A simple but efficient concept of blended teaching of mathematics for engineering students during the COVID-19 pandemic
AA simple but efficient concept of blended teaching of mathematicsfor engineering students during the COVID-19 pandemic
Saray Busto, Michael Dumbser and Elena GaburroDepartment of Civil, Environmental and Mechanical Engineering, University of Trento,Via Mesiano 77, 38123 Trento, Italy
Abstract
In this article we present a simple but efficient technological and logistic concept for the realization ofblended teaching of mathematics and its applications in theoretical mechanics that was conceived, testedand implemented at the Department of Civil, Environmental and Mechanical Engineering (DICAM)of the University of Trento, Italy, during the COVID-19 pandemic. The concept foresees traditional blackboard lectures with a reduced number of students physically present in the lecture hall, while thesame lectures are simultaneously made available to the remaining students, who cannot be present, viahigh quality low-bandwidth online streaming .Based on our first key assumption that traditional blackboard lectures, including the gestures andthe facial expressions of the professor, are even nowadays still a very efficient and highly appreciatedmeans of teaching mathematics at the university, this paper deliberately does not want to propose anovel pedagogical concept of how to teach mathematics at the undergraduate level, but rather presentsa technical concept of how to preserve the quality of traditional blackboard lectures even during theCOVID-19 pandemic and how to make them available to the students at home via online streamingwith adequate audio and video quality even at low internet bandwidth. The second key assumption ofthis paper is that the teaching of mathematics is a dynamic creative process that requires the physicalpresence of students in the lecture hall as audience so that the professor can instantaneously fine-tune theevolution of the lecture according to his/her perception of the level of attention and the facial expressionsof the students. The third key assumption of this paper is that students need to have the possibility tointeract with each other personally, especially in the first years at the university.We report on the necessary hardware, software and logistics, as well as on the perception of theproposed blended lectures by undergraduate students from civil and environmental engineering at theUniversity of Trento, Italy, compared to traditional lectures and also compared to the pure online lecturesthat were needed as emergency measure at the beginning of the COVID-19 pandemic.
Keywords: simple technical concept for blended teaching; transmission of traditional blackboard lec-tures of mathematics via high-quality/low-bandwidth audio & video streaming; bidirectional communication;blended chalk talks
The context of this work is the global COVID-19 pandemic, during which many governments worldwide haveimposed severe restrictions of all kinds of activities, including a complete shutdown of traditional lecturesat schools and universities which affected up to 83% of the total enrolled learners in the world, i.e. almost1.5 billion people [22]. At the University of Trento, Italy, regular lectures completely ceased on March 5 th online teaching , which was a common choice of many universities worldwide [4].In view of the favorable pandemic development in Italy during the summer months of 2020, at theUniversity of Trento teaching activities with students present in the lecture hall were permitted again forthe first semester of the academic year 2020/2021 (mid September 2020 to mid December 2020). However,due to national and regional COVID-19 restrictions, the number of students allowed to enter each lecturehall was reduced to 50% of its nominal capacity, see the Decree of the Italian Prime Minister of August7 th [6]. This restriction required the introduction of a suitable concept of blended teaching , where partsof the students are physically present in the lecture hall and the others are enabled to follow the lectures online at home via streaming over the internet. The blended teaching concept proposed in this paper has a1 a r X i v : . [ m a t h . HO ] O c t articular focus on those lectures which in pre-COVID times were traditionally held at the blackboard andwhich were usually highly appreciated by the students in the past.The ideas outlined in this paper are therefore based on a first key assumption that traditional blackboardlectures or chalk talks, which include the gestures and the facial expressions of the professor, are evennowadays still a very efficient means of teaching mathematics at the university level [10, 1, 16, 24]. The second key assumption of this paper is that the teaching of mathematics is a dynamic and creative process that requires the physical presence of students in the lecture hall as audience so that the professor caninstantaneously fine-tune the evolution of the lecture according to his/her perception of the level of attentionand the facial expressions of the students, in addition to the questions asked and the comments made bythe students. The situation is similar to the one of an actor performing live in a theater in front of a bigaudience [2]. The authors are convinced that this particular relationship between the professor and theaudience not only improves the performance and the quality of the teaching for the audience present in thelecture hall, but also the quality for those who follow the lectures online. In the opinion of the authors, asimilar emotional experience is completely impossible when a professor teaches a pure online lecture merelyin front of a computer screen, without any possibility to directly see or perceive the emotions of his/heraudience. The third key assumption of this paper is that students need to have the possibility to interact with each other personally [18], especially in the first years at the university when students should have anopportunity to get to know each other and to socialize [25], although this seems to be a contradiction to thesocial distancing measures adopted during the COVID-19 pandemic. Allowing the students to physicallycome to the lecture halls in order to live the lectures and exercises together as a common experience, despitethe anti-COVID rules, seems to be still more attractive than following pure online lectures alone in front ofa computer screen.As a consequence, our concept aims at enabling those students who can follow the lectures only onlineto have an experience that is as close to a real classroom experience as possible, permitting the studentsonline to communicate also directly with the professor and allowing them to have a high quality view ofthe professor and the blackboard, combined with high audio quality. These are all together nontrivialrequirements, in particular due to pandemic internet bandwidth restrictions. According to our three keyassumptions, this paper therefore deliberately does not present a novel pedagogical concept of how to teachmathematics at the university, but on the contrary, aims at showing a simple but efficient technical concept of how to preserve the quality of traditional means of teaching mathematics at the university level in thecontext of the COVID pandemics as far as possible.Innovative concepts of blended teaching in pre-COVID times were discussed in [12, 23], while recentcontributions in the field [9, 8, 11, 5, 17, 13] also have a particular focus on the use of blended teachingconcepts during the COVID-19 pandemic.The rest of this paper is organized as follows: in Section 2 we present and motivate the concept of blendedteaching developed and implemented at DICAM during the first semester of the academic year 2020/2021.The motivation of our blended teaching concept is also made in the light of the pure online teaching that wasadopted as compulsory emergency measure during almost the entire second semester of the academic year2019/2020. In Section 3 we describe the details of the technological and logistic realization of the concept,in particular also the hardware and software requirements, the special training of the professors before thestart of the semester and the organization of the technical support for blended teaching that was madeavailable during the semester. The quality of the adopted concept was quantitatively evaluated by both,professors and students via online questionnaires. The results of this evaluation are presented and discussedin Section 4. The paper closes with some concluding remarks in Section 5. The electronic supplementarymaterial of the paper contains some screenshots of how the lectures were perceived by students who followedthe lectures online. In order to illustrate and to motivate the blended teaching concept elaborated and implemented by DICAMduring the first semester of the academic year 2020/2021 (Sections 2.3-2.4), we first briefly describe thetypical structure of the courses in pre-COVID times (Section 2.1) and also draw some conclusions from thepure online teaching phase that was mandatory in spring 2020 at the beginning of the pandemic (Section 2.2).2able 1: Survey of DICAM made among its students in June 2020 at the end of the emergency onlineteaching of the second semester of 2019/2020. Total number of students participating in the survey: 445.Not all questions were mandatory.
Questions Answers with absolute numbers
1. Which online teaching modality do you prefer? asynchronous (47)synchronous without registration (17) synchronous with registration (257) depends on the lecture (67)depends on the professor (42)no opinion (15)2. Seeing the body language and the facial 0 - no opinion (20)expressions of the professor makes the 1 - not at all (1)lecture more interesting? 2 - a bit (17)
3. The use of the blackboard as a traditional 0 - no opinion (29)means of teaching is useful? 1 - not at all (1)2 - a bit (11)
4. Do you consider the option to attend the lectures of the first semester of 2020/2021 only online? 1 - yes (162)
All courses at DICAM in the areas of mathematics and its applications, including theoretical fluid mechanicsand solid mechanics, which are under consideration in this study, follow the traditional scheme of theoreticallectures combined with classroom exercises. In addition, for courses offered at the bachelor level, there arespecial group exercises organized in small work groups, led by MSc or PhD students (tutors). The groupexercises are based on the elaboration and discussion of exercise sheets in small work groups and makeuse of a flipped-class concept, where students first elaborate the exercises at home and then discuss theresults with the tutors in the classroom [14, 7]. Online surveys and structured interviews with the studentrepresentatives held in pre-COVID times revealed a clear preference of the students of DICAM for traditionalblackboard lectures, documented in the
Yearly report of the joint committee of professors and students ofDICAM , which is not available for public view.
With the shutdown of regular lectures in March 2020, all teaching activities at DICAM suddenly needed tobe held entirely online. In addition to the combined online teaching platform Moodle plus Kaltura , whichwas already available in pre-COVID times, for the emergency online teaching the University of Trento alsoprovided its professors with licenses for the software ZOOM . Online teaching could be held either in a synchronous manner by direct online streaming of the lecture content via ZOOM, or in an asynchronousway by pre-registering the lectures and uploading them into the combined Kaltura-Moodle platform. Thepersonal experience of the second author of this paper made with the pure online teaching activities fromMarch to June 2020 was overall rather negative, mainly due to the complete lack of an instantaneous feedbackfrom the students (missing facial expressions, comments and questions) even during synchronous teaching,since all students kept their microphones and webcams systematically switched off in order to save internetbandwidth, but also due to the lack of the blackboard as a traditional means of teaching mathematics at theuniversity. In a systematic survey made by the Department in June 2020, at the end of the emergency onlineteaching during the second semester 2019/2020, and to which 445 students of DICAM responded, the clearpreference of the students for online teaching was the synchronous online lecture with the registration ofthe lecture made available to the students via the Moodle-Kaltura platform afterwards. In the same onlinesurvey the students also expressed a clear preference for traditional lectures at the blackboard , confirmingthat the body-language of the professor is important and that the possibility to see the professor rendersthe lecture more interesting. For a summary of the main results of this survey, see Table 1, from which italso becomes evident that the majority of the students did not consider the option to attend lectures onlyonline in the case a traditional lecture would again be possible in the subsequent semester. https://moodle.org and https://corp.kaltura.com/ https://zoom.us Given the clear preference expressed by the students of DICAM in favor of traditional blackboard lectures actually held in the lecture hall and given also the reciprocal importance of the body language and thefacial expressions of the professor seen by the students and, vice versa, the ones of the students seen by theprofessor, the Department has therefore decided to adopt a simple blended teaching concept which tries tocreate an environment that is as normal as possible , both, for the professors and for the students.The concept consists in the high quality transmission of traditional blackboard lectures that are actuallyheld in the lecture halls in front of up to 50% of the students who are allowed to be physically present andto make this experience available as much as possible via low-bandwidth online streaming to the remainingstudents who have to follow the lectures online at home due to the COVID-19 restrictions. The two mostimportant pillars on which our blended teaching concept relies are the high quality view of the blackboardand the professor, combined with high audio quality to capture the speech of the professor, not only forthe students present in the lecture hall, but also for those online. Under pandemic internet bandwidthrestrictions, both pillars were anything else than trivial to realize, but in the next section we will givetechnical details of how these objectives can be reached with standard hardware and software. Furthermore, bidirectional communication is integral part of the blended teaching concept discussed in this paper, allowingthus the students who follow the lectures online to communicate directly with the professor, and makingtheir contributions, questions and comments also available to all the students who are physically present inthe lecture hall. As already stated in the introduction, the blended teaching concept adopted by DICAM deliberately does not present a novel pedagogical concept of how to teach mathematics, but on the contrary,aims at showing a simple but efficient technical concept of how to preserve the quality of traditional means ofteaching mathematics in the context of the COVID pandemics as far as possible. The three main objectiveswere: i) to preserve the high quality of traditional blackboard lectures which were usually appreciated bythe students in the past pre-COVID era also during the COVID pandemic and to make this form of lecturealso accessible to all students who were not able to attend the lectures in person, in particular also tothose with low internet bandwidth ; ii) to allow students to interact personally with each other and with theprofessors, complying with all the restrictions due to the COVID pandemic like maintaining a minimumdistance between each other and the obligation to wear a face mask during the entire period in which thestudents are present in the building; iii) to allow professors to continue using their well-established traditionalteaching concepts as far as possible, even under pandemic conditions. The same blended teaching conceptwas also adopted for the group exercises led by the tutors, allowing small work groups of students to attendthe group exercises in person, while the others were following online.The obvious shortcomings of the blended teaching concept illustrated in this section are the ratherstringent requirements on the computer hardware and software to be used in the lecture hall, combinedwith the necessary technological skills that needed to be acquired by the professors before and at thebeginning of the semester.To realize the concept detailed above, all lecture halls of the Department needed to be technicallyupgraded with an appropriate audio and video system, since no special equipment for blended teachingwas present at DICAM in the pre-COVID era. The Department furthermore organized a series of specialtraining sessions, in which the professors were trained to use the necessary hardware and software in orderto get ready for blended teaching before the beginning of the semester. In order to allow the students toget a preview of how the blended teaching would be in the first semester of 2020/2021 and in order to testthe equipment and to show professors the technical possibilities, the students were invited to join some ofthese training sessions online.
In order to establish a priori which students were allowed to enter the lecture hall in a given week, and whichwere not, the Department has carried out an online survey before the beginning of the semester in which thestudents could express their intention whether they wanted to attend lectures in person, or not. The choicewas free , but binding . As a result of this survey, in which only about 18% of all students chose to followlectures exclusively online, the Department divided those students who wanted to attend lectures personallyin sub-groups that would be allowed to come to the lecture halls based on a weekly rotation principle so4hat all students had the same number of weeks in which they could attend the lectures in person and inwhich they needed to follow the lectures online, respectively. A maximum nominal capacity of 50% of eachlecture hall combined with the percentage of students who decided to attend all lectures only online allowedmost of the students of DICAM to be actually present in the lecture halls for most of the weeks.An important choice of the adopted concept was to allow each professor to use his/her own laptopfor the blended teaching, for two reasons: i) using their own laptops, professors can use their preferredcomputer environment and operating system with which they have most experience and which they aremost acquainted with; ii) using their own laptops avoids touching common computer keyboards and pointingdevices and therefore solves the problem of disinfection of these devices between one lecture and the other.To reduce the stress induced by the obligation of wearing face masks continuously while present in theUniversity building and to reduce the pressure on the public transport system, the timetable was re-organizedin a morning block (8:30-13:30) and an afternoon block (14:30-19:30), so that some students were presentonly in the morning block and others only in the afternoon block. As anti-COVID measure the Departmentallocated one and the same lecture hall only for at most two different groups of students, with an interval ofone hour left between the two groups that was needed for cleaning purposes. Furthermore, one medium-sizelecture hall was kept empty as strategic reserve in case of COVID-related disinfection measures or in caseof technical difficulties in another lecture hall. The adopted timetable leaves a total amount of at most 25hours of real lectures in the lecture hall per group, which is not always sufficient to fit the entire timetable ofeach group of students. To mitigate the effects of this decision, before the start of the semester, all professorsof the Department could choose in a free but binding manner whether to offer their lectures purely online,or whether they wanted to adopt the blended concept outlined above. Most professors preferred the blendedoption for their courses (70%), but those 30% who chose the online teaching were enough to fit all blendedcourses into the given 25 hour limit. The pure online lectures were mostly held in synchronous mannerand could be followed by the students only at home and not from the university building. For this reason,the pure online lectures were scheduled only at a 2 hours distance from blended lectures, in order to allowstudents to move from the university building to their homes, and vice versa.The entrance and the exit of the university buildings were controlled electronically via a smartphoneapp that was specifically developed by the ICTS services of the University of Trento and which required thescanning of a QR code upon entry and exit of the university buildings. The students who were allowed toattend lectures in a given week were authorized top-down by an electronic authorization system that wascoupled with the cellphone app. Queues at the entrance were reduced by slightly shifting the start of thelectures at the MSc level and those at the BSc level by 15 minutes.
To realize the concept described above, the personal laptop of each professor became the crucial hub for theacquisition and distribution of the audio and video streams to be sent online. As videoconferencing systemwe employed ZOOM, already licensed by the University of Trento during the first phase of the pandemic anddue to its very good performance concerning audio and video live streaming even in the case of low availableinternet bandwidth. In order to minimize technical problems a priori , two completely redundant systemswere installed in each lecture hall. A videocamera system that allows to transmit traditional blackboardlectures, but also classroom experiments , as well as a graphics tablet and digital pen system [26, 15]. In thismanner, each professor was also offered the free choice of which means he/she wanted to use for teaching,eventually also a combination of both (videocamera + tablet). The videocamera system was also mandatoryfor those lectures which involve classroom experiments, very frequent in theoretical solid mechanics [3], seee.g. . The resulting main challenges that needed to be overcome to implement this strategy were thefollowing: • The lecture halls at DICAM were not at all prepared for blended teaching and thus needed to bespecifically equipped; • Achieving sufficiently high video resolution online that allows to read complex mathematical formulasclearly, despite the existing COVID bandwidth and HD video feature restrictions; • Achieving at the same time a sufficiently high audio quality both in the lecture hall and online, inparticular capturing the speech with high quality while the professor is turned towards the blackboardwhile writing and allowing also a clear bidirectional communication; • The fact that rather complex and relatively new technology needed to be handled by each professorduring his/her blended lectures; The highly heterogeneous computer hardware and operating systems resulting from the choice of allow-ing each professor to use his/her personal laptop, which also made the training and technical supportparticularly challenging and widen the necessary adapters to connect to the standard hardware installedin each lecture hall.In order to convey an idea of the scale at which we worked, let us also note that the concept presented in thispaper was applied to the entire Department, covering more than 50 courses from the fields of mathematics,physics, chemistry, engineering and social sciences. In what follows, we will further comment the abovechallenges indicating the strategies employed to surmount them.
The implementation of the developed blended teaching concept required the lecture halls to be furnishedwith a completely new set of electronic devices. The initial equipment of the classroom accounted for ablackboard, the projector system and, in large lecture halls, also a sound system so that the professor canbe clearly heard on site. On top of this we introduced: • Personal laptop. As already mentioned, the particular setup designed gives the professor the opportunityto employ his/her own laptop aiming at minimizing the novelties yielding from the use of new technicaldevices. Consequently, the laptop of the professor became the main control device of the blended teachinglectures. • Camcorder. To properly capture the blackboard and transmit physical experiments a full high definitioncamcorder was needed. It was further equipped with a directional microphone to record the speech ofthe professor in small classrooms. For large blackboards, instead of the standard camcorder proposedhere, it was necessary to employ a wide angle lens camera (e.g. PTZ Minrray UV5C40) controlled by IRremote control to allow switching between different parts of the blackboard and different levels of zoom. • Camlink 4K. The transmission of a high quality video signal from the camcorder to the computer requiredfor a 4K HDMI to USB converter. Let us note that although the quality broadcast by these devices goesup to 1080p at 60 fps or 4K at 30 fps, to reduce bandwidth consumption we suggest to limit the videocapturing program to 1080p at 25fps. • Active USB 3.0 extension cable. Typically the camcorder and, consequently, the camlink are far awayfrom the laptop so a USB 3.0 extension cable is needed. To properly preserve the video signal and providethe needed power supply for the camlink, an active cable was employed. • USB Hub 3.0. To minimize the number of connectors to be plugged into the laptop, they were allgathered in an unique USB hub of four ports that transmits input and output signals to and from thecomputer. At least SuperSpeed USB (USB 3.0) cables, connectors and ports are needed to transfer allthe signals, being preferred the use of USB 3.1 or 3.2 ports over USB 3.0 ports. • Graphics tablet and digital pen system. The alternative system to the blackboard was a rubber grip HD22 inch graphics tablet not hand sensible (i.e. a pen display), so that the writing is as close as possibleto traditional handwriting on a piece of paper, used together with the preferred interactive whiteboardsoftware. To be able to import and export pdf documents and save the lecture notes we have suggestedthe use of the OpenBoard software. Communication of the graphics tablet with the computer wasachieved via an input HDMI signal that duplicated the laptop screen and an output USB signal for therecording of the handwriting. • HDMI splitter. The laptop screen must be shared both with the students in the lecture hall using theprojector system and with the graphics tablet. To duplicate the signal an HDMI 4K splitter is employed.Since most projectors at DICAM are only equipped with a VGA input port a HDMI to VGA converteris connected to the HDMI cable exiting form the HDMI splitter. • Airlink. To facilitate bidirectional communication the comments of online students were broadcastthrough the pre-existing sound system of the large lecture halls using an airlink connected to the laptopvia bluetooth. For small and medium classrooms (up to 100 students) and without a pre-installed soundsystem an alternative was the use of a speakerphone (Jabra Speak 810) that can be connected to thelaptop using the audio jack or via bluetooth. The latter device allows listening to the online commentsin the lecture hall and captures also the voice of the people present in the classroom to be transmittedonline, while the former device only allows the online students to be heard in the lecture hall. https://openboard.ch/index.en.html Equipment Cost estimate in EUR
Laptop of the professor 0Panasonic HC-V770 camcorder 408Elgato Camlink 4k HDMI to USB converter 130Ugreen 10m active USB 3.0 extension cable 43Anker USB hub 3.0 13Wacom Cintiq 22 graphics tablet 9534k HDMI splitter Ablewe 16Primewire 2m HDMI cable 10Ugreen HDMI to VGA adapter 10BT DW 20BR Klark Teknik bluetooth airlink 89Jabra talk 25 bluetooth ear microphone* 28
Total amount: 1700 *one ear microphone was needed for each professor to comply with anti-COVID regulations • Ear microphone. In large lecture halls and when the professor is turned towards the blackboard, the useof a directional microphone was not enough to properly capture the speech with high quality. To solvethis problem a personal bluetooth ear microphone was employed by each professor. • Adapters. The resulting hardware of each lecture room, as explained below, requires the personal laptopof each professor to be connected thorough one HDMI and one USB/A port. Due to the great hetero-geneity of modern computer hardware, a large set of adapters has been made available allowing to usealso VGA, DisplayPort, mini DisplayPort, mini HDMI, micro HDMI and USB-C ports.A detailed list of the above components and their estimated cost can be found in Table 2.
A sketch of the connections among the different devices is included in Figure 1. On the one hand, to allowhigh quality capturing of the blackboard, the full HD video camera is connected via HDMI cable to a camlink4K which allows the transition to a USB 3.1 signal transmitted using an active USB extension cable to anUSB hub connected to the laptop of the professor. The alternative and/or complementary device for theblackboard is the pen display which transfers the data collected via a USB 3.1 cable connected to the USBHub. Meanwhile, the signal of the computer arrives to the tablet using an HDMI cable. To allow the displayof the laptop screen both in the graphics tablet and in the classroom projectors an active HDMI splitter4K is employed. Consequently, a single HDMI cable will take off from the laptop arriving at the HDMIsplitter from where two different HDMI cables transmit the same signal to the tablet and the projector; ifnecessary a HDMI to VGA adapter is employed. Let us note that the HDMI splitter is also connected tothe USB hub from which it receives the needed power supply. The speech of the professor is picked up froma bluetooth ear microphone and collected in the computer. To ease bidirectional communication the laptopis connected using a bluetooth airlink to the sound system of the lecture hall.
High quality low bandwidth video streaming via screen sharing.
In order to share visual informa-tion, the lecture halls were equipped with full HD video cameras, that capture the blackboard content, andgraphics tablets. In presence students can see the contents directly at the blackboard or on the projectorscreens. For online students the visual information were streamed via ZOOM. But ZOOM automaticallyreduces the video quality to 640 × far too low to transmit the con-tent of a blackboard with complex mathematical formulas, containing also small indices and superscripts,properly to the online students. The only option to overcome this intrinsic limitation and to obtain a propertransmission of the video signal of the blackboard in permanent full HD resolution (1920 × share screen feature of ZOOM. While this was rather obvious in the case of the use of a graphicstablet, it required the use of a third party video capturing software to capture and transmit the signal comingfrom the video cameras installed in the lecture hall. We found the following free video capturing software7igure 1: Sketch of the technical realization of the blended teaching concept at DICAM.particularly useful: VLC and OBS on Windows and Linux and Quicktime on Macintosh computers. Thereasonable compromise in this choice lies in the reduced framerate of the video, but maintaining the full HDresolution at all times, which is crucial to transmit the static content of the blackboard in optimal quality. Audio streaming.
The bluetooth ear microphone is crucial for blackboard lectures in order to suppressbackground noise and allowing the professor to talk while writing on the blackboard. This ear microphone,which serves to transfer the audio in high quality to the students attending the lecture online, is worn inaddition to the standard classroom microphone that serves to amplify the audio signal in the lecture hall.
Bandwidth measurements.
A series of experiments has shown that with our strategy of video streamingvia screen sharing the average framerate of the video signal of a traditional blackboard lecture transmittedonline via ZOOM was still about
24 fps at permanent full HD resolution, while the total bandwidthrequired in download by the online students was on average only
700 kbps , and hence fully adequate evenfor low bandwidth ADSL and average 4G connections. These results confirm that the adopted strategyis adequate for the high quality online streaming of mathematics lectures for most students with averageinternet connection.
Recorded lectures.
As a backup solution and to mitigate internet connection problems and difficultiesrelated to different time zones, most lectures were also recorded using ZOOM. They were then made availableto the students using the online teaching platform Moodle plus Kaltura video cloud service. As it is reflectedin the results of the questionnaires described in Section 4, the possibility of recording lectures may lead toan added value on the learning experience by allowing also the students attending in a synchronous way toreview particular parts of the lectures when autonomously studying the subject.
The former setup of the on site equipment has been designed aiming at minimizing the complexity of theconnections from the professor point of view. When arriving in the lecture hall the laptop of the professorneeds to be physically connected only with a single input/output USB/A cable (coming from the USB hub)and one HDMI cable (towards the HDMI splitter). Then, the sound system and the ear speaker are pairedvia bluetooth. Once all connections are established the ZOOM meeting is opened selecting the correct inputand output sound devices and the share screen mode is activated. At this point the professor should selectthe methodology he/she would like to employ for the lecture: and https://obsproject.com/ . Blackboard . In this case the auxiliary video capturing software is opened (VLC, OBS, Quicktime), thecamcorder is selected as input source and the regular video stream of ZOOM must be turned off. II. Graphics tablet . OpenBoard or the preferred interactive whiteboard software is employed. Thestudents in the lecture hall will be able to see the screen of the tablet on the projector screen.
III. Third party software . While sharing the screen any third party software like classical mathematicalprograms such as Matlab, Maple, R Studio, Mathematica, or PDF and Powerpoint files can be shown.Since all three possibilities rely on screen sharing via ZOOM and all devices are simultaneously connected,changing between the different options becomes straightforward!
Despite the lecture setup described above aimed at being as simple as possible from the professor point ofview, the blended teaching concept may happen to be a complete novelty for the teaching and technicalstaff and for the students.Thus, already before the start of the lectures, we organized a series of special training sessions , in whichthe professors were trained to use the necessary hardware and software in order to get ready for blendedteaching before the beginning of the semester. During the first part of these sessions, the new equipmentwas presented via demonstrations of how each of the three possible lecture modalities (namely the use ofblackboard, graphics tablet or third party software) was practically working. Moreover, in order to allow thestudents to get a preview of how the blended teaching would have been in the first semester of 2020/2021,they were also invited to join some of these training sessions remotely via ZOOM and to ask any questionsthey had. The presence of hundreds of online students during the demonstrations allowed to show andconvince the students and professors of the effectiveness of the adopted concept, included the bidirectionalcommunication. In the second part of the training sessions, we gave the possibility to each professor (inturn) to personally test the new equipment in order to really familiarize with it, verify the compatibility oftheir personal laptop with the standard hardware of the lecture halls and be aware of the eventually neededadapters. This was also an occasion for training the technical staff and a special group of students that washired for adjoint help during the semester.Indeed, to allow blended lectures to start and proceed smoothly, a continuous technical support wasorganized throughout the entire semester , operated by the technical staff of DICAM and by this group ofspecially trained students. During the first week, we offered a top-down supporting service, being a personof our staff present at the beginning of each lecture in each room ready to facilitate the lecture setup. Duringthe rest of the semester, due to the high level of autonomy reached by each professor, the offered servicewas changed to the bottom-up or on-demand type, i.e. only in case of necessity the professor could requestthe intervention of the technical staff always present in the building. Here we present quantitative results of the evaluation of the blended teaching concept illustrated in theprevious sections. Evaluation was carried out separately by the professors and the students via specificonline questionnaires. The concept presented in this paper was applied to the entire DICAM department,covering more than 50 courses and 18 lecture halls. For a sample of interest in the context of this journal,we considered all the courses involving teaching of mathematics and its application which result also to berepresentative of each year of study, namely the course of
Analysis 1 (BSc, first year),
Analysis 2 (BSc,second year),
Theoretical solid mechanics (BSc, third year),
Theoretical fluid mechanics (BSc, third year)and
Numerical analysis for PDE (MSc, first year). We received a total of 509 answers from the students,and we collect the opinions of the 6 professors leading the didactic team of each course. The data of thequestionnaires was collected after one month of blended lectures.More than half of the total answers comes from students attending the courses mostly in presence, athird of them attended mostly online and a part of them chose the preferred modality on a daily basedepending on personal necessities. Almost the totality of the received answers shows a general satisfaction for the implemented blended teaching concept and a clear preference for blended teaching with respect topure online teaching, see the detailed results reported in Figure 2. Indeed, the overall video and audioquality was very positively judged by around 85% of the students, see Figure 3 for more details about theanswers. Moreover, the key assumptions guiding the conception of our blending teaching approach wereconfirmed by the opinions of DICAM students: see Figures 4-5 where we summarize the results of check box -type questionnaires asking which new features introduced with blended teaching were important for them.With respect to pure online teaching, students appear to appreciate the major and easier interaction with9
Figure 2: Questionnaire results on the opinion on blended teaching versus pure online teaching (b) andgeneral satisfaction for our blended teaching implementation (c), from students attending in presence and/oronline according to (a). Total answers received: 509. Absolute values inside the graphs, approximatepercentage in the legend.
Figure 3: Questionnaire results on the video (a) and audio (b) quality of our blended teaching implemen-tation. Total answers received: 509. Relevant absolute values inside the graphs, approximate percentage inthe legend.professor and colleagues and the increased effectiveness of lectures thanks to the use of the blackboard andthe possibility to easily see professors body-language and expression. With respect to standard traditionalteaching, they appreciated the new high flexibility of switching between in presence and online lectures, notonly for COVID related emergency reasons, but also for normal everyday life organization. The availabilityof recorded lectures was greatly appreciated also in the free comment space.For what concern professors, they show a clear preference for the blended teaching concept with respectto the pure online teaching; in particular, they highly appreciated the possibility to continue using traditionalblackboards, showing experiments and having a true interaction with the students physically present in thelecture hall. Some of them are also willing to maintain several of the concepts here introduced even whentraditional teaching will be again possible, considering indeed that the possibility of recording, the increasedflexibility and the new available technological instruments can provide an added value to the lectures andwiden the reached target.
Moving beyond: innovative didactic concepts for the numerical analysis course.
Given theavailable new technological equipment and in order both i) to mitigate the adjoint difficulties students canperceive due to the pandemic crisis, but also ii) to provide additional and high quality learning opportunities,a specific teaching concept was designed and tested for the course
Numerical analysis for PDE (MSc, firstyear) held in 2020/2021 by the first two authors of this paper. For the contents of the course we referto [19, 21]. In addition to the blended theoretical lectures at the blackboard, according to the technicalconcept outlined in this paper, the course offered: i) weekly synchronous online computer exercises with fromscratch implementation of the studied numerical methods, ii) weekly exercise sheets with reference solutionsprovided under the form of a podcast/screencast , i.e. audio and video recordings of the commented solutionsof the exercise sheets, iii) two projects concerning the numerical solution of simplified real life applications, tobe developed in small groups and with students documenting their findings in a written report and presentingthe methods and results in class, following the concepts of a continuous assessment of the students [20] andthe flipped classroom principle [7, 5]; iv) mixed use of Italian and English language to also transmit specifictechnical vocabulary and the capacity to convey subject related concepts at international level.After five weeks of lectures, corresponding to almost the 50% of the entire course, the 25 studentsanswering the questionnaire were overall satisfied of this new offer, all of them found useful the weaklyexercise sheets and the commented solutions in the form of podcast, and 22 students appreciated the mixedlanguage approach with 18 of them thinking this results in an added value for the course.10
Figure 4: New features appreciated in blended teaching vs. pure online teaching. Total answers received forthe check box -type questionnaire: 509. Absolute value at the end of bars, approximate relevant percentageinside bars.
Figure 5: New features appreciated in blended teaching vs. traditional teaching. Total answers receivedfor check box -type questionnaires: 509. Absolute value at the end of bars, approximate relevant percentageinside bars.
In this paper we have shown all the technical details to realize an economically affordable and simple butefficient technical concept for the realization of blended teaching of mathematics for engineering studentsduring the COVID-19 pandemic. The concept is based on the three key assumptions i) that traditionalblackboard lectures, including the gestures and facial expressions of the professor are still a very efficientand highly appreciated means of teaching mathematics at the university; ii) that a lecture in mathematicsis a creative process that requires the physical presence of an audience so that the lecture can be bestadjusted to the needs of the students and finally iii) that undergraduate students need a minimum level ofdirect personal interactions and the possibility to get to know each other, especially in the first years. Allthree basic assumptions, as well as the perception of the audio and video quality have been quantitativelyverified at the aid of systematic online surveys that were sent to all students. The overall level of satisfactionwith the blended teaching concept presented in this paper was about 96%. A series of direct measurementsrevealed that the total internet bandwidth required in download for full HD video streaming via screensharing with ZOOM was rather low (only about 700 kbps) and thus makes the methodology applicablealso during pandemic internet bandwidth restrictions and makes blended teaching also available for thosestudents who have a fairly slow internet connection. If necessary and if possible, this concept could beadapted also in subsequent semesters.
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Acknowledgments
The authors would like to thank the following professors, students and technical staff of University ofTrento for the technical and logistic support that was necessary for the realization of the blended teachingconcept proposed in this paper. Professors: Prof. Dr. A. Vitti; technical staff of UniTN: S. Bernardini, C.Casagranda, I. Cristofolini, M. Filippi, M. Paoletto and F. Romagnoli; students: G. Bagattini, M. Bassetti,M. Bressanin, C. Cassar`a, M. Dalpiaz, M. Facchin, F. Leali, A. Lonardi, R. Panziera, C. Paoli, G. Scarcella,L. Trentini and D. Vallenari.The authors also would like to thank all the professors in charge of the courses in analysis and theoreticalsolid and fluid mechanics for their kind support and patience: Prof. F. Bagagiolo, Prof. D. Bigoni, Prof. L.Fraccarrollo, Prof. N. Pugno, Prof. G. Rosatti and Prof. A. Valli.Special thanks also to Prof. Dr. Oreste S. Bursi, Director of the Department of Civil, Environmental andMechanical Engineering, for granting all the necessary support and freedom to realize the concept detailedin this paper.
Saray Busto obtained her PhD degree in mathematics summa cum laude in 2018 at the University ofSantiago de Compostela, Spain. She is working in the field of numerical analysis for hyperbolic partialdifferential equations.
Michael Dumbser obtained his PhD degree in aerospace engineering summa cum laude in 2005 at theUniversity of Stuttgart, Germany. He is working in the field of numerical analysis for hyperbolic partialdifferential equations. Since 2018 he is Dean of Studies of the Department of Civil, Environmental andMechanical Engineering (DICAM) of the University of Trento, Italy. Together with C.D. Munz andS. Roller he was winner of the teaching award 2003 of the Ministry of University and Research of theState of Baden-W¨urttemberg, Germany, for the lecture
Numerical gasdynamics held at the Universityof Stuttgart, Germany, in 2003.
Elena Gaburro obtained her PhD degree in mathematics summa cum laude in 2018 at the Universityof Trento, Italy. She is working in the field of numerical analysis for hyperbolic partial differentialequations.