Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment
Abstract
:1. Introduction
1.1. Purpose of the Article
- To identify the challenges encountered during COVID-19-induced distance learning through a cross-national comparison of five European countries;
- To develop a theoretical framework and design requirements for online learning environments in mathematics education that address the challenges of distance education;
- To present the ASYMPTOTE system as one example for the theory-driven development of an online learning environment;
- To self-report the extent to which the ASYMPTOTE system meets the identified challenges of distance learning and the theory-based design requirements; and
- To prepare the field for a future systematic empirical evaluation of the ASYMPTOTE system.
1.2. Structure of the Article
- Loss of personal interaction;
- Lack of adequate formative assessment;
- Deficit of curricular resources;
- Lack of technical equipment; and
- Lack of digital competencies.
1.3. Working Definition of Online and Distance Learning
“In contrast to experiences that are planned from the beginning and designed to be online, emergency remote teaching (ERT) is a temporary shift of instructional delivery to an alternate delivery mode due to crisis circumstances. It involves the use of fully remote teaching solutions for instruction or education that would otherwise be delivered face-to-face or as blended or hybrid courses and that will return to that format once the crisis or emergency has abated. The primary objective in these circumstances is not to re-create a robust educational ecosystem but rather to provide temporary access to instruction and instructional supports in a manner that is quick to set up and is reliably available during an emergency or crisis.”
2. State of the Art: Distance Education in Europe
2.1. Distance Education in Germany
2.2. Distance Education in Greece
2.3. Distance Education in Italy
2.4. Distance Education in Portugal
2.5. Distance Education in Spain
2.6. Distance Education in Europe: An Interim Conclusion
2.6.1. Loss of Personal Interactions
2.6.2. Lack of Adequate Formative Assessment
2.6.3. Deficit in Curricular Resources
2.6.4. Lack of Technical Equipment
2.6.5. Lack of Digital Competences
3. Theoretical Framework
- Section 3.1 and Section 3.2: To take into account the need of personal interaction at distance, we refer to the well-known Community of Inquiry model and to e-pedagogies;
- Section 3.3: To address the lack of technical equipment and of digital competencies, we follow a mobile learning approach; and
- Section 3.4: To deal with the lack of formative assessment during COVID-19 distance education, we discuss the concepts of learning trajectories and learning paths. Building on this, we introduce the idea of learning graphs.
3.1. Community of Inquiry
3.1.1. Definition of a Community and Learning Community
3.1.2. Definition of a Community of Inquiry
3.1.3. The Community of Inquiry Model
- Social presence refers to the “ability of the community of inquiry participants to project themselves socially and emotionally, in all aspects of their personality, through the communication media that they use” [48] (p. 94);
- Cognitive presence refers to “the degree to which the participants are able to construct and confirm meaning by using thought and dialogue in a learning community” [50] (p. 55);
- Teaching presence refers to the role played by the teachers in the “design, facilitation and management of the cognitive and social processes from an educational point of view” [50] (p. 55).
- The teacher plays the role of a mediator and facilitator in the establishment of a community of inquiry [50]. In fact, he/she is called on to create organizational and educational conditions so that a quality collaboration between learners can take place. Therefore, especially in an online learning environment, in which learners can easily be distracted, become passive, or feel isolated and disconnected from their peers and teacher, it is important to establish connections between those three presences in order to create and maintain an active, interactive, collaborative, and engaging online learning environment.
3.2. E-Pedagogy and Online Instruction
3.2.1. A Model for Online Pedagogy
- At least two people that work or learn together, regardless of their location;
- People with special needs that can be assisted through technology; and
- Learning designers, academics, teachers, and trainers.
- Understanding the online learning processes;
- Technical skills to use the software features;
- Online communication skills (non-verbal, verbal, and written);
- Content expertise to share with and support students’ personal learning; and
- Personal characteristics, such as empathy, creativity, confidence, and flexibility.
3.2.2. The Role of the Teacher in Online Pedagogy
3.3. Mobile Learning
3.4. The Learning Graph Concept
3.4.1. Computer-Based Learning Environments
3.4.2. Individualized Online Learning
3.4.3. Learning Paths and Learning Trajectories
- A learning path is defined as a sequence of learning activities selected by the student and adapted to the student’s individual needs;
- A learning trajectory is a pre-selection of learning activities by the teacher based on the didactical considerations of a student’s learning process, and focusing on its evaluation.
- Course (or area), for example, the Linear Algebra course;
- Lesson (or general topic), for example, in the Linear Algebra course, the general topics are matrices, determinants, systems of linear equations, etc.;
- Topic (or concrete topic): for example, in the general topic matrices, the concrete topics are elementary operations on rows/columns of a matrix, elementary matrices and equivalence of matrices, row echelon form and reduced row echelon form, rank of a matrix, etc.; and
- Learning objects (or tasks) are the small units of learning, and are constructed regarding a certain learning objective.
3.4.4. Learning Graphs
- Main tasks are mandatory, in the sense that all learning paths and all learning trajectories that can be defined in the learning graph include all these vertices;
- Support tasks and challenge tasks are vertices that can belong to a learning path but do not belong to any learning trajectory;
- Each support task or challenge task is related to one, and only one, main task, and the set of directed edges E has the following kinds of edges:
- Vertices that are main tasks are total ordered, and there is a directed edge from the i-th to the (i + 1)-th vertex;
- For each main task with a non-empty set of support tasks, these tasks, together with their main task, are total ordered, where the main task is the root, the first element of the ordered set. In this ordered set, there is a directed edge from the -th to the (i + 1)-th vertex, and another edge in the opposite direction, from the (i + 1)-th to the i-th vertex;
- For each main task with a non-empty set of challenge tasks, these tasks, together with their main task, are total ordered, where the main task is also the root, the first element of the ordered set. In this ordered set, there is a directed edge from the i-th to the (i + 1)-th vertex, and a directed edge from each challenge task to the main task that immediately follows the main task related to these challenge tasks, in the order defined in the subset of main tasks.
- Whenever a subsequence exists , where is a main task, and , , are support tasks, it means that the support tasks to were used (most likely is accessed when a student cannot solve yet);
- If the opposite direction of the subsequence above exists, namely , it means that after processing the support task , the student is able to work on ;
- For the other hand, if a subsequence exists , where is a main task, and , , are challenge tasks, it means that the learner answered each task correctly and chose to proceed along the branch of challenge tasks;
- If an edge (, ) exists in the path, it means that, regardless of whether the learner answered the task correctly , he/she chose to proceed to the next main task, ;
- If is not a final vertex of the graph (the set of final vertices consists of the main and challenge tasks at the bottom), it means that the learner decided to finish his individual learning path before the end, e.g., for not having been successful, or simply by choice.
4. Theory-Based Design of Mathematics Online Environments
4.1. Design Requirements
- Loss of personal interactions, which are usually essential parts of the educational process, e.g., students–teacher interaction, communication among students;
- Lack of adequate formative assessment: diagnosis, evaluation of the learning process, individual support for different student contexts (lower-performing, students with special needs, etc.;
- Deficit in curricular resources for dealing, deeply and widely, with the distance learning context;
- Lack of technical equipment concerning the availability of devices, such as computers, smartphones, tablets, etc., and stable internet access, singularly affecting students with lower socioeconomic status; and
- Lack of digital competences in the school staff, of teachers, students, and parents.
4.1.1. Principles for Online Learning Activities by Garrison
- Plan for the creation of open communication and trust;
- Plan for critical reflection and discourse;
- Establish a community and cohesion;
- Establish inquiry dynamics (purposeful inquiry);
- Sustain respect and responsibility;
- Sustain inquiry that moves to resolution; and
- Ensure assessment is congruent with intended processes and outcomes.
4.1.2. Principles for Online Teaching by Sorensen and Baylen
- Enabling student–teacher interaction;
- Facilitating cooperation among students;
- Empowering active learning;
- Providing prompt feedback;
- Managing time on task;
- Communicating high expectations; and
- Respecting diverse ways of learning.
4.2. The ASYMPTOTE System
4.2.1. The ASYMPTOTE Idea
4.2.2. ASYMPTOTE Learning Graphs
- Main tasks (yellow) are mandatory tasks and form the backbone of an LG. In a desirable scenario, each main task covers an aspect of the overall topic. Hence, a student who solved all main tasks encountered and learned the minimum requirements for this topic. This implies that students should solve as many main tasks as possible.
- Support tasks (green) are linked to the right side of a corresponding main task and provide related tasks on a lower level, which can help solve the main task afterward. This might be an easier version of the task, or a repetition of a topic needed in order to solve the main task. Multiple support tasks can be assigned to one main task and solving them will never pose any drawbacks for the students.
- Challenge tasks (purple) are located on the left side of the main task and are supposed to be more difficult than the latter, challenging those students who finish early or seek to dive even deeper into the topic. Challenge tasks are unlocked upon solving their respective main task or preceding challenge tasks since more than one challenge task can be associated with one main task.
4.2.3. ASYMPTOTE Tasks
4.2.4. The Web Portal: Teacher’s Side
4.2.5. The App—Student’s Side
4.2.6. The Digital Classroom
4.3. Analysis of the ASYMPTOTE System
- Loss of personal interaction;
- Lack of adequate formative assessment;
- Deficit of curricular resources;
- Lack of technical equipment; and
- Lack of digital competencies.
4.3.1. Lack of Technical Equipment and Digital Competencies
4.3.2. Deficit in Curricular Resources
4.3.3. Lack of Adequate Formative Assessment
4.3.4. Loss of Personal Interaction
5. Final Remarks
5.1. Developing a Theoretical Framework for Online Education Tools
5.2. Development and Analysis of the ASYMPTOTE System
5.3. Outlook on the ASYMPTOTE System
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Challenge | GER | GRE | POR | ITA | ESP |
---|---|---|---|---|---|
Loss of personal interaction | x [13,14,16] | x [23] | x [32] | x [28] | x [16] |
Lack of Adequate Formative Assessment | x [13,15,16,18] | x [23,24] | x [32,34] | x [18,27] | x [16] |
Deficit of Curricular Resources | x [16] | x [21] | x [33,34] | x [26] | x [36] |
Lack of Technical Equipment | x [14,15,19] | x [23,24] | x [34] | x [29,30] | x [37,38,39,40] |
Lack of Digital Competences | x [13,14,16] | x [22,23] | x [31,33,34] | x [29] | x [37] |
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Barlovits, S.; Caldeira, A.; Fesakis, G.; Jablonski, S.; Koutsomanoli Filippaki, D.; Lázaro, C.; Ludwig, M.; Mammana, M.F.; Moura, A.; Oehler, D.-X.K.; et al. Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. Mathematics 2022, 10, 1628. https://doi.org/10.3390/math10101628
Barlovits S, Caldeira A, Fesakis G, Jablonski S, Koutsomanoli Filippaki D, Lázaro C, Ludwig M, Mammana MF, Moura A, Oehler D-XK, et al. Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment. Mathematics. 2022; 10(10):1628. https://doi.org/10.3390/math10101628
Chicago/Turabian StyleBarlovits, Simon, Amélia Caldeira, Georgios Fesakis, Simone Jablonski, Despoina Koutsomanoli Filippaki, Claudia Lázaro, Matthias Ludwig, Maria Flavia Mammana, Ana Moura, Deng-Xin Ken Oehler, and et al. 2022. "Adaptive, Synchronous, and Mobile Online Education: Developing the ASYMPTOTE Learning Environment" Mathematics 10, no. 10: 1628. https://doi.org/10.3390/math10101628