the learning process mainly through synchronous interim presentations. Interim presentations include those sessions designed particularly for students to individually present their pre-submission workin-progress assignment and obtain timely and focused feedback and advice from their instructors (i.e., a number of supervisors who are involved in supervision in the RbDP subject). This will help students learn and improve their work for the final submission. The importance of timely and clear formative feedback has been acknowledged in relevant studies [69]. Other work-in-progress tutorials and reading seminars offer students the opportunity to obtain formative feedback from their peers and instructors. Summative assessment in this subject includes two main components: lecture/seminar contribution and a written research proposal attracting 30% and 70% of the total mark, respectively.

During the lockdown, to include the component of interim presentations in the blended online delivery mode, different channels were created in the Microsoft Teams, each of which included about 16 students presenting their works individually to an internal/external crit and receiving immediate synchronous feedback and advice. Nevertheless, a specific form of summative assessment, including the 30% lecture/seminar contribution, was suspended as the individual contribution could no longer be fairly assessed online during the lockdown. Thus, the assessment changed into a 100% research proposal submission with a higher word count.

#### *5.3. Digital Platforms*

As previously noted, LC has been the primary online learning and teaching platform in different degree programmes across Cardiff University. Subject description, schedule outline, seminar and tutorial structure, interim presentation schedule, learning material, reading list, assessment brief, group allocation, list of the subject team as well as the supervisors involved in the next subject, supervisors' research themes, and presentation materials were all available on LC. Students were also provided with supporting documents such as research proposal templates and guides (e.g., library search guide, preliminary draft research proposal template, individual writing and reflection guide, and reading summary template).

We have primarily used a mix of Learning Central and Microsoft Teams as the key online platforms to deliver the subject material during the lockdown period. LC has been used as the main platform to facilitate asynchronous learning and teaching while Microsoft Teams has been utilised to enable a range of synchronous learning and teaching activities. We have noticed some of the critical capacities and limitations of both platforms in teaching urban design research methods online. The core subject materials, such as lecture slides, reading lists, and assessment briefs, have been made available on LC so that individual learners would be able to download and access them anywhere and anytime. The LC platform, though, has been found challenging and not particularly user friendly when it came to synchronous teaching and learning. In contrast, the Microsoft Teams platform has become quite useful and more user friendly in enabling an engaging learning environment for lectures and seminar discussions. Both platforms fell short in the extent to which they could effectively simulate the whiteboard as a collaborative platform for sharing ideas and diagrams. Collaborative drawing is particularly difficult in both platforms, partly because it relies on the degree to which the teaching team and individual learners

have access to related hardware, including digital pens and drawing boards. We also noticed the following limitations using Microsoft Teams as the primary online platform for coordinating synchronous learning and teaching: all the team members were added manually, which was quite time-consuming given the large size of the cohort; there were limited number of participants visible on screen at once; anonymous file sharing and archiving seemed impossible since all members could access any shared files by either students or tutors.

#### **6. Discussion**

Moving towards online teaching during urban public health emergencies such as the COVID-19 outbreak has become necessary rather than optional as the demand for the development and implementation of adaptive learning spaces and the integration of virtual reality and innovative digital learning pathways is growing. At stake is to avoid normalising hasty transitions to online teaching in the face of such global challenges. While the condition of emergency may justify immediate action, it is the role of academia to remain reflective of its practice. The COVID-19 outbreak might be an opportunity for universities to learn from the rapid changes and adaptations during this unprecedented time, and as such rethink the extent to which many courses rely on face-to-face teaching on campus. Nonetheless, the COVID-19 pandemic cannot be simply considered as an excuse to prioritise online teaching and dismiss traditional face-to-face learning. Forms of blended teaching and learning are already underway to at once harness the capacities of both online and face-to-face teaching and hopefully manage the limitations of both when it comes to learning. Focusing on the learning experience is critical in the process of integrating traditional and online forms of teaching and learning and implementing blended learning [70]. In what follows, we open the discussion in relation to the capacities and challenges of online mode of teaching.

One of the significant challenges associated with blended online teaching delivery is about the extent to which online platforms can enable and sustain small-group learning and student-to-student communication. This is mainly at stake in the context of urban design pedagogy, which often aims to enhance teamwork skills among different learners through small group teaching and peer learning. This is linked to the idea put forward by Exley and Dennick [71] that communication is integral to effective small group teaching in higher education. While online teaching enabled student-to-teacher communication, it fell short in sustaining student-to-student communication, which is even more important in urban design subjects relying on effective teamwork and collaboration among students within small groups. Teaching urban design research methods during the lockdown period has shown that blended online modes of teaching delivery have less effectively enabled discussions among students. This partly supports Dumford and Miller's [14] argument that students taking online courses are less willing to participate in collaborative learning, interactions with diverse peers, compared to those in the traditional classroom. This also means that students are less likely to develop core professional qualities including communication, interpersonal and practical skills [24]. Facilitating synchronous communication through discussions among individual learners has also become more challenging using online platforms such as LC and Microsoft Teams. The challenges of establishing eye contact with students, forming sub-groups, and encouraging active engagement have made online synchronous small group teaching and learning activities less productive. Synchronous discussions sessions have been more effective as individual learners had the opportunity to raise questions using oral and/or textual means of communication. Nevertheless, it is worth noting that similar to Bryson and Andres's [72] observation, managing multiple cues from students including those who engage in voice-based discussions whilst observing and responding to the questions in the chat box in the synchronous discussions sessions can be particularly challenging for the teaching staff.

While the transition to online teaching may offer more flexibility in terms of the university-based timetabling and location, it poses critical concerns regarding the challenge of home-based timetabling. Arranging appropriate places for on-campus face-to-face teaching has been a burgeoning challenge for many academics and professional staff involved in timetabling. Desirable physical spaces for teaching certain subjects face-to-face may not often be available on campus when needed. One of the key capacities of online teaching lies in the ways in which academic staff can allocate more time to focus on actual teaching and learning activities and subject materials instead of spending a considerable amount of time to organise suitable physical spaces on campus corresponding a desirable schedule, which often ends up in working with what is available, rather than what is desirable. Nonetheless, scheduling synchronous interactive teaching and learning has become problematic due to the challenge of managing different geographical locations and time zones of international students [42,73] along with the challenge of developing a functional arrangement for home-based teaching and learning. Many students, particularly those self-isolating as protection against COVID-19, may not have access to the appropriate space to effectively concentrate and engage with online synchronous learning activities. Many academic staff members with home-schooling and caring responsibilities have to manage double burden of paid work with unpaid care work. As such, they struggle with the challenge of arranging a suitable physical space and time with minimum disruption for online synchronous teaching activities. This has been particularly experienced by female academics with younger dependents, often engaged disproportionately in household and pastoral activities, in the face of emergency online LTA transition [42,74].

Practices of online teaching and learning cannot be simply generalised as differences can play a crucial role in the ways in which they play out in reality. Attracting a mix of international and local students from different backgrounds has become integral to how many universities can most effectively work, mainly in the context of the global North. In the UK, for instance, a considerable proportion of the annual tuition fee income in many higher education institutions is made up by Chinese international students [75]. Having said that, hasty transformations to online teaching and learning are likely to remain blind to such differences. While there is no systematically complied data on the extent to which international students consider studying abroad in the current climate of uncertainty, it would be naive to assume that online learning works similarly for different students. While local and international students cannot be considered as homogenous groups, a common characteristic of international students is about their endeavours to leave primary networks of support in pursuit of higher education in different contexts [76] (p. 201). For many international students, going through the challenge of moving to another country for education and finding an appropriate place to stay during their study may seem unnecessary when they can effectively benefit from a mix of synchronous and asynchronous online learning. This might be substantially different for many local students who have physical access to on-campus learning environments.

Using online platforms can arguably facilitate more equitable opportunities, particularly for those students who are likely to be less involved with teaching and learning activities. This lends itself well to the argument that "virtual identity will be unfettered by physical attributes such as gender, race, or disabilities" [23] (p. 10). It is critical to note that providing equal access to appropriate hardware such as laptops or tablets and infrastructure such as broadband and stable internet connection needs to be addressed first before we can discuss the issue of equity in relation to online platforms. As such, individual learners with different learning capabilities are empowered to participate more effectively in discussions and interact with their tutors asking questions and communicating their comments. These include different forms of communication, such as textual conversations, along with oral comments and questions. Some reticent students appeared to be more comfortable using text-based communication rather than oral communication. The use of technology can potentially enable a more inclusive access to lecture and discussion session materials. Students can get back to the discussed material from lectures or discussion sessions by checking the chat history and reading the minutes. This can provide opportunities for deeper and more critical reflection particularly for those students in different time zones.

Effective adaptation to online modes of pedagogy is subject to accessibility of new, relevant, and regularly updated technological tools and services on laptops and other mobile devices. More importantly, the challenge for many universities and educational institutions is to provide their academic staff and students with necessary guides to develop their technological literacy skills. Nevertheless, as discussed in the 2019 EDUCAUSE Horizon Report, merely facilitating the basic technological literacies among students and instructors is no longer sufficient to respond to and support the complex needs of people in a digitally mediated society [29] (p. 14). Hence, focusing on the distinction between technological fluency and technological literacy alongside further leveraging the technological fluency is crucial in the age of pandemic crisis to support personal and professional development and acquiring skills in the education such as creativity, critical thinking, independent problem solving, effective collaboration and self-directed learning. The demand for adaptive learning and teaching environments, digital learning innovations, and pedagogically sound teaching and learning designs will increase in the face of the COVID-19, and those universities investing in integrating more learning designers and instructional design experts will be better placed in their strategic attempts to design or redesign programmes. Having said that, it is worth noting that decisions about technology should not take priority over the content and the learning outcomes [72].

Online pedagogical approaches and the use of technology can facilitate parallel modes of online teaching. Examples of this have been evidenced in the RMT experience where the subject leader and tutors could simultaneously address multiple questions and comments, written and verbal, raised by students. Using a mix of audio, visual, and textual means of parallel communication, along with screensharing, has enabled the teaching team to address different questions and engage with individual learners simultaneously. Using live text-based communication for raising questions or responding to questions has been found particularly popular online as it allowed individual learners to receive an immediate response by one of the teaching team members. This is linked to the ways such synchronous communications help e-learners feel like members of a community rather than isolated individuals communicating with their computers [77]. The Microsoft Teams platform has enabled effective management of parallel presentations across different groups using channels functionality and live screensharing. Screensharing is a key feature of using technology in synchronous teaching and learning. In addition to the possibility of delivering live talks and presentations, screensharing has provided the critical benefit of immediate synchronous feedback from both tutors and students. Using the tool, it is possible to also share visual content as part of the lecture and seminar activities and leave the chat and messaging features open for live student-to-student and student-to-teacher communication as well as synchronous Q&A sessions. Such increased engagement in both lecture and seminar sessions can result in deeper learning through the representation of multiple viewpoints. This supports the idea that "technology can now provide immediate, nuanced feedback on student progress, drill down in areas of misunderstanding, tailor curriculum to personal needs, and create new ways for students to interact with their peers and teachers – all factors known to drive learning effectiveness" [24] (p. 20).

Establishing eye contact is integral to face-to-face teaching and learning. Yet, it is a burgeoning challenge for online platforms to at least enable a degree of such contact via digital technology. The importance of such a contact for a successful online learning has been previously outlined, which is mainly due to the fact that learning is a social act [36]. We argue that the rights to see and to be seen are taken for granted in the face-to-face teaching environments. However, in online teaching and learning, the discussion of such rights can pose challenges as cameras can be easily switched off, and participants, including tutors and students, can choose to become visible or remain invisible during synchronous teaching and learning. The use of technology also matters here to enable or constrain the capacity of seeing all those attendees with open cameras simultaneously. For instance, such a capacity is constrained in Microsoft Teams as only a limited number of attendees can become visible on the screen during an online session. There have been ongoing

conversations about how to address this limitation in Microsoft Teams, yet the point is not necessarily limited to the capacities of specific online platforms. While it might not be possible to simulate the nuances of face-to-face interactions in online settings, the task is to critically reflect on the extent to which the rights to see and to be seen in online learning environments can be negotiated to enable active engagement.

#### **7. Conclusions**

Drawing on the experience of teaching the Research Methods and Techniques subject during the early lockdown in the UK, we discussed the rapid transition from face-to-face to online teaching and pointed to the associated challenges and opportunities in relation to the learning and teaching activities, assessment and feedback, and digital platforms. We also outlined some key considerations to inform the development of more adaptive and resilient approaches to online teaching in the context of unprecedented global health crises such as the COVID-19 pandemic. Much less acknowledged, yet no less crucial are challenges such as the development of core professional qualities, including communication, interpersonal and practical skills, along with the integration of thoroughly selected online technology to most effectively redesign teaching activities and deeply engage students. We argue that it is critical to move beyond fixed pedagogical frameworks to harness the productive capacities of adaptive teaching. As discussed, pedagogy should be given primacy over technology in the wake of the COVID-19 pandemic and emergency online teaching and learning. In this sense, the pandemic can also be considered as an opportunity to deliberate over its impacts and associated changes in a way that contribute to the pedagogical reinventions as well as the evolution of online education.

The question of equity is paramount, yet it cannot be simply reduced to dichotomous thinking outlining online teaching in contrast to face-to-face teaching. Online and face-toface teaching can both become problematic when it comes to the provision of more equitable opportunities for different learners. Addressing diversity and the inequality of access to infrastructure, such as suitable hardware and required software as well as a stable internet connection, is critical for enabling a more inclusive online teaching and learning in the first place. Regardless of the specific capacities and limitations of online platforms, it might not be possible for all individual learners to equally and effectively benefit from synchronous teaching and learning due to limited access to adequate infrastructure, software and hardware. Normalising the condition of emergency cannot justify the ways in which hasty practices of online teaching dismiss differences, including the pre-existing inequalities concerning digital technology and its literacy. Face-to-face teaching is not necessarily a more just alternative as it can also dismiss differences and normalise or even intensify the pre-existing inequalities. While a blend of synchronous and asynchronous online teaching may provide more equitable opportunities for whom access to face-to-face teaching is limited, face-to-face teaching can also provide more equitable opportunities for those with limited access to the required infrastructure. The discussion, though, is not simply about selecting one and dismissing the other. The task is to focus on the intersections and productive capacities of online and traditional campus-based forms of learning and how they can most effectively co-function to facilitate learning outcomes and provide more equitable opportunities for different learners.

**Author Contributions:** Conceptualization, N.P. and H.K.; methodology, N.P.; writing—original draft preparation, N.P. and H.K.; writing—review and editing, N.P. and H.K.; visualization, H.K. and N.P.; project administration, N.P. All authors have read and agreed to the published version of the manuscript.

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

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors wish to acknowledge the valuable contributions of the teaching team, including Angela Ruiz del Portal, Monisha Peter, Juan Usubillaga, and Juan Fernández, to the Research Methods and Techniques (RMT) subject.

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

#### **References**


## *Article* **Teaching Mathematics at Distance: A Challenge for Universities**

**Rosalinda Cassibba 1, Daniela Ferrarello 2, Maria Flavia Mammana 3, Pasquale Musso 1, Mario Pennisi <sup>3</sup> and Eugenia Taranto 3,\***


**Abstract:** The focus of this research is how Sicilian state university mathematics professors faced the challenge of teaching via distance education during the first wave of the COVID-19 pandemic. Since the pandemic entered our lives suddenly, the professors found themselves having to lecture using an e-learning platform that they had never used before, and for which they could not receive training due to the health emergency. In addition to the emotional aspects related to the particular situation of the pandemic, there are two aspects to consider when teaching mathematics at a distance. The first is related to the fact that at university level, lecturers generally teach mathematics in a formal way, using many symbols and formulas that they are used to writing. The second aspect is that the way mathematics is taught is also related to the students to whom the teaching is addressed. In fact, not only online, but also in face-to-face modality, the teaching of mathematics to students on the mathematics degree course involves a different approach to lessons (as well as to the choice of topics to explain) than teaching mathematics in another degree course. In order to investigate how the Sicilian State university mathematics professors taught mathematics at distance, a questionnaire was prepared and administered one month after the beginning of the lockdown in Italy. Both quantitative and qualitative analyses were made, which allowed us to observe the way that university professors have adapted to the new teaching modality: they started to appropriate new artifacts (writing tablets, mathematical software, e-learning platform) to replicate their face-to-face teaching modality, mostly maintaining their blackboard teacher status. Their answers also reveal their beliefs related to teaching mathematics at university level, noting what has been an advantageous or disadvantageous for them in distance teaching.

**Keywords:** COVID-19 pandemic; university mathematics professors; teaching mathematics at a distance; blackboard teacher; teacher beliefs

### **1. Introduction**

Once upon a time, there was a world that believed in technology and connections between people, but one day a viral pandemic stopped everything and compelled the entire world to sit down and think. It was the COVID-19 disease, caused by a new virus that started to infect people in China at the end of 2019 and spread worldwide in 2020. From Wuhan (China), the virus, called SARS-CoV-2, spread across nearby countries in Asia first, and then moved across the world. On 20 February, the first infected person was certified in the north of Italy. Within a few days, the Italian government had decided to close schools and universities all over the country, since the virus was spreading further, and the whole of Italy was "closed" in quarantine: stores, restaurants, and factories as well as schools and universities were closed to the public. On 11 March, 12,462 people had been infected by SARS-CoV-2, and 827 people had died in Italy. This number was fated to grow to over one million people. Schools and universities were still closed in May 2020.

**Citation:** Cassibba, R.; Ferrarello, D.; Mammana, M.F.; Musso, P.; Pennisi, M.; Taranto, E. Teaching Mathematics at Distance: A Challenge for Universities. *Educ. Sci.* **2021**, *11*, 1. https://dx.doi.org/10.3390/educsci1 1010001

Received: 28 October 2020 Accepted: 18 December 2020 Published: 22 December 2020

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

**Copyright:** © 2020 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/).

In the first week of March 2020, the Italian Ministry of Education, University, and Research called on schools and universities not to abandon students who were quarantined at home and to start distance teaching.

Figure 1 summarizes the number of infected people in Italy by the end of the first Italian quarantine (June 2020).

**Figure 1.** Trend of COVID-19 cases in Italy until June 2020 (taken from https://lab24.ilScheme24.ore.com/coronavirus/ accessed on 30/06/2020).

As shown in Figure 1, there were more than 230,000 infected people out of 60 million inhabitants in Italy in the middle of June 2020 (0.395% of the population). There were not as many cases when distance teaching began, but we thought that the worst was yet to come.

The situation induced by the COVID-19 emergency required us to make an extra effort not only as individuals, but also as educators. We believe that the worldwide emergency requires us to reflect on its consequences for mathematics education and research, in a connected and technological world that suddenly found itself connected only through technology. We used a great deal of technology before the pandemic and believed it was a good mediator of mathematics education between teachers and learners, but we were forced to use only the mediator, and we have to reflect on the importance of the main characters in education: the teachers and learners.

Many studies in mathematics education demonstrate the importance of artifacts, and technological artifacts in particular, becoming instruments to mediate mathematical topics [1–3], but in this situation we were alone with these artifacts and the mediators were far away. Schools in Italy were accustomed to using technological devices (even when teaching face-to-face) and teaching aid platforms. In fact, thanks to law 107/2015 (https://www.gazzettaufficiale.it/eli/id/2015/07/15/15G00122/sg), the Digital Animator was introduced to Italian schools in 2015, which supports headteachers in the design and implementation of digital innovation projects (internal training, involvement of the school community, and the creation of innovative solutions with the use of technology). Nothing similar is planned for Sicilian universities. Moreover, university mathematics courses are traditionally taught by chalk and blackboard, at least in Sicily, where there are universities with ancient traditions (the oldest is in Catania, founded in 1434). The shift to distance learning was therefore a serious challenge for their professors.

The focus of our research is how Sicilian university mathematics professors faced the challenge of teaching via distance education during the COVID-19 pandemic, using a new technology (a distance learning platform) promoted by their universities. In addition to the emotional effects of the pandemic, there are two aspects of teaching mathematics at a

distance to consider. The first, without judging the suitability of this approach, is related to the fact that lecturers at university level generally teach mathematics in a formal way, using many symbols and formulas that they are used to writing for their students to see. The second aspect is that the way mathematics is taught is also related to the students to whom the teaching is addressed. Not only online, but also in face-to-face modality, teaching mathematics to students on the mathematics degree course involves a different approach to lessons (as well as to the choice of topics) than teaching mathematics on another degree course [4].

Our study population comprises all the university professors in the three Sicilian State universities that teach mathematics, on both mathematics and non-mathematics degree courses (e.g., engineering, computer science, etc.). We will specify this in the methodology, but we anticipate that, at least as far as Sicilian universities are concerned, the mathematics or physics degree courses have less students than the other degree courses in which mathematics is taught.

The research questions that guide our study are as follows:


The paper consists of five sections in addition to the introduction. In the next section (Section 2), we present the theoretical background, including features of e-learning environments, the use of artifact in teaching/learning mathematics, the process of objectification, the role of corporeity in the teaching/learning of mathematics, the concept of teacher beliefs, and a teacher's need for virtue when faced with unforeseen situations, such as the COVID-19 pandemic. The methodology that guided the research is presented in Section 3, with a description of the participants involved in the study and an illustration of how the data was collected and analyzed. The results section (Section 4) is dedicated to the exposition of both quantitative and qualitative analyses. The final section (Section 5) is dedicated to discussion and proposes lines for future research.

#### **2. Theoretical Background**

With the advent of the pandemic, universities have had to arrange various forms of e-learning in order to complete their teaching activities for the 2019/2020 academic year. E-learning delivers content through electronic information and communications technologies (ICTs). There are several definitions of e-learning. Here we assume the following: ICT is used to support distance teaching/learning processes, based on both e-content delivery and active and/or collaborative learning approaches [5].

To propose and manage e-learning means working within a complex system, involving not only the content to be delivered, but also theoretical models, technological and methodological choices to be made, the use and coordination of human resources, and the integration processes of the organization adopting e-learning as an additional way to acquire new knowledge and skills [5]. There are different kinds of e-learning activities. There are e-learning activities in which materials are provided for self-education (e.g., [6]) and also e-learning activities in virtual spaces able to host collaborative learning communities, organized in real learning groups, or in communities of practice [7], where each member increases their knowledge and skills by building them with the rest of the group, based on the cognitive problems typical of a given profession (e.g., [8,9]).

Issues arise in e-learning in mathematics, regarding the design of effective learning objects, when provided at distance. Borba et al. [10] discuss the use of digital learning objects in mathematics education, in blended teaching, but also in MOOCs and virtual learning environment. "It seems clear that digital technology involves "deconstructing" the notion of the classroom" ([10], p. 605), and this is more and more true when the classroom does not physically exist anymore.

The management of e-learning activities also involves various figures who are involved with its different aspects: administrative, technological, and didactic. An e-learning system involves the overall management/responsibility of the system, analysis of training needs, path design, teaching management/responsibility for the path, tutoring (network/coaching/mentoring/counselling), knowledge/competence of the content, evaluation of the learning and training process, in-depth knowledge of the e-learning platform, IT administration of the platform, knowledge/competence of the organization's ICT systems, information retrieval, knowledge management, the design and implementation of e-content (graphic story-boarding and multimedia development, didactic communication, etc.), an administrative/operational office, monitoring design and management, quality analysis, and so on [5]. In short, it is a complex system that involves more than simply choosing an e-learning platform in order to achieve the final goal, that is, to create good e-learning paths.

To use technological artifacts (as for other artifacts) in an effective way from an educational point of view means to achieve an *instrumental genesis*, in the sense introduced by Rabarderl [11]. The process can be long and difficult, because it requires two phases, which Rabardel and Samurcay [12] call *instrumentalization* and *instrumentation*. The first phase is concerned with the approach to the artifact, and, for example, with the progressive awareness of its potential and its limits. The second phase, which is deeper, is devoted to rising and developing the artifact's schemes of use, with the appropriation of social utilization schemes for the artifact and/or the arising and development of private schemes. The sudden closure of universities and the switch to distance teaching required efforts to appropriate new artifacts (platforms, devices, etc.) in the senses of both instrumentalization and instrumentation.

We have to consider that "this type of school closure has never happened on this scale before. It will require all stakeholders to rethink how education happens during this emergency scenario and, then beyond. [ ... ] Designing the learning experience for students must be differentiated when possible. It is not just as simple as putting your course online. Teachers need to think and choose how they can incorporate a blended learning approach and which tools will best serve their students and pedagogical practice. They need to consider what is accessible and fit for purpose, as well as ways in which to bring connectivity, relationality, and humanity into a distance learning model" ([13], p. 1).

In the particular case of mathematics, we must remember the importance of the embodiment component. Andrà [14] compares the blackboard teacher and the body teacher. The former manages communication through the written word and symbolic language, in which the blackboard is always at the center of attention, because the teacher is writing on it or indicates or underlines a written part on it; for the latter, communication is characterized by an intensive use of iconic and metaphorical gestures, which mainly involve an imaginative and figurative component.

There are several ways to represent mathematical objects: formal mathematical language, iconic representations, etc. The learning process that leads students to recognize the same mathematical object seen from different points of view is called *objectification* [15]. Teaching a discipline like mathematics, made of abstract objects that you cannot touch, often requires the use of metaphors to achieve the objectification of mathematical topics, which students can understand in terms of something already known. According to theorists of the embodied mind [16], people use physical objects or situations to understand complex topics in depth. They specifically use conceptual metaphors: this is not simply a metaphor in the poetic sense of the word, but rather a cognitive mechanism that projects the inferential structure of a source domain into a target domain. It is a map, in the mathematical sense of the word, between the two domains (source and target), preserving all the properties of the two elements corresponding in the map. When using metaphors, it is important that teachers make use of their body and gestures to help students envision

in their mind the new mathematical objects in terms of objects they are familiar with and are able to visualize and manipulate. See [16] for more details. The use of different representations, such as metaphors, in conjunction with formal mathematical language, is useful, because several studies have demonstrated that students have difficulty with the process of objectification [17].

There is a risk of losing the dimension of the body teacher, in favor of the blackboard teacher in the transition from traditional classroom teaching, involving presence, to distance learning, or e-learning. The professors involved in our research were very tied to the blackboard and mostly represented mathematical objects using formal mathematical language. They thus found themselves suddenly deprived of their "safe place".

The ways in which professors are comfortable teaching, their "safe teaching place", are related to their mathematical and pedagogical knowledge and to their beliefs. More than 30 years ago, in Shulman's famous paper "Those who understand" [18], educators pointed out the crucial role of integrating mathematical and pedagogical knowledge. Here we deal only with the Mathematics Teacher's Specialized Knowledge (MTSK) model, introduced by Carrillo et al. [19], inspired by the research of Ball et al. [20] on mathematical knowledge for teaching (MKT). Carrillo and the other authors of the MTSK model discussed the "precise images by which the teacher's practice can be interpreted in the light of those aspects which most influence it, based on the knowledge underlying this practice" ([19], p. 5).

The two domains of the MTSK model are the Mathematical Knowledge and Pedagogical Content Knowledge, divided into various sub-domains as shown in Figure 2. Teacher beliefs are at the center, due to the close relationship between beliefs and the two knowledge domains. By "beliefs" we mean the more or less coherent set of personal truths, mental images, conceptions, meanings, and preferences of teachers introduced by Thompson in 1992 [21], which strongly influence what happens in class and, therefore, student learning. In the MTSK model, beliefs are distinguished (although the boundary is fragile, as shown in Figure 2) as beliefs about math and beliefs about the teaching and learning of math. Beliefs as a mediator between knowledge and practice are discussed in [22], and much work has been published about primary and high school teachers, but the role of beliefs at university level has not yet been fully investigated, as claimed by Mora and Rodriguez [23]. Fukawa-Connely et al. [24] studied teacher beliefs and practices at the tertiary level, and found an interesting contradiction between professors' beliefs about mathematical teaching and their classroom practice: 85% of studied professors (in abstract algebra) used lectures as standard pedagogical practice, 82% answered that lecturing was the best way to teach. However, 56% agreed (plus 26% more who slightly agreed) with the statement "I think students learn better when they do mathematical work (in addition to taking notes and attending to the lecture) in class", showing a mismatch between beliefs about student learning and actual teaching practice. Even when teachers recognize that a constructivist approach is more effective for student learning, they continue to use a transmission-oriented methodology.

If this mismatch is important in a normal situation, then it becomes more serious in an emergency such as that induced by COVID-19, with the sudden immersion in distance teaching.

The new pandemic dimension requires, in the emergency, the even greater involvement by teachers, who must complete their work in new way even without further training. They are called on to activate the creative capacity that Berthoz [25] attributes to our brain, which he calls "vicariance". It is the vicariant component of the human brain that allows people to use multiple and unexpected strategies to achieve a goal, to replace one sense with another (such as when we move in the dark after an accident). Vicariance, says Berthoz, is a simplex principle that refers to the adaptive character of the individual in situations, environments, and interactions with others.

In the following sections, we will see how university professors implemented vicariance for the transposition of knowledge to their students during distance teaching, which

is less structured in an e-learning environment, even when they were usually blackboard teachers, during the COVID-19 pandemic.

**Figure 2.** The Mathematics Teacher's Specialized Knowledge model.

#### **3. Methodology**

*3.1. Participants*

The research involved 27 university mathematics professors. They were voluntary respondents to an anonymous questionnaire, addressed to professors who taught mathematics at the three Sicilian state universities (Catania, Messina, and Palermo) in the second semester of the 2019/2020 academic year. The participants represented one-third of the entire population of state university mathematics professors (82) teaching in Sicily, regardless of their semesters of activity [26].

Eighteen of the professors who answered the questionnaire taught only one course, seven taught two courses, and two taught three, for a total of 38 courses. The focus of the questionnaire, as we will specify in more detail in the next section, was to identify strengths or weaknesses highlighted by the shift to distance learning in each course taught. Since those who teach two or three courses teach different subjects to different students, we considered the 38 courses independent of the fact that some were taught by the same person. The data below thus refers to 38 responses.

#### *3.2. Data Collection and Method of Analysis*

An anonymous questionnaire to collect data was prepared by the Mathematics Education Research Group (MERG) of the Department of Mathematics and Computer Science at the University of Catania, Italy (which includes Ferrarello, Mammana, Pennisi, and Taranto). It was based on in-depth interviews conducted with experienced professors teaching three different university mathematics courses during the first few weeks of the pandemic (March 2020). This initial step provided data for structuring the different sections and specific contents of the questionnaire.

Three strands of mathematics courses can be identified in Sicilian universities:


(3) Basic mathematics courses offered for science degree courses (e.g., biology, geology, natural sciences, agriculture, computer science, architecture, economics, etc.), where mathematics is (often) little appreciated by students, generally offered to classes with many students.

The questionnaire was made up of four sections: the first gathered general information; the second investigated teaching habits and emotions related to courses held before the COVID-19 pandemic. The third section investigated new teaching habits and emotions related to the courses held during the COVID-19 pandemic. The fourth and last section included questions about the technologies used for distance learning. Each section contained open-ended, semi-open, closed, and Likert scale questions. We validated the questionnaire by sharing it with a group of six experts in mathematics education and educational psychology. After including their suggestions for modifications to the questionnaire, we conducted a pilot study, administering it to three additional university math professors, who only suggested a few small final changes.

The questionnaire, produced using Google Forms, which is an open source application for online surveys, was administered to the final participants about one month after the start of the lockdown in Italy. The MERG contacted the Directors of the Mathematics Departments of the three Sicilian State universities by email, with the request to distribute the questionnaire to all professors teaching math courses that semester. The data collection lasted one month. The data that we will illustrate in the next section therefore captures a precise moment: April 2020.

The analyses were carried out by MERG, in collaboration with psychologist colleagues (Cassibba, Musso), using Version 24 of the Statistical Package for the Social Sciences (SPSS). The analyses are both quantitative and qualitative. In the quantitative analyses, we generally reported the frequencies of the responses or their cross-tabulation, associated, when appropriate, with nonparametric statistics (i.e., chi-square test, Kruskal-Wallis test, Mc-Nemar test, and Median test) given that the data was categorical or ordered categorically. Because of the largely exploratory approach of our study, and to ensure the high sensitivity of statistical tests in the initial phase of our research project, we set the critical *p* value for significance at 0.10. This a priori choice was also connected to the high sensitivity of the chi-square test to sample size, while the distribution of the variables seemed less problematic considering the use of nonparametric statistics. The responses to the open-ended and semi-open questions were subjected to thematic analysis. The analysis followed the principle of data reduction and the generation of themes, which allowed an in-depth reading of the meaning-making processes related to the closed-ended questions. Specifically, the analysis process was structured in (a) open coding for the generation of the themes; (b) comparison with existing knowledge for the reorganization and grouping of the themes that emerged; and (c) selective coding, to extract illustrative examples of central experiences. The classifications and identification of the themes were carried out by the study authors, reaching a good degree of agreement (k = 0.83); in cases of disagreement, a discussion was initiated, which led, in all cases, to a final shared decision. We used qualitative data in this manuscript to better interpret quantitative results, without their in-depth descriptive analysis.

#### **4. Data and Analysis**

The sample of respondents had the following characteristics: 61% were men; 39% were women (Figure 3). Eleven percent were up to 40 years old, 34% were between 41 and 55 years old, and 55% were over 55 years old (Figure 4). This reflects the general state university mathematics professor population in Sicily well in terms of gender and age, with proportional differences under 5% [26].

**Figure 3.** Gender of the sample.

**Figure 4.** Age of the sample.

Fifty-five percent of respondents taught at the University of Catania, 34% at the University of Messina, and 11% at the University of Palermo (Figure 5). Sixty-eight percent of respondents taught on a Bachelor's degree course and 32% on a Master's degree course. Sixty-six percent taught in Mathematics or Physics, 18% in Engineering, and 16% in "Other" (Figure 6)—the three categories of degree courses specified in the previous section.

**Figure 5.** Universities at which the sample teaches.

**Figure 6.** Degree courses of the sample.

Compared to the distribution of mathematics professors across the three state universities in [26], those in the University of Palermo were underrepresented (37% of the population), while those at the University of Catania (41% in the population) and the University of Messina (22% in the population) were overrepresented. These three universities and their professors have very similar characteristics, however, given that the rules for their functioning (e.g., recruitment procedures, number of courses provided, credits per course) are clearly established at both national and regional levels.

Fifty-eight percent of professors had taught their course for less than five years and only 34% had done so for more than 10 years. Before filling in the questionnaire, 37% had taught four to eight distance learning lessons and 63% had taught more than nine distance learning lessons. All respondents gave their lectures at a distance via the Microsoft Teams e-learning platform, as this was chosen by the three universities involved in the study. The didactic offices on Microsoft Teams created as many virtual classrooms (Teams) as courses provided by the university. Table 1 shows the number of students who were members of a Team and the percentage of students regularly attending distance learning, for each degree course. We can see that the majority of degree courses in mathematics or physics (56%) had between 11 and 40 students and 60% of these students attended distance classes assiduously (attendance between 75% and 100%). Most engineering degree courses (57%) had more than 100 students, most of whom (43%) attended distance learning (attendance between 75% and 100%). The other degree courses, including mathematics courses, varied between 41 and 100 students (50%), or over 100 (33%), and 50% of these students had an attendance rate of between 0% and 50%.


**Table 1.** Cross-tabulation between the number of students who were members of the Teams and the percentage of students who attend distance learning, compared to the degree courses (*n* = 38).

> Using a multiple-choice question, we asked the professors how they used to prepare their lessons before the COVID-19 pandemic. The same question was asked in the section "During COVID-19". Table 2 shows that, with the transition to distance learning, the percentage of professors who prepared everything in detail has increased. The chi-square

test, *χ*2(4) = 22.86, *p* < 0.001, allows us to confirm that the passage to distance teaching has pushed the professors in a non-random way to better prepare their lessons.

**Table 2.** Lesson preparation (*n* = 38).


Before the COVID-19 pandemic, as Table 3 shows, no professor had ever lectured online. They all lectured at the front of the class using blackboard and chalk. Thirteen percent also used slides (.ppt or .pdf files), and 11% also used mathematical software.

**Table 3.** How did you previously teach a lesson? (multiple answer options)—(*n* = 38).


The symbolic and formal writings of mathematics had to be digitized during the COVID-19 pandemic, so we asked the professors how they adapted to this. Table 4 shows that the writing tablet was considered a worthy substitute for the blackboard, and in fact 61% of the professors continued to manually write the symbolic and formal writings of mathematics with a tablet. Thirty = seven percent used mathematical software, 42% showed slides—resources prepared before the lesson (.ppt files or sheets that were handwritten beforehand and then scanned to be shown on screen as .pdf files). In fact, someone wrote:

*I do not have a writing tablet, blackboard, or anything else, so the only way is to write by hand before the lesson, scan the many sheets and insert them on the PC to share during the lesson: hard work.*

**Table 4.** What do you use to digitize the formal and symbolic writings of mathematics? (multiple answer options)—(*n* = 38).


The McNemar test showed that there was a significant increase in the use of slides, from 13% to 42%, *p* = 0.01, and there is also a significant increase in the use of mathematical software, from 11% to 37%, *p* = 0.03.

We investigated how often professors used their handwriting during their distance learning, using a writing tablet and sheets of paper that they then converted into .pdfs for projection. The answers were: *never* (23%), *sometimes* (21%), *often* (16%), and *always* (40%). Table 5 shows that those who chose to use their own writing did so to improve teaching effectiveness and content exposure (58%) or to recreate the traditional atmosphere of class (19%). Some of the answers given by professors, for example, were:

*It is easier to show the progress of an exercise.*

*I believe that the professor's personal writing makes the text "less cold" and more effective from a didactic point of view.*

**Table 5.** Explain how much you use your writing (writing tablet, sheets shown to students, etc.)—


We were interested in understanding what actions the professors took, and how often they were teaching using a personal computer in distance learning. In particular, we asked

if they activated the camera, shared their screen, and asked students to share their screens, and asked them to explain their habits. Sixty percent *always* activated the camera (Table 6). The open-ended responses that explained this answer are related to choices for relational and communication reasons. For example:

*To have more contact with students.*

*Students follow better.*

(*n* = 38).

*I like the idea of eye contact.*

*It is important that students see me, both to create a "classroom" relationship and because I often show objects or "help" myself with gestures.*

Those who did not use a camera for distance learning explained that they preferred other educational tools or did not do so for privacy reasons. For example:

*I do not think it is necessary and I prefer students to focus on the content of the presentation.*

*[* ... *] since my class consists of 180 students, I prefer not to show myself on video to avoid any unpleasant episodes.*

Although it was a small percentage of teachers who did not turn the camera on, we wondered if this choice was related to the number of students following their distance teaching, or whether it was related to the degree course. The Kruskal–Wallis Test, in both cases, did not support this hypothesis, *p* > 0.50.

Eighty-seven percent of professors shared their screens frequently (Table 6, *often* + *always*). The open-ended responses showed that professors took this action because they needed to show resources that they had prepared for the lesson (63%) or because they needed to build the lesson in front of the students (37%). For example:

*Sharing is necessary to show what I have prepared, but also to show further examples, to do exercises, to focus on key steps* ... *using a writing tablet.*

*I think it is necessary to share the screen in a presentation, especially for mathematical formulas. I couldn't do without it.*

*During a three-hour lesson in front of the class, I fill four blackboards at least ten times, because I always have to write, now with no other way I show the many papers I write before each lesson, so I always talk and share.*

*I use Mathematica software. Students see either my notebook where I explain the topic, or my notebook where I solve a problem.*

**Table 6.** Frequency with which a certain action takes place on the PC during the distance lesson (*n* = 38).


Using natural language in an informal way, mathematical language and iconic representations (diagrams, function graphs, charts, etc.) did not undergo significant variations during the mathematical lectures taught at a distance. In fact, as Table 7 shows, 87% of professors continued to use these three signs (natural language in an informal way, mathematical language, and iconic representations) in the same way as before the COVID-19 pandemic. This means that the modality of distance learning had not affected the way in which the terminology proper to the discipline and its iconic representations were used in teaching practices. This is independent of the number of students attending that particular course (Median test, *χ*2(2) = 0.53, *p* > 0.50). Almost all the professors (95%) used gestures less than before or in the same way as before. In particular, the median test, *χ*2(2) = 8.67, *p* = 0.013, shows that professors who had more students (percentage of attendants between 75% and 100%) reported using gestures in the same way as before, while those who have few students (percentage of attendants between 0% and 50%) reported having used fewer gestures.

**Table 7.** Frequency of formats during distance learning compared to the usual presentation of topics? (*n* = 38).


School teachers on some social networks in Italy often noted that during the quarantine: "distance teaching requires twice as long to prepare a lesson and you can explain half the things you have prepared". We asked the university mathematics professors how much they agreed with this, especially the second part. Table 8 shows that 82% (*definitely disagree* + *quite disagree*) disagreed with this statement, and the distribution of the answer options is significantly different, *χ*2(3) = 27.05, *p* < 0.001).

The open answers explaining the degree of agreement reveal that 18% found the distance modality ineffective. Twenty-three percent used similar modalities to their previous ones, and 59% used new teaching modalities to try to maintain the same standard as when teaching in person. The fact that the same modalities used in person were adopted even at a distance, and that new "compensatory" tools were used (such as prepared notes, slides, etc.), allows us to conclude that teaching on Teams had not reduced the number of topics explained by professors. Open answers from the professors included:

*With distance learning, having already prepared the material/presentation to share during the lesson (which then becomes teaching material available to students), it is possible to explain more quickly and therefore explain more topics than in traditional lessons.*

*The use of the blackboard meant more time to explain the topics. Students don't have to take notes. I provide them at the end of each lesson.*

*Actually, with distance learning you do more with the same amount of time.*

*I spend lot of time handwriting what I would write on the blackboard while I explain, and because I can't see the eyes of the students I'm not inclined to repeat concepts or demonstrations, and so I do everything I set out to do.*

Something more emerges from the open answers: the professors managed to transpose even more knowledge than they were able to transpose in person. Some said that this was probably due to not having to write on the blackboard and wait for the students to transcribe the notes, others said that by sending the (previously prepared) notes to the students, they could afford to go faster. Some also said that more was done because there was a lack of interaction with the students.

**Table 8.** How much you agree with these statements: "with distance learning you can only explain half the things you have prepared"? (*n* = 38).


We investigated long-distance professor–student relationships through the two following questions. First of all, we used a Likert scale to ask whether the professors could perceive whether the students were keeping up with them in the lesson, and then used an open question to ask what strategies they adopted for perceiving this. Twenty-four percent said *definitely not*, 40% *more no than yes*, 26% *more yes than no*, and 10% *definitely yes*. In most cases, therefore, professors were not able to perceive whether students were keeping up with them in the lesson, and this is also demonstrated by the chi-square test analysis: *χ*2(3) = 6.42, *p* < 0.10. A Kruskal–Wallis test showed that this inability depends on neither the number of students attending the course, *χ*2(2) = 0.699, *p* = 0.70, nor on the degree course, *χ*2(2) = 0.960, *p* = 0.62. The double entry table (Table 9) correlates the strategies adopted by professors with the previous answer. We can see that those who claimed they were able to perceive that the students were keeping up with the lesson did so by asking the students directly whether they were following the explanation (30%), by asking the students questions about the content they had explained (27%), or by deducing it from the interventions made by students (24%).

One comparison was related to concerns about the use of distance learning that had been raised before the COVID-19 pandemic, with respect to concerns about distance learning during the COVID-19 pandemic. Table 10 shows that before starting distance learning due to the pandemic, 74% (*pretty concerned* + *very concerned*) were concerned about the thought of having to give their lessons online. This percentage dropped to 40% during the pandemic wave. This suggests that the professors' concerns were lessened when practicing distance learning.




**Table 10.** Likert-scale response percentages about concerns regarding distance learning before and during COVID-19 pandemic (*n* = 38).

As noted in the methodology section, our sample respondents adopted Microsoft Teams as the e-learning platform for distance learning. We emphasize here that none of the professors in the universities at Catania, Messina, or Palermo had received training in the use of this platform. This is certainly due to the fact that the academic community found itself suddenly (within five days) required to provide distance learning in order to continue guaranteeing the right to university education, despite the health emergency and the pandemic situation. Although professors discovered the Teams functions on their own, some expressed their willingness to continue using it. In fact, professors plan to continue using Teams and/or the other platforms at the end of the COVID-19 pandemic (Table 11). Twenty-six percent said they do not want to use any platform, and 5% were unable to respond. Teams was confirmed as the choice of 58% of respondents. Whereas 39% had been using other platforms, there is now increased willingness to use a digital platform, Teams, in the future.

**Table 11.** Which of these e-learning platforms do you plan to continue using after the end of COVID-19 pandemic? (multiple response options)—(*n* = 38).


We wanted to investigate whether the age of the respondents affected this choice. It emerged that 77% of those up to the age of 55 said they wanted to continue using Teams or similar, while 57% of those over 55 said they did not want to continue using it. The older a professor, the less willing they are to continue using distance learning platforms. This assumption is confirmed by the fact that the distribution of the answer is significant, χ2(1) = 4.35, *p* < 0.10.

Using open questions, we asked the professors to comment on how much they felt they had gained and lost through distance learning. Table 12 shows the cross-tabulation of the thematic categories of answers that emerged for both issues. The chi-square analysis related to this contingency table was not significant, χ2(12) = 15.72, *p* = 0.21, meaning that the association between the two thematic variables were no different from chance. However, considering each variable individually (see the total column in the Table 12), the frequencies of the identified categories were significantly different for the loss in distance modality, *χ2*(4) = 22.26, *p* < 0.001, with the "Human exchange" category more frequent compared to the other categories. No differences were revealed for the gain in distance modality variable.


*Educ. Sci.* **2021**

, *11*, 1

We note that compared to earnings, 21% of professors believed they benefited from an improvement in terms of their didactical and technological skills:

*I discovered other ways of teaching, through the use of technology.*

*I learned how to use the iPad board and the Microsoft Teams platform.*

Twenty-three percent believed that the distance modality had a positive impact on learning/involvement of students.

*The ability to produce a PDF file that reproduces exactly what I wrote on the board. In this way students will find faithful notes and avoid transcribing inaccuracies that often cause confusion on important issues such as definitions or various observations.*

*A greater sense of responsibility on the part of the students, who have understood that to follow well they must "study" punctually and in advance.*

*The blackboards are published, the lesson is recorded, I have the ability to use software and also to show a video, which in traditional lessons I did not do because it was too laborious.*

Fifteen percent said that having to do the lesson at a distance improved the planning of the lesson, and another 15% said they suffered less stress on a physical and organizational level.

*The in-depth planning of the lessons.*

*The lesson is smoother, and the material I have prepared will still help me in the years to come.*

*Comforts.*

*Time.*

The majority (26%) said they had not benefited from any earnings.

The majority (43%) complained about a loss of human exchange. Twenty-seven percent complained of losing interactions with students for learning purposes, and another 27% claimed to have lost both.

*A part of human contact, useful to transmit the passion for discipline.*

*Eye contact with students.*

*Human contact with students.*

*The ability to see positive or negative reactions to what is proposed not explicitly manifested through interventions.*

*When I saw the empty eyes of so many students I understood that they hadn't understood me and so I repeated it all with other words until I saw their eyes full: I lost the joy of having been able to fill those eyes.*

We emphasize that student cameras were generally off and that the Teams platform does not allow the presenter to see more than one student when they share the screen, or more than nine when they do not. The presenter thus cannot see the students' eyes.

#### **5. Discussion and Conclusions**

The e-learning system is a complex system that involves several kinds of capabilities (and people). It is not easy to change in a few days from the way one has taught for years to a new way, without any training, while worried about the health, economy, and social perspective of your country. We asked how, in this situation, professors were able to move to distance teaching. The problems of adapting ways of teaching to the new e-learning environment are particularly relevant when teaching mathematics, because of the frequent use of symbols and formulas, as well as gestures and body. Let us review how the university

professors adapted themselves to the new teaching modality, attempting to teach "in the same way" in this new environment. We discovered that professors moved from lecturing with chalk and blackboard (100% used them) to lecturing with writing tablets (61%), which they had never used before, and slides or mathematical software (79%), which they had used to some extent (only 15.8% used slides or software before the pandemic). Most of the professors involved in our research started a process of instrumental genesis, through the appropriation of new artifacts (writing tablets, mathematical software, e-learning platform) in an *instrumentalization* phase: they managed to use them, found their potential and limits, but only to recreate the same teaching they were used to without the artifacts. So far, they had not reached an *instrumentation* phase, with the proper use of the artifacts with appropriation of their schemes of use. The professors we dealt with had a strong belief about teaching math (core in the MTSK model [19], together with math belief): that lecturing is the only way to teach mathematics. For instance, a professor stated: "*I do not have a writing tablet, blackboards, or anything else so the only way is to write by hand before the lesson, scan the sheets that are many and insert them on the PC to share during the lesson: hard work*." They thus continued in the "same way", by using different artifacts, technological ones. Writing tablets and other strategies were used to show their personal handwriting, because almost 60% believed that it was important to improve teaching effectiveness and content exposure (and not only to recreate a sort of classroom environment). No one claimed to have chosen the writing tablet so that they did not have to prepare the lectures in advance and so to save time, suggesting that the use of personal writing was not a comfort choice but rather a didactic one, due to personal beliefs about mathematics, according to this belief which has to be written, and written by hand, because "*I believe that the professor's personal writing makes the text "less cold" and more effective from a didactic point of view*". The use of slides and mathematical software also seems to have been a didactic choice, and not a comfort choice. It required an extra effort, especially in terms of the details to be prepared for the lessons. Nevertheless, professors preparing the lectures in all the details increased from 39.5% to 68.4%. It was probably anxiety and worry that drove them to make detailed preparations, to prevent possible trouble. We want to stress that 81.8% of professors who started to prepare their lessons in detail during the emergency scored their worry about distance teaching as 3 or 4 on a Likert scale from 1 (not worried) to 4 (very worried).

The use of handwriting, slides, and software discussed so far is especially valid for "blackboard teachers" [14], those who, for instance, did not activate their camera because they "*prefer that students focus on the content of the presentation*". As for the "body teachers" [14], those who, for instance think that "*it is important that students see me, both to create a 'classroom' relationship and because I often show object or 'help' myself with gestures*", we find out that only 5.3% used gestures more often than before, regardless of the number of students. Those with a higher percentage of students use them in the same way and no less than before. Therefore, to answer our second research question, the number of students does not apparently affect the use of gestures. Using natural language in an informal way, mathematical language and the iconic representations was also independent of the number of students attending that particular course.

As for the disadvantages of distance teaching, 97.2% of answers reported having lost interaction for human exchange or learning purposes. Today, we are very used to technological devices, and we use them both for personal and didactic reasons: artifacts [12] can mediate mathematical topics, exactly as musical instruments can mediate the composer's feelings when we listen to music. In the situation illustrated in this paper, we had "instruments", but the players and the audience were so far from each other that we wonder whether the concert will be a success or not. We think that face-to-face communication is important in mathematics education, as in musical concerts, from both points of view: that of the students (the audience) and the teachers (the players). Attending a concert is not the same as watching it on the television, even if it is a live concert, and it is not the same thing to play in front of a reactive audience or in an empty theatre. We want to emphasize that there is a big difference between thinking about a course formatted as an on-line course

and adapting a course designed to be a face-to-face course as a distance course. In the musical metaphor, a player who goes to record a new disk is alone in the recording studio, and can play the music until the record is perfect (on-line courses). Alone in the theatre, a player can also execute a perfect performance, but without infusing the audience with the feelings involved in the music (distance courses in the emergency). Looking into the eyes of "audience" enable an understanding of whether teaching is effective or not. Some professors "lost the joy of having been able to fill those eyes". Another said "*I like the idea of eye contact*".

The final and central question to be answered is about the benefits of distance teaching and the opportunities that arise from difficulty. Fifteen point four percent of professors reported that extra time was a benefit (because, they said, you save the time traveling to and from the office) or comfort (because, they said, you are at home). Twenty-five point six percent claimed to have gained nothing. We want to emphasize that the other 59% found benefits in terms of better teaching or learning. In particular, 20.5% found an improvement in their didactical or technological skills. Fifty-eight percent wished to continue using the Teams platform, which no one had used before the emergency and everybody learned without any training. As shown in the previous section, the choice, as expected, is affected by age (the older professors are the least willing to use digital platforms). We hope that those professors who want to use the artifact will develop an instrumentation phase in the instrumental genesis process.

It is said that a crisis is a terrible opportunity to learn and grow up, and we ask whether we, as academics, were able to take this as an opportunity. We think that the professors we analyzed, starting from a worrying situation, showed a competence of vicariance, trying to solve unexpected problems, trying to change their habits, and trying to find something to learn. In fact, a gain took place when they acquired new skills that they will use in the future.

Several professors who helped in the research were available to be contacted again for further research. Our aim is to validate our results with them through interviews and focus groups. This further step will also take into account the fact that the COVID-19 pandemic situation is still ongoing and that they are still teaching at a distance.

We would also like to point out that in the same period during which we administered the questionnaires to university professors, a specular questionnaire was administered to the students of the three Sicilian universities (Catania, Messina, Palermo), with the aim of analyzing the distance teaching from the students' point of view in terms of emotions, learning, and advantages/disadvantages. We therefore intend to engage with the subsequent analysis to show the other side of the coin.

The game is not over!

**Author Contributions:** Conceptualization: R.C., D.F., M.F.M., M.P. and E.T.; methodology: R.C., D.F., M.F.M., P.M., M.P. and E.T.; data curation: R.C., D.F., M.F.M., P.M., M.P. and E.T.; formal analysis: D.F., M.F.M., P.M., M.P. and E.T.; investigation: D.F., M.F.M., M.P. and E.T.; resources: D.F., M.F.M., M.P. and E.T.; writing—original draft preparation: R.C., D.F., M.F.M., P.M., M.P. and E.T.; writing—review and editing: R.C., D.F., M.F.M., P.M., M.P. and E.T.; project administration: D.F., M.F.M., M.P. and E.T.; funding: R.C. and M.F.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research was supported by the research project "Programma Ricerca di Ateneo UNICT 2020-22 linea 2, EEEP&DLaD".

**Institutional Review Board Statement:** Institutional Review Board approval was not required since data did not include any personal identifying information. However, the study was conducted according to the guidelines of the Declaration of Helsinki.

**Informed Consent Statement:** Institutional informed consent from Directors of the Mathematics Departments of the three Sicilian State universities participating in the study was obtained on behalf of all subjects involved in the study.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions regarding the participating university Departments.

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

#### **References**

