Primary school teachers’ views and practices across the hybrid classroom in Greece: an investigation about teaching language and mathematics
Article issu de la 18e conférence EUTIC: Humanisme numérique et durabilité sociale, MSH Bordeaux, 11-13 octobre 2023 organisée dans le cadre de l’Appel à projets MSHBx 2023 EUTIC2023.
Andreas MOUTSIOS-RENTZOS
Mathematics, History, Philosophy and Didactics of Mathematics Laboratory, Department of Pedagogy and Primary Education, National and Kapodistrian University of Athens, Greece
moutsiosrent[at]primedu.uoa.gr
Abstract
In this paper, the focus is on the hybrid space of the technologically expanded classroom of the primary school, as constituted in the synthetic interaction of the physical and the digital spacetime. In previous works, we discussed theoretical aspects of the spacetime of hybrid learning environments concentrating on the interdisciplinary opportunities, with a particular focus on the teaching and learning of mathematics. In this study, semi-structured interviews were conducted with three primary school teachers in Greece investigating their views and experiences about the teaching of language and mathematics (as most curriculum time is allocated to these courses) across the physical and the digital aspects of the hybrid learning environment. The results of the phenomenological analysis revealed both incongruencies and convergences across the hybrid classroom spacetime with respect to teaching language and mathematics in primary school in Greece.
Keywords: hybrid learning environment, interdisciplinarity, mathematics education, language education
Résumé
Dans cet article, l’accent est mis sur l’espace hybride de la salle de classe technologiquement élargie de l’école primaire, tel que constitué dans l’interaction synthétique de l’espace-temps physique et numérique. Dans des travaux précédents, nous avons discuté des aspects théoriques de l’espace-temps des environnements d’apprentissage hybrides en nous concentrant sur les opportunités interdisciplinaires, avec un accent particulier sur l’enseignement et l’apprentissage des mathématiques. Dans cette étude, des entretiens semi-structurés ont été menés avec trois enseignants du primaire en Grèce pour étudier leurs points de vue et leurs expériences sur l’enseignement des langues et des mathématiques (car la majeure partie du temps du programme est allouée à ces cours) sur les aspects physiques et numériques de l’environnement d’apprentissage hybride. Les résultats de l’analyse phénoménologique ont révélé à la fois des incohérences et des convergences à travers l’espace-temps de classe hybride en ce qui concerne l’enseignement des langues et des mathématiques à l’école primaire en Grèce.
Mots-clés : environnement d’apprentissage hybride; l’interdisciplinarité; didactique des mathématiques; didactique des langues
1. Setting the scene
In this paper, the focus is on the hybrid space of the technologically expanded classroom of the primary school, as constituted in the synthetic interaction of the physical and the digital spacetime (Giberti et al., 2022; Gil et al., 2022; Shapiro & Garner, 2021). In a previous work (Moutsios-Rentzos, 2023), I discussed theoretical aspects of the space and time of such hybrid learning environments concentrating on the interdisciplinary opportunities that such a spacetime may entail, while Ι also investigated the primary school teachers’ experiences, views, and practices about the links of the space of the physical, digital, hybrid learning environment in particular with the teaching and learning mathematics. Following these, it may be argued that the implicitly and explicitly established social system of the school class is violently questioned, as within the digital environment the spatiotemporal and societal rules may not be the same, which requires appropriate engineering and planifications to preserve a desired level of teaching and learning compatibility, as well as of social coherence, sustainability of the hybrid class. At the same time, it was posited that such hybrid learning environments may constitute the communicational space that may act as the learning bridge that is essential for the interdisciplinary thinking/teaching/learning of the various protagonists to emerge. On the other hand, it was also argued that the spatiotemporal characteristics of the hybrid learning environment may or may not render learning environment permeable to communicational interactions between courses of different disciplines.
The proposed approach (Moutsios-Rentzos, 2023) drew upon a phenomenological, systemic perspective (Bertalanffy, 1968; Davis & Simmt, 2003; Jacobson & Wilensky, 2006; Moutsios-Rentzos & Kalavasis, 2016; Sokolowski, 2000) and on Lefebvre’s (1991) differentiation amongst the perceived space, the conceived space, the lived space, in order to discuss the pedagogical school class subsystem at the interaction of “a) the designed space, the designers’ space (e.g., the architects, the programmers etc.), b) the constructed space, the space as constructed by its users, and c) the given space, the space as identified by the laws of physics of the material world within which we (inter)act” (Moutsios-Rentzos, 2023, p. 257). Moreover, “various functions of the pedagogical space, organized (e.g., working in groups, co-teaching, inclusive educational practices etc.) or spontaneous (e.g., games during breaks), are closely inter-related with the properties of this space” (Moutsios-Rentzos, 2024, p. 673–674).
In Moutsios-Rentzos (2024), the aforementioned theoretical approach was employed to empirically investigate the primary school teachers’ experience with the hybrid space and their teaching practices on mathematics, as they move across its digital and physical aspects. The investigations were guided by an explicit focus on whether the teachers attempt to promote qualities of mathematics learning as linking links (Moutsios-Rentzos & Kalavasis, 2016; Moutsios-Rentzos et al., 2017). The findings of that study identified that the teachers converged in their attempting to pedagogically engineer the digital space to meet the spatiotemporal characteristics of the physical space. However, three distinct ways that the teachers were related to the teaching and learning mathematics phenomena in the hybrid space:
Mathematics teaching cannot occur in the synchronous hybrid space—denial of the new technological means as being appropriate for and/or relevant to mathematics teaching and learning.
The hybrid space may be engineered to fit some of the requirements of the mathematics teaching and learning —partial acceptance the new technological means as being appropriate for and/or relevant to mathematics teaching and learning.
The hybrid space may be engineered to fit all requirements of the mathematics teaching and learning —acceptance the new technological means as being appropriate for and/or relevant to mathematics teaching and learning.
(Moutsios-Rentzos, 2024, p. 678)
In this paper, I extend the empirical investigations by including the primary school teachers’ views and experiences with the hybrid learning environments with respect to the teaching of both language and mathematics in Greece, thus explicitly addressing whether the teachers promote learning as linking links within mathematics, as well as amongst mathematics and other disciplines (in this case, language). The two courses were chosen as representatives of the two courses that most of the curriculum time is allocated. Moreover, from a societal, communicational, and epistemological perspective, language constitutes the main means for communication in contemporary societies, whilst mathematical notions and language seems to dominate the communicational space of modern sciences. It is hypothesized that the teachers, as they move across the hybrid learning environment, they are experiencing implicit, invisible transformations that may affect their teaching practices. It is also hypothesized that the different ontologies, epistemologies, and pedagogies that are linked with the different courses may act as a crucial differentiating factor differentiating the quality and degree of these transformations.
Consequently, the main research question of the reported study is: What are the views and teaching practices of primary school teachers about language and mathematics across the hybrid classroom?
2. Methods and procedures
2.1. The participants and the educational context
The multiple case study (Sena, 2024) was conducted with two in-service teachers in public Greek primary schools and it is part of an ongoing larger project (see also Moutsios-Rentzos, 2024). In the Greek educational system, primary school consists of six Grades (6-12 years old students), with most of the courses taught by the same teacher (except, for example, foreign languages, arts, gymnastics etc.). Primary school teachers are pedagogues, usually holding a four-year bachelor’s degree (‘ptychio’). During their undergraduate studies, they have to pass, amongst others, general pedagogical courses, discipline-specific courses (Greek language, mathematics, physics etc.) and courses about its didactics, while they also have to attend obligatory practicum.
For the purposes of this paper, two primary school teachers were included: Maya and Flora (fictional names). Both teachers were purposively chosen to be highly trained with respect to mathematics education and to differ in their school experience. Considering their overall teaching experience, Maya is a relatively novice teacher with 3 years of teaching in school experience. On the other hand, Flora is an experienced teacher with 19 years of teaching in school experience, as well as administrative school experience (4 years).
Regarding mathematics, Maya holds a master’s degree in Mathematics education and she is a PhD candidate in Mathematics Education. Flora holds a master’s in Educational Technology with her dissertation focused in the teaching and learning of a mathematical content employing ICT. Moreover, these were reflected in Maya’s and Flora’s very positive identification with respect to their being good at mathematics and at teaching mathematics: self-identification and by significant others (colleagues, principals, parents, and students; drawing upon Abreu et al., 2002).
Considering language, the two teachers did not hold any additional to their ptychio degrees (nor attended any additional training about language), nor about language teaching. Nevertheless, they both appeared to hold very positive identification with respect to their being good at language and at teaching language. When asked to compare their identification in the two courses, both teachers appeared to be more positively identified about mathematics. For example, Flora responded (note that the time in ‘[ ]’ denotes the start of the quote in each interview)
Researcher: Do your colleagues consider you to be good at mathematics?
Flora: Yes, because they are addressed to me. They all come to see how I did the course and discuss if they have any difficulties. [05:50]
Researcher: What about language?
Flora: Okay, they [colleagues] think I am good, but they’re not addressing me, as I said [in mathematics]. […] they think I’m good, but they’ll ask me for syntax grammar. They won’t ask me for writing reports. Mostly about syntax I am asked about grammar.
Moreover, the teachers’ ICT and distance learning training and expertise is considered to be a crucial factor of the present study. Flora appears to be very well trained (further supported by her masters training), while Maya is mainly self-trained. Furthermore, their identity appeared to accord with their training: Maya seemed to hold a relative neutral identity about ICT, whereas Flora seemed to positively position herself with respect to ICT.
Figure 1 – The key features of e-class
Screenshot from https://www.openeclass.org
Figure 2 – The key features of e-me
Screenshot from https://e-me4all.eu
Regarding ICT and distance teaching in Greece, following a post-pandemic law, the teachers are now obliged to employ digital methods as Emergency Remote Teaching (Nilsberth et al., 2021); for example, in the case that extreme weather conditions prevent the use of the physical class. The ICT tools that are provided by the Government to the teachers in the public schools in Greece are both synchronous and asynchronous. Cisco Webex is provided (https://www.webex.com) to the teachers for synchronous teaching. Webex is not designed specifically for education, but for generic distant collaboration. Moreover, the teachers may build their digital classroom, using two platforms (see Figure 1 and Figure 2): a) the electronic school class (e-class; https://eclass.sch.gr), which is based on the Open e-class platform (https://www.openeclass.org), and b) the digital education platform e-me (https://e-me.edu.gr), which is based on the broader e-me project (https://e-me4all.eu): “a collaborative, social and extendable Digital Educational Platform, a digital working and collaboration space for pupils and teachers.” These platforms have been designed for educational purposes, but they seem to differ in their interface and their characteristics, thus allowing for the construction of a digital teaching and learning space with different characteristics.
2.2. The investigations
In the broader study, we focused on the teaching and learning of mathematics and language in the physical space, the digital space, and the transition from one space to the other, including questions to the teachers about: their mathematics/language teaching self-efficacy and autonomy; the learning theory upon which their mathematics/language teaching is structured; their pedagogical practices; their valuing of the digital mathematics/language class; their awareness of the limitations and the possibilities of the digital class etc. In this paper, in line with Moutsios-Rentzos (2024), I report on findings with respect to the following themes of questions about both mathematics and language, which specify the aforementioned main research question of the study:
- Views about distance teaching (synchronous and asynchronous; including Emergency Remote Teaching), both on its own right and in comparison with in-person teaching. First, we asked the teachers to choose spontaneously five words to describe their positioning about being “good”, “useful”, “appropriate” and, subsequently, to elaborate on these.
- Reflections about teaching practices about distance teaching (synchronous & asynchronous; including Emergency Remote Teaching), both on its own right and in comparison with in-person teaching; use of in -class discussion, whiteboard and ICT, desks formation, permanent elements of space (windows open, curtains, art etc.), non-permanent elements of space (windows open, curtains, art etc.), functional diversity (“parallel support”) etc.
In the broader study, several sources of data were employed: interviews, follow-up interviews, and focus groups. In this paper, we concentrate on the data collected through the initial semi-structured, in-depth, video-recorded interviews (Flora’s interview lasted 62 minutes, whereas Maya’s 79 minutes).
Considering data analysis, for the purposes of this paper, phenomenological analysis was conducted (Moustakas, 1994; Wertz, 2005) directly on the video recordings through Atlas.ti. Phenomenological analysis was chosen as it “descriptively delineates the invariant characteristic(s) and clarifies the meaning and structure/organization of a subject matter” (Wertz, 2005, p. 168), thus aiming to reveal the intentional relationships of the interviewees with teaching mathematics and language in the hybrid classroom.
3. Results and discussion
Echoing the findings reported in Moutsios-Rentzos (2024), in this paper we mainly focus on the synchronous digital class, as both Maya and Flora did not seem to differentiate the asynchronous digital class from the homework they assign in the physical class. For example, Maya notes that in asynchronous class the teacher does not really know who provides the answers (note that the time in ‘[ ]’ denotes the start of the quote in each interview).
Maya: Now, whether the child made the post or whether the parent made it, I couldn’t know. [54:45]
Similarly, Flora states that it is important for her to systematically assess the asynchronous contributions (as in homework) to appropriate engineer teaching.
Flora: […] you need to correct the asynchronous ones [exercises] to identify the mistakes of the week so that the mistakes can be used didactically and the children can improve […] and we can have a direct picture [of their learning]. [12:22]
Considering their first reactions about online and offline teaching, both Maya and Flora started by stressing that the use of specially designed interactive ICT tools in the distance teaching of mathematics.
Flora: More difficult. Namely … more use of technology is needed in distance synchronous [teaching] to enable students to understand […] be more interactive. [09:35]
Maya: Very difficult. Lack of supervision […] Great difficulty. Especially, in the lower grades of primary school. [12:35]
This does not appear to be the case for the teaching of language. For example, Maya notes that in language an effective form of teaching could just involve communicational activities, similar to the ones that happen in the physical class:
Maya: […] we might start a simple sentence “The sun shines”, one child would continue “The sun shines in the sky”, the next “The sun shines today in the sky” and somehow, that is, all together make a sentence. […]a lot of speech production, which fits into all sections of the book. [51:50]
Maya goes on to express her strong disagreement with the distance teaching of mathematics, employing a denial stance:
Maya: Let me say that I believe that in mathematics distance teaching is not feasible, because you cannot have supervision of what the child writes and because always in mathematics, I will not say many times, you have to see exactly what you write in the notebook, so that, what can I say, to say about the value of a digit, that each digit is written correctly in its place. Or, about geometry, how to hold the ruler, how to use the measuring instrument, you need that. [16:39]
Flora does not appear to share Maya’s reservations about teaching mathematics in the hybrid space. Flora seems to hold an acceptance stance, in the sense that she appears to consider appropriate teaching is feasible given the appropriate tools and teacher training with these tools. For example, considering working in groups during class, Flora notes that in the distance synchronous class things happen as in the physical synchronous class.
Flora: [in the physical class] again there is discussion, they get up … this is what the typical lesson is like [in the digital class] They all take turns again. With Webex. That is, they raise their hand […] and if they don’t raise their hand, I’ve jotted down their names and put a check so everyone can take turns saying it. […] When we have a physical lesson for them to speak, they raise their hand. Always. And in Webex they press the button. [they are] in ‘mute’ because you hear things from within […] they mostly work in teams at Webex. […] I do split room and join each team. […] I have a very limited time, that is, with a maximum of two minutes in each team. […] at least three [children per team]. Because our classes are not large. Three to four. [41:26]
In this excerpt, Flora’s intentional relationship with distance teaching, identified as acceptance, along with her expertise in ICT appears to guide all her decisions. She uses the affordances of the platform to create a teaching and learning environment that accords to the way that she teaches in the physical classroom. Nevertheless, it should be stressed that she evaluates the appropriateness of her practices based on the degree that they accord with her views about what appropriate mathematics teaching is and not based on a superficial matching with the teaching of the physical class teaching.
Furthermore, Flora stresses that her ICT training enabled her to successfully survive the novel learning environment and to also support her colleagues, which highlights the importance of appropriate teacher education programs.
Flora: And something else is that more training is needed. Yes, of course, more training is needed, because we were invited to do a Webex course […] if I did not have the knowledge I had from the University of Piraeus [referring to her master’s] I would not be able to respond because no one else knew in my school […] and I had to help the others. [17:50]
Maya’s reservations are manifested in her strongly negative portrayal of her role as a teacher in the mathematics digital classroom, which is in stark contrast with her strongly positive view of herself as a teacher in the mathematics physical classroom.
Researcher: I will ask you how you feel about your role as a teacher when mathematics is taught in person [24:27]
Maya: Nice, useful, important, I feel like I’m helping kids.
Researcher: When language is taught in person, how do you feel?
Maya: The same, the same words.
Researcher: When teaching mathematics remotely, how do you feel about your role as a teacher?
Maya: I feel like I’m making fun of myself and others. That is, that there is no lesson.
Researcher: The ‘others’ are the children?
Maya: Both children and parents. Who similarly make fun of me that we are having a lesson at that time.
Things appear to be different when considering language, as Maya notes that in the digital language classroom.
Maya: I feel like something is happening with a few children, with low participation, not with everyone […] that’s how it feels. [26:22]
In the last two excerpts, Maya’s intentional relationship with distant teaching may be discerned. She feels inadequate and in contrast with her high teaching self-efficacy of her teaching in the physical class. It appears that her relationship with the hybrid environment seems to prevent her from usefully implementing her desired practices. Echoing Flora’s comments about ICT training, Maya’s negative relationship is hypothesized to be also linked with her lack of appropriate training in the digital environment, as she notes that “I had to train myself in the use of the new tools.” At the same time, this relationship appears to differ in the two courses. It is posited that her differentiated level of expertise in mathematics and language may be linked with this. Maya is very well-trained in mathematics teaching; she is aware of the qualities that the mathematics teaching should bear. Thus, the distance between her expectations and her capacity of realizing these expectations in class seem to diverge more in the case of mathematics than in the case of language.
Consequently, with respect to the teaching of language, Maya seems to hold an overall acceptance stance.
Maya: In language things are a little better, because there is a lot of speech production that can be both oral and written. He can even write in conversation, in chat, the child. So that’s why it’s ‘saved’. [17:23]
However, Maya’s stance changes to denial in the case of teaching language only in the beginning of the first two grades of primary school.
Maya: For language, first grade and second don’t say, it can’t work remotely at all. Because it is the children in the food who then begin to write and read. That is, first class could not work at all. Monday, maybe from the middle of the year onward. [18:08]
Flora also seems to hold an acceptance regarding the teaching of language, as her teaching can be engineered to fit the desired requirements.
Flora: Language exercises, drill exercises. So it makes no difference [19:27]
Nevertheless, she appears to hold strong reservations about the time management and allocation of the digital classroom and its effects especially in the teaching of language.
Flora: Yes, because at school it [class hour] was 45 minutes […] at Webex it was 20-25. So, it was a time constraint that we had. If you had the same time… If I had the same amount of time, I could combine the benefits of physical presence and distance. [15:50]
Overall, both Maya and Flora converge in their views that, in general, the teaching of mathematics and of language differ in their requirements. They both acknowledge the effect of the nature of the subject matter in the teaching practices employed. For example, Maya notes:
Maya: […] basically what is similar in language and mathematics is that I allow the children to talk a lot […] In language the children talk more, because there is the conversation [she means as part of the nature of the course]. In maths it’s a longer distance, because [in the digital classroom] there’s no such thing as writing together or taking the child’s pencil and showing him/her something how I should do this. And that’s what creates my insecurity that I can’t help.
Maya feels that the hybrid learning environment appears to be more compatible the requirements of the teaching of language than of the teaching of mathematics. For Maya, this resulted in her feeling of not being a good mathematics teacher. This situation appeared to be supported by Flora’s comments about her colleagues in school.
Flora: They thought [her colleagues] physical presence was much better than distance. In mathematics especially. That is what my colleagues have said. That they had a hard time in math. While in language they did not have difficulty. In mathematics they found synchronous teaching. [because] Many of them did not know how to use technology. And they took a stylus and did what they did in class. […] In the language they [her colleagues] found no differences. While in language, I find it much more difficult. Because of time. It’s difficult. [52:47]
In this excerpt, Flora appears to differ in her view about the level of difficulty of distance teaching, identifying language teaching as more difficult. We wish to stress that Flora’s difficulty is within her acceptance stance. The teaching for both courses maybe engineered to the required qualities, but it is more difficult for her to achieve that in language teaching. For Maya (and presumably for Flora’s colleagues), difficulty is situated within denial or partial acceptance. Thus, Maya’s difficulty is interiorized in her not satisfactory self-identification as a mathematics distance teacher, whilst Flora’s difficulty is registered as a peripheral pragmatic constraint which does not affect her teaching self-efficacy.
Concluding remarks
In this paper, we implemented a theoretical perspective about the teaching and learning affordances of the hybrid space hybrid classroom spacetime with respect to teaching language and mathematics in primary school in Greece. We investigated the existence of unidisciplinary and interdisciplinary bridges and fractures within the space of the digital class.
The teachers showed a high level of awareness of the existence of a hybrid teaching and learning space, as indicated by their reported engineering to the digital learning environment to meet the physical learning environment.
The teachers appeared to be mainly concerned about the synchronous teaching, as the asynchronous digital class was dealt in a similar manner as preparing homework and, consequently, they did not experience differences from the physical class.
Our hypothesis that the teacher’s stance (denial, acceptance, partial acceptance) would be affected by their differentiated experiencing the teaching requirements of language and mathematics was confirmed. It appears that the intentional relationships of the teachers with the subject matter, with mathematics appearing to require more technologically demanding transformations. This may also be linked with the fact that these teachers were highly trained in mathematics teaching. Current research focuses on highly trained teachers in language teaching to investigate the links between subject-specific teaching expertise and the hybrid learning environment.
Furthermore, the familiarity with the employed technological means appeared to crucially affect the teachers’ experiencing the hybrid classroom and especially with the teaching of mathematics at the expected high level that both teachers required. Future research may focus on the effect of the teachers’ being trained in the employed hybrid environments.
Consequently, it is argued that the proposed theoretical approach allowed us to identify fractures in the hybrid primary school classroom that appear to be strongly linked with the teaching and learning qualities that are special to each course. Language and mathematics were chosen as the core components of most of the contemporary educational systems, thus crucially affecting their effectiveness. Considering the ongoing radical technological transformations, it is posited that further research should be conducted to support the teachers to effectively engineer the spacetime of the novel hybrid learning environments, to allow for the students’ developing qualities of learning that are appropriate for a complex, interdisciplinary lifeworld.
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mshbordeaux (14 octobre 2024). Primary school teachers’ views and practices across the hybrid classroom in Greece: an investigation about teaching language and mathematics. Maison des Sciences Humaines Bordeaux. Consulté le 15 janvier 2026 à l’adresse https://doi.org/10.58079/12hl7


