Digital Videos and Critical Mathematics Education: knowledge displacements in educational action

Vídeos Digitais e Educação Matemática Crítica: deslocamentos do saber na ação educativa

Abstract

This paper aims to critically examine how the mathematical discourse in the video “The Geometry of Bees” is expressed in terms of mathematics and multimodality. Based on an analysis of multimodal discourse, grounded in social semiotics, from the perspective of the construct ‘humans-with-media’ and critical mathematics education, we proceeded to analyze the narrative in question. The methodology included modal data collection and multimodal transcription. The video was selected for its relevance to the application of mathematical concepts and its critical approach to geopolitical and environmental issues. We conclude that the producers-with-media construct a discourse that encapsulates social contexts, physicality, and languages, and is constituted through the interaction of various levels of world knowledge and even technology, giving meaning to the video narrative, which serves as an agent of knowledge displacement in educational action.

Palavras-chave
Vídeos Digitais; Análise do Discurso Multimodal; Educação Matemática Crítica

Resumo

Este trabalho objetiva compreender criticamente como é expresso, em termos de matemática e multimodalidade, o discurso matemático do vídeo A Geometria das Abelhas. Com base na análise do discurso multimodal, alicerçada na Semiótica Social, na perspectiva do construto Seres humanos-com-mídias e na Educação Matemática Crítica, procedemos à análise da narrativa em questão. A metodologia incluiu coleta de dados modais e transcrição multimodal. O vídeo foi escolhido por sua relevância na aplicação de conceitos matemáticos e sua abordagem crítica de questões geopolíticas e ambientais. Concluímos que os produtores-com-mídias constroem um discurso que encapsula contextos sociais, fisicalidade e linguagens, e se constitui mediante a interação de diversos níveis de conhecimento de mundo e, inclusive, tecnológico, para dar sentido à narrativa do vídeo, sendo este agente de deslocamento do saber na ação educativa.

Keywords
Digital Videos; Multimodal Discourse Analysis; Critical Mathematics Education

1. Preliminary Considerations

Human communication is a complex phenomenon that encompasses a range of expressions, including both verbal and nonverbal forms. Digital videos are rich in different modalities, which combine to form contextually rich meanings. This article aims to critically examine how, in terms of mathematics and multimodality, the discourse is expressed in the video A Geometria das Abelhas [henceforth, The Geometry of Bees], registered in the Festival de Vídeos Digitais e Educação Matemática (FVDEM) [Digital Video and Mathematics Education Festival]. This study reports a subproject (Carvalho, 2023)¹ integrated into a larger project, whose objective is to understand the nature of digital videos in mathematics education (ME). This subproject focuses on the relationship between videos and critical mathematics education (CME).

Theoretically based on the construct humans-with-media (HwM) and social semiotics, and dialoguing with CME, which intertwines Paulo Freire’s pedagogy, Carvalho (2023) focused on videos that address critical ME concerns. These videos are considered agents of the displacement of knowledges, as they encapsulate social contexts, physicality, and diverse languages, contributing to the construction of a multimodal narrative that opposes a monocultural view of top-down and hegemonic mathematics.

The Geometry of Bees is part of a cultural context influenced by the sociopolitical and historical moment experienced in Brazil since 2016, with the removal of democratically elected then-president Dilma Rousseff, initiating a series of refined acts of oppression that resulted in the loss of workers’ rights, the increase in extreme poverty, and unemployment. This scenario expanded in 2018/2019 with the rise of a right-wing government (Arroyo, 2019), which was further exacerbated in subsequent years by the COVID-19 pandemic, altering and deepening the processes of oppression, access to healthcare, and income. This also affected the Mathematics Education agenda in Brazil, reinforcing trends that were already present, such as the use of digital technologies, EMC, and the Philosophy of Mathematics Education (Borba, 2021), which gained new momentum during the pandemic.

Engelbrecht and Borba (2024) state that advances in computer technology have significantly changed the way mathematics is used, shifting the focus from calculation to the development of mathematical thinking. This scenario presents both opportunities and challenges, particularly in the critical dimension of mathematics, which encompasses all aspects of social life (Skovsmose, 2001).

The presence of digital technologies in ME has historically been analyzed as a developing digital culture, as described by Borba, Scucuglia, and Gadanidis (2014). They identify phases that marked the integration of digital technologies into educational practices since the introduction of computers into mathematics classrooms in the 1980s. The first phase involved the use of Logo software and programming, with a focus on the teaching and learning process. In the following decade, the emergence of software with user-friendly interfaces, i.e., computer algebra systems (Mathematica, Maple, and others), dynamic geometry, and graphic calculators enabled pedagogical advances, leading to the intensification of teacher education courses, characterizing the second phase (Borba; Scucuglia; Gadanidis, 2014).

At the beginning of the 21st century, the Internet transformed education with online distance learning, marking the third phase of digital technology in higher education. The fourth phase was characterized by the rapid expansion of the Internet and its integration into everyday activities, enabling real-time videoconferencing and the increasing use of videos in educational and scientific processes, although not all productive sectors have adopted these technologies on a large scale (Borba; Scucuglia; Gadanidis, 2014).

The COVID-19 pandemic, which began in the first quarter of 2020, accelerated the adoption of digital technologies and revealed profound social inequalities in digital inclusion and access to education in Brazil (Borba, 2021). As a result, many mathematics classrooms began to operate online, giving rise to the fifth phase of digital technologies in ME, characterized by a boom of lives and the increased use of videos by students and teachers (Borba; Souto; Canedo Júnior, 2022). This scenario highlighted the need for continuous adaptation to new forms of teaching and learning facilitated by technology.

In this sense, FVDEM, since its 1st edition in 2017 (Carvalho; Costa; Borba, 2022), meets this need by proposing the production of videos, at a national level, connecting with schools through social networks, educational communities, and research groups. This blended event aims to encourage the creation of videos as a space for the school, university, and broader community to express and create mathematical narratives (Carvalho, 2023; Cunha; Borba, 2025; Borba et al., 2025). The festival, highlighted in the UNESP PPGEM, is “a locus of research, of research extension and, as a repository and locus of virtual visits, it exerts a power of action for teaching and learning” (Carvalho; Costa; Borba, 2022, p. 11). Furthermore, FVDEM is important in ME because it values curriculum construction from the bottom up, starting in the classroom and involving teachers, students, and communities from diverse Brazilian regions and cultures.

Videos are dynamic tools that stimulate the senses and promote mathematical learning (Borba; O’Halloran; Neves, 2021). They combine different forms of digital communication, such as images and sounds, using technologies such as cameras and editing software. This study demonstrates how students-with-media integrate social, physical, and linguistic contexts, interacting with diverse levels of knowledge. From the segmentation of The Geometry of Bees, we analyze how video serves as a means to displace knowledge, challenging and enriching the critical understanding of mathematics in the educational context.

2 Theoretical assumptions

In this article, the vision of digital technology is grounded in the construct HwM, in which humans and non-humans collectively produce knowledge and modify, through an intershaping relationship, their ways of being, doing, and existing in the world with themselves and with others. Borba, Souto, and Canedo Júnior (2022, p. 24-25) affirm that “humans construct media, and media construct what it means to be human at a given historical moment”. This implies that technologies, historically, alter, transform, and condition what a human being is. For example:

[...] influencers were considered for their good speaking, good writing, or even for having a specific skill. Today, an influencer is someone who has a significant number of followers on social media, changing their place in the world. Hence, we believe that the way we perceive human beings and their actions is modified and in an intershaping relationship with technologies (Carvalho; Gimenez; Borba, 2022, p. 4).

From this perspective, technology alters the way human beings interact with the world, transforming humanity itself and shaping its culture. In another direction, O’Halloran (2009, np) notes that “Digital technology is multimodal social semiotic technology” because it provides means to combine semiotic resources (SR), unfolding in new and innovative ways in society in and for the production of meanings.

The multimodal approach is consolidated in the articulation of the diverse resources used in contemporary social practices, aiming at communicating. In this study, the term “semiotics” refers to SRs, such as language, visual images, and mathematical symbolism, and the term mode is used “[...] to refer to the channel (auditory, visual, or tactile, for example) through which semiotic activity takes place” (O’Halloran, 2005, p. 20). Therefore, the FVDEM video is a multisemiotic and multimodal digital text, as it employs more than one semiotic resource and multiple modes of communication. Such SRs, when mobilized and integrated, construct discourses. These are understood, from a social semiotic perspective, as “socially constructed knowledge of (some aspect of) reality.” (Kress; Van Leeuwen, 2001, p. 4). In this way, HwM are producers of discourse present in digital videos (Carvalho, 2023).

Therefore, we understand mathematics as a multisemiotic discourse (O’Halloran, 2005) and as a form of multimodal semiosis (O’Halloran, 2015). O’Halloran (2005, p. 10) investigated the relations between language, symbols, and images in mathematical discourse, understanding mathematics “[...] as ‘multisemiotic’ constructions; that is, discourses formed through choices from the functional sign systems of language, mathematical symbolism, and visual display”. These discourses in the FVDEM videos employ not only speech and embodied action, but also mathematical symbolism, diagrams, and images, which are introduced into the discourse through verbal and gestural references, thereby lending meaning to the video.

More specifically, O’Halloran, Tan, and Wignell (2016) understand SRs as systems of experiential, interpersonal, and textual meanings, which fulfill, respectively,² differentiated societal metafunctions: structuring experience and making logical connections in the world; establishing social relationships; creating a position in relation to the world; and organizing these meanings [ideational (experiential and logical) and interpersonal] into multimodal ones. Thus, every example of mathematical communication is, “[...] thus conceived to involve not only signification of mathematical concepts and relationships but also interpersonal meanings, attitudes and beliefs” (Morgan, 2006, p. 220).

From a Freirean perspective, the discourse of human beings can be grasped through reality. In the educational context, Freire (2020a) discusses discourse as a codification to be decoded, seeking its social significance. In this logic, the author related the decoding process, among other aspects, to the demystification of science and technology, in opposition to the model of education that serves the dominant elites, relegating criticality and reflexivity about the world to maintain the status quo.

These understandings are consistent with the concerns of CME studies, which focus on the use and function of mathematics in practice, whether in advanced technological applications or in everyday life, to develop critical citizenship (Borba; Skovsmose, 2004). D’Ambrosio (2008) believes that mathematics can be effectively instrumental in promoting social access. Therefore, CME is understood as the expression of concerns about the sociopolitical roles that mathematics can play in society (Skovsmose, 2010; Borba, 2021).

Freire (1996, p.118) states it is necessary, in educational practice, to “effectively communicate what is found in the understanding or intelligence of the world itself”. And this goes through the questioning of mathematics in action (Skovsmose, 2010) operated in digital discourse. Mathematics in action is

[...] those practices that include mathematics as a constituent part of themselves, for example, technological innovation, production, automation, management and decision-making, financial transactions, risk estimation, and cost-benefit analysis, among others. Such practices contain within themselves actions based on mathematics that can be a cause for reflection (Skovsmose, 2010, p. 51-52).

Skovsmose (2010) notes that the operationalization of mathematics manifests itself in different contexts and combinations, such as in everyday situations. This does not escape the discourses present in the videos (Carvalho, 2023). In a video, a fact, a theorem, or an image is not necessarily presented in the same way as in textbooks, classrooms, class notes, magazines, newspapers, or social media. This is due to the multimodal composition of the video, which enables virtual access to places, situations, and contexts that are far beyond the physical limits of producers and viewers, resulting in displacement in knowledge during the construction of the narrative. This allows both understanding and composing discourses.

It is worth noting that, in the video, this content is recontextualized and integrated into the narrative according to the producers’ sociocultural context and interests. In this movement, the principle of resemiotization is observed, which is concerned with “how meaning changes from context to context, from practice to practice, or from one stage of a practice to the next” (Iedema, 2003, p. 41, our translation). This process refers to the choices of SRs within and across multimodal phenomena (Borba; O’Halloran; Neves, 2021). This allows for a displacement in knowledge in educational practice that is observed, in this case, in the video, making communication critical, as it seeks to “understand the meaning of the meaning” (Freire, 2020b, p. 90). Thus, we understand that video discourse can express these displacements, favoring the epistemological curiosity (Freire, 2020a) of producers-with-media, which is built on the critical capacity to express mathematical ideas beyond common sense.

3 Digital videos and their fundamentals

The FVDEM video is a digital product that conveys mathematical concepts and incorporates a comprehensive package of knowledge about the world, society, history, and transdisciplinarity, contributed by students, teachers, the school community, and others involved in its development (Carvalho, 2023). In most situations, such production emerges from the teacher’s encouragement in the classroom. This occurs when students and educators choose to participate in FVDEM, which is an action that shapes the classroom through the production of knowledge resulting from experimentation with technologies, just as the classroom shapes FVDEM (Domingues, 2020), with production based on their knowledge/instruments embedded in the sociocultural contexts of which they are a part.

Borba and Oechsler (2018) discuss that videos take on several different characteristics and purposes, given that they can be used to record classes, to explore a reflection on practice or as a teaching resource in the classroom, in addition to the production of videos by students and teachers. FVDEM, from the perspective of knowledge production, promotes a culture of creating digital videos focused on ME. The research developed on the festival encompasses a diversity of theoretical approaches to the production and use of videos in the classroom, which open up possibilities for understanding the complexity of the interface between digital videos and ME.

The digital video in the project at hand is understood as a multimodal medium and as a means of producing meaning. Based on Borba and Villarreal (2005), we understand that media are material means (instruments, tools, things) and immaterial means (orality, writing, computing, thought) used to produce meaning and significance. In the list of media, we can mention: digital cameras, smartphones, computers, image editors, Internet, pencil and paper, social networks such as Facebook, Instagram, and WhatsApp.

Some research on digital videos in ME was developed at PPGEM at Unesp. They highlight specific contributions to video production in the context of ME. These surveys were linked to research projects Vídeos Digitais na Licenciatura em Matemática [Digital Videos in the Mathematics Degree], Festivais de Vídeos Digitais [Digital Video Festivals] and Educação Matemática e Sala de Aula em Movimento: Entre o Presencial e o Virtual [Mathematics Education and Classroom in Motion: Between the In-Person and the Virtual], based on the notion of HwM (Borba, Villarreal; 2005), in which technologies shape the production of meanings and the reorganization of mathematical thinking, which sometimes correlates with the third generation activity theory (Engeström, 2001; Engeström; Sannino, 2010), sometimes with social semiotics (Kress; Van Leuween, 2001; O’Halloran, 2005, 2011), among other fields of study.

Each study explores digital video as a multimodal medium that articulates SRs for mathematical communication (Neves, 2020). In its singularity, each research reveals: a) didactic potential and pedagogical potential (Silva, 2018); b) that the video production process is influenced by the context of its producers (Fontes, 2019); c) the sociocultural vision of mathematics in society (Oliveira, 2018); d) signs of learning in its production process (Oechsler, 2018); e) that the mathematical language present in the videos and in the participants’ discourse is something flexible, with some plasticity and humor, and can favor the transformation of the public image of mathematics (Domingues, 2020); f) it can influence how data is produced in modeling practices (Canedo Júnior, 2021); g) that the media used in the production of the videos harmonize to produce discourses (Souza, 2021); h) the shaping of the subjects’ actions, causing effects of estrangement from the naturalization in mathematics teaching, which can favor the transformation of the public image of mathematics (Gimenez, 2023); i) that the videos play an active role in constructing the change in human awareness, both of those who produce them and of those who watch them, i.e., the video has the potential to act in social transformation, especially as an agent of shift of knowledges in educational action (Carvalho, 2023); j) the production of videos involves a commitment to educating critical students, who become capable of using the knowledge produced in favor of a more egalitarian and democratic society, enabling social transformations (Costa, 2023).

These studies demonstrate that video has didactic and pedagogical potential, revealing that the sociocultural context of the producers influences its production process and shapes individuals’ actions (Borba, 2021). In this study, we emphasize critical movements, such as CME, with a fundamental concern for the sociopolitical aspects of ME, such as critical positioning, democratic and civic formation, and social justice (D’Ambrosio, 2005).

4 Methodology

The methodology of this study follows the social semiotic approach, articulated in conjunction with multimodal research, as outlined by Bezemer and Jewitt (2010). This approach involves three main steps: collecting and recording modal data, visualizing and gathering samples, and transcribing and analyzing the data. The choice of this approach is justified by its ability to capture the complexity of multimodal interactions present in educational videos.

For data collection, we used the video The Geometry of Bees, produced by students of the biology teaching degree course at UNESP, enrolled in the 3rd FVDEM. The video was selected for its relevance and exemplary application of mathematical concepts in everyday contexts, as well as for its critical nature, addressing geopolitical and environmental issues, denouncing the political disregard for the environment, education, and human rights in the Brazilian context. Multimodal transcription was performed using Taylor’s method (2013), which combines static images (frames) with meta-textual descriptions in a table. This process enables the identification of relationships between the various semiotic resources present in the video, including narration, on-screen subtitles, and visual interactions.

To analyze the data, we segmented the video narrative into takes and sequences, separating them into sections (scene transitions), similar to what is observed in carnival plots in Brazil (Carvalho, 2023), based on the systemic functional multimodal discourse analysis (SF-MDA) for moving images (O’Halloran, 2004). This analytical approach helped us examine the way language is used in context, the actions and events represented, the discursive interactions, and the visual organization of information into coherent units of meaning. The chosen units of analysis were the takes (short scenes) and the sequences (a set of scenes), enabling a detailed and contextualized analysis of each moment in the video.

5 An analysis of the video The Geometry of Bees³

The context of the video is the product of the interaction of a collective of biology-undergraduates-with-media that focuses on geometric structures to address the geometry of the alveolar structures that make up bee hives. It is a narrative with artistic characteristics, as its producers used combined language resources to create effects of estrangement, background music, metaphors, and real-world images (Gimenez, 2023). This video is a styleframe⁴, made up of several photographs/frames in sequence that, when played at a specific speed, give the illusion of movement. This type of video combines the concept with the visual elements.

From the perspective of the analytical approach, we identified six sequences, an analytical unit of the filmic text involved in a set of scenes (segment of moving images) in several scenarios in multiple units of space/time around a larger theme, The Geometry of Bees, presenting camera edits, in a “logical cause-effect relationship” (O’Halloran, 2005).

We also observed thematic, not spatial, continuity in each sequence. We considered an initial take that enabled the analysis of three metafunctions: ideational, interpersonal, and textual. These sequences enable the identification of moments that were created as segments or sectors, mapping the narrative of the “text” discourse. These moments are expressed in Figure 1.

Figure 1
– Video analytical model

Although the video’s discourse is primarily marked by oral language and frames/photographs, we observed the presence of short videos/animations using written language, mathematical symbolism, in some parts, superimposed on dark background frames. Music, in combination with images and spoken language, is present, marking moments that invite reflection or indicating playful moments, but does not demarcate a change in sequence in the narrative. We identified some sounds; however, they do not have a significant role in the composition of the discourse, i.e., they do not express a thematic or spatial relationship in conjunction with other SR.

Moment 1: The awakening of critical sense

The first frame of the video, including the written text Any resemblance to reality is not a mere coincidence, begins by addressing the viewer (experiential metafunction), as it communicates and directs them to real-life facts without naivety, through semiotic metaphors found throughout the plot. The emphasis on written language with the presence of sound is intended to sensitize and awaken the observer’s critical sense in advance (interpersonal metafunction). The take (opening scene with the frame fixed) as a whole shows the textual configuration based on the articulation/integration of the SR involved. The black and white background colors, combined with written language, convey that the video aims to get straight to the essence of things, to the facts (it expresses an idea, an attitude), as shown in Figure 2.

Figure 2
– Frame of the take (0”- 4”)

Colors, according to Van Leeuwen (2006), are multimodal SRs with communicative action to represent ideas, attitudes, and establish coherence. The ideational metafunctional meaning suggests ideals; the interpersonal expresses attitudes such as seriousness, informality, and fun, for example, and the textual establishes harmony and coherence.

Moment 2: Instrumentalization of knowledge

We observe images that materialize spoken language, with a focus on interdisciplinarity. Some of the images contained in the video not only represent reality, but also produce experiential and logical meanings in the world. They provide a means of projecting onto the viewer the possibility of constructing knowledge about aspects and facts of their culture permeated by values, beliefs, and social practices. We also observe sequences marked by:

Scientific/biological aspects based on the fact that insects, plants, and dinosaurs are not things – see Figure 3:

Figure 3
– Some frames of the first sequence (5”- 43”)

Historical aspects when using the extinction of the dinosaurs as a backdrop to locate the Mayan people as humans, not things with their particular culture: they worshipped deities of the sun, the moon, and agriculture – see Figure 4:

Figure 4
Some frames of the second sequence (44’- 1’7”)

Finally, there is the insertion of economic aspects in the plot to show the impact of agribusiness on a country’s economy, and that Brazil is an agro-exporter, with some relevance in the global economic scenario – see Figure 5:

Figure 5
Some frames of the third sequence (1’7” - 2’05”)

At this moment, the scenes present scientific, historical, and economic aspects, which can be interpreted through semiotic metafunctions, according to O’Halloran, Tan, and Wignell (2016). The experiential metafunction organizes visual elements to represent biological knowledge, such as the structure of bees, and historical contexts, including ancient cultures. The interpersonal metafunction brings the viewer closer to the critique of the economic impact of agribusiness, inviting them to reflect. The textual metafunction cohesively structures this sequence, linking the themes and favoring an understanding of the addressed context.

Moment 3: Reporting in social practices

We identified scenes portraying xenophobia, corruption, environmental destruction, lack of investment in education, health, and security, among other aspects. These questions are expressed through semiotic metaphors, as in the excerpt (2’56” to 2’58”), which says that President Jair Bolsonaro has many oranges⁵. The X on the oranges (resource with both logical and interpersonal meaning) in Figure 6 demonstrates disapproval of this type of practice.

Figure 6
Some frames of the 4th sequence (2’06” to 3’12”)

Such scenes point to three displacements. The first is the displacement of meaning. The X on the oranges not only refers to the fruit itself, but also symbolizes disapproval of the corrupt practices associated with President Jair Bolsonaro. This displacement transforms an everyday object (the orange, see footnote 5) into a symbol that carries social and political criticism, characterizing the second displacement: a shift in context. The mention of xenophobia, corruption, and environmental destruction displaces the discussion from specific issues of political management to a broader critique of the government’s social and ethical practices. The inclusion of these different issues in the same context suggests an interconnection between them, expanding the scope of the analysis and the impact of the criticism, encompassing the third displacement: a shift in focus.

We point out that the focus may initially be on criticizing President Bolsonaro. Still, when talking about oranges, the discourse shifts to the corrupt practices that are sustained through strategies of deception and manipulation. Thus, the focus shifts from the figure of the president to the consequences and implications of corruption, creating a space for reflection on how these practices affect society.

Moment 4: Mathematics in action in discourse (fifth sequence: 3’13” - 4’41”)

Here, we observe the presence of images that represent geometric aspects to justify the twinned hexagonal-based prismatic structures of the bee’s alveoli and show that the alveoli in the shape of hexagonal prisms could store more honey than those in square and triangular shapes. Still, to maximize the alveolar spaces, its bottom approaches an inclination of 13º, forming three equal diamonds. The speech presented points to the fact that bees produce their combs so that they have maximum honey storage capacity. Thus, at this moment, symbols and geometric shapes (semiotic resources) act as carriers of cultural and social meaning. The idea of resemiotization— the process of transforming meanings when moving between contexts —can be highlighted when the video’s discourse shifts mathematical knowledge from pure theory to an environmental and social context, reinterpreting it in an accessible way.

Opening the multimodal transcription of this sequence into perspective (Figure 7), we highlight the formation of the meaning of the concept, the object of knowledge of biology and the mathematical object, which merge and do not differentiate in the expressive process of discourse (recontextualization).

Figure 7
– Multimodal transcription (section 3’13” - 3’40”)

This process is mobilized and constituted based on what is socially known and linked to the practice of producers as undergraduates in biology, for example, a house as a home and alveoli as respiratory structures, to introduce the definition of alveoli as the home of bees that have an internal structure where things are stored (honey, larvae, and eggs). The images used are SRs that fulfill experiential functions, as they qualify the experience by describing the context, specifically defining the bee house as prismatic structures with a twin hexagonal base, as evident in the articulation between the image and oral language presented in Figure 7.

In addition to the concept formation process, we observe that this is accompanied by subtle investigative propositions throughout the characterization of what the hexagonal-based prismatic object is through resemiotization. The authors detail through the frames understandings obtained through visuals about what a hexagonal polygon is (it can have equal or different sides), whether it is regular and has equal sides, etc., and visually explaining the properties of hexagons in terms of sides and internal angles. They also promote the idea that a triangle contains others, in which some sides can be shared, as shown in Figure 8.

Figure 8
– Multimodal transcription (section 3’40” - 4’09”)

Evidence of a mathematics investigation is the placement of the image where the area of the rectangle corresponds to 72 cm², looking for measurements for the base and height of the cardboard, in which, by fixing one of the sides, it is possible to obtain areas of triangles, squares and hexagons, whose areas assume respectively, 6.92 cm², 9 cm² and 10.38 cm². The idea would be to consider the divisors of 72, whose measurements can form triangles, squares, and hexagons with those mentioned areas. This openness to mathematical investigation brings logical meanings that can spark creativity. This awakening can occur through a mathematical investigation of reality and mathematics itself. In the context of school mathematics education, this can be achieved through visual experimentation using cardboard and/or GeoGebra software or even through formal demonstration, involving writing, mathematical symbolism and images in mathematics teaching degree courses.

At this point, the video highlights the efficiency of hexagonal structures in bee honeycombs. This scene exemplifies the theoretical concept of resemiotization, in which mathematical knowledge about hexagons is recontextualized to bring forth an ecological vision. Here, the hexagon is transposed from abstract concept to practical application, exploring how its geometric properties (such as maximizing space while saving resources) enable structural efficiency in honeycombs (Figure 9). This approach not only allows for mathematical calculations, but also links these properties to environmental sustainability. This displacement in context aligns with the proposal of critical mathematics. By transcending abstract calculation, it addresses real-world issues and promotes critical awareness of ecological impacts.

Another aspect of the video that lends itself to discussion is the process by which the graduates, the producers of the video in question, create meaning based on the choices made between the frames articulated in oral language (Figure 9). The use of hexagons and their structure in the discourse transcends mathematics, addressing issues of efficiency and the environmental impact of bees, by characterizing the structure of the bottom of the cells as allowing for greater storage of honey, eggs, and larvae. Thus, students + media express mathematical knowledge in an authorial and critical way, showing them as active agents in learning. The transcripts displayed in Figures 7 and 8 also indicate that they exercise this power of action, especially when making comparisons or raising questions about geometry and the structure of bee cells.

Figure 9
– Multimodal transcription (section 4’10” - 4’42”)

The creation of the word is understood in a Freirean sense, as the word here refers to Freire’s (1996) proposition, in which students create their own understanding of the universe of study, to the point that the students themselves have a proactive stance in the conception and communication of the object being understood. Thus, we can see undergraduates coding their individual and collective lived experiences as products of culture, recreating meanings with resources known to them, often based on common sense, and communicating, in this particular case, about the geometry of bees – mathematics in action. Thus, they become meaning makers, and as creators, they are learners, in line with comments in Figure 9.

Therefore, it is possible to consider that the act of learning is also a semiotic work, as it articulates concepts with visual elements based on reality and, in a context, in the construction of the meaning of the scientific object to be communicated/expressed. In the frames, the visual elements and the spoken language interact to fulfill the role of orchestrating the video’s discourse. For a moment, the video is a digital artifact understood as a multisemiotic and multimodal digital text (Carvalho, 2023), but which assumes a leading role as an author in the production of knowledge (Borba, 2021), given its role in the construction of knowledge, in a shared interaction in the mathematical action present in the discourse, which is also constituted in the subjectivity of the person speaking, in the expressed acts and in the social actions addressed in the plot.

We now return to the aspect of creating meaning to affirm the presence of digital technologies in the constitution of the new meaning formed from those known resources/signs, understood in the context of the culture and the situation (plot) present in the video. The roles of artifact and authorship present to the spectator are overcome by the function of contextualization/codification of the object of knowledge in the production of a new meaning constructed anew, different from those found in textbooks and scientific books, in classrooms and in alternative learning spaces, such as virtual environments and social networks. The interaction between human beings and the media not only transforms the way we learn but also shapes the educational experience itself, highlighting the reciprocal nature of this intershaping relationship. The multimodal analysis and resemiotization of mathematics illustrate how social semiotics and the HwM construct enable a displacement in knowledge. This process transforms the traditionally abstract mathematical concept into a language that interacts with environmental and social issues, making it relevant and contextualized.

Moment 5: Reflective action as a possibility for change (4’36” - 5’36”)

We also highlight the role of the soundtrack, which begins at minute 5’12”, marking the transition to the final sequence and awakens and sensitizes the viewer to the change, as a result of the aesthetic action of the discourse and multimodality as language and experience. According to Neves (2020, p. 202), “the soundtrack gives the video an emotional side to the mathematical discourse”, and this contrasts with the formal nature of mathematics as a multisemiotic discourse. The author also highlights that the break in formality, accompanied by music, modifies the atmosphere established in the video, which distances itself from a video model more faithful to the procedures used in mathematics classes adopted in most schools.

In the video, the soundtrack, a digital technology, enhances awareness and supports an invitation to change attitudes in the process of putting the spoken word into action. Music can assume an emancipatory power of action and take on a leading role in addressing social and environmental challenges, when articulated with frames that highlight irresponsibility towards human beings and nature, addressing issues such as hunger, environmental degradation, deforestation, marine pollution, and neglect towards Brazil’s historical heritage.

To Borba and Skovsmose (2004), CME aims to train citizens who question the role of mathematics in society. Figure 10 reveals that the digital discourse of the video, the result of humans-with-media’s agency, examines the environmental impact of agriculture, suggesting a mathematics that considers ethical implications (Carvalho, 2023).

Figure 10
Some frames of the 6th sequence (4’36” - 5’36”)

Furthermore, this sequence shows that scenes have been translated by frames present in Figure 10, which expresses how questions of survival and transcendence (D’Ambrosio, 2005) are raised in the video’s discourse and also evidenced in the speech mode transcription of the excerpt (4’36” - 5’36”):

Larvae are not pollinators, unlike workers. Workers are very important for agriculture, as they pollinate flowers. Without flowers, many species could be driven to extinction, just as happened with the dinosaurs. Non-insect dinosaurs, animals with bodies divided into three parts, two antennae, and six legs, were wiped out by meteors. One of them fell in Mexico, which, besides craters, has Mexicans. US people don’t like Mexicans, just like Trump. Furthermore, Trump doesn’t like the environment, just like the president of Brazil, a head of state who does not fulfill his duties. Bees perform their functions, being responsible for pollination, which will generate food. Without bees, we would have no food or life. However, we don’t need to lose our lives to realize the problem of environmental irresponsibility. Other species, such as birds, bears, and monkeys, are disappearing. Thus, it is in our hands to protect biodiversity, as we lack the fulfillment of the State’s basic function. (Video: The Geometry of Bees, 2019).

We highlight that the video relates the absence of environmental peace with mathematics, as shown in the images in Figure 10. The video reports that the numbers related to deforestation and hunger are not a priority for the government, as it articulates its arguments using numbers, deforestation, and survival as key points. As D’Ambrosio states (2005, p. 107), “[...] there is effectively a morality associated [...] with mathematical knowledge”. Issues such as the amount of deforested land, habitat destruction caused by pollution, and the impact of agribusiness on food insecurity are discussed. D’Ambrosio (2005) recalls that modern science, based on mathematics, offers both tools for a good relationship with nature and instruments of mass destruction. Such narratives show an active mathematics in the digital world, the result of the collective action of HwM developed under the perspective of the knowledge cycle, defended by D’Ambrosio (2008), integrating previous knowledge and new knowledge, opening possibilities for 21st-century education in mathematics education.

6 Final Considerations

The video analysis details how biology-undergraduates-with-media approach a multidisciplinary discourse involving mathematics. We used several media that were active (agency, power of action) in their creation (Borba, 2021). Short videos, images from the Internet, and video editors were used to create content that explores social, economic, and environmental issues relevant to students’ lives, encouraging displacements of knowledge. This practice yields a semiotic landscape, in which physicality manifests itself through assertive postures that promote a more conscious society.

The video’s mathematical discourse, segmented by moments, interweaves mathematical ideas with social critiques and political concerns, adopting an interdisciplinary and transdisciplinary approach. Mathematics addresses geometric aspects, such as regular polygons and the optimization of prism volume, illustrated by honeycomb cells. In this context, the inclined bottom, at approximately 13 degrees, maximizes volume and saves material, exploring patterns of symmetry and structural efficiency that are present in both mathematics and nature. The six-minute video uses multimodality to present mathematical meanings in a way that engages with reality, incorporating a strong critical and socio-ecological component. Produced by a collective of humans-with-media, the video acts as an agent in new collectives, including the readers of this article, reflecting the intershaping relationship between humans and media. Thus, students not only use technologies, but are also shaped by them in their learning and knowledge production processes.

The video The Geometry of Bees addresses concepts of biology, economics, and environmental issues. Through a multimodal analysis, we observed that it not only presents the structure and organization of bees, but also connects these elements to a critique of sustainability and environmental preservation. The hexagonal structure of the honeycombs is highlighted as a symbol of ecological efficiency, promoting reflection on sustainability in both natural and human contexts. The use of visual metaphors and color symbolism reinforces messages about environmental impact and social responsibility.

Thus, the video exemplifies the HwM construct, as the students involved in the creation exercise agency by selecting and organizing images, texts, short videos, and sounds to communicate a mathematical discourse of civic criticism (Borba, 2021). On the other hand, the media, in this case the video, has agency by transforming mathematics into an even more multimodal phenomenon. This production demonstrates how digital technologies, when meaningfully integrated into education, can foster awareness and promote pedagogical practices that connect science, society, and environmental responsibility.

The analysis of mathematical discourse, immersed in multimodality, reveals the importance of a mathematics education that not only teaches mathematics but also contextualizes it within a framework of social and environmental issues, preparing students to be conscious and active citizens. Therefore, forums like FVDEM now have the agency to bring together videos, such as those produced by students and teachers, and serve as a democratic platform for videos, including this one, which has the power of action (agency) in extension, research, and teaching.

Acknowledgments

We thank the State University of Feira de Santana (UEFS) and São Paulo State University (UNESP) for supporting this research. We also thank the Research Group on Informatics, Other Media, and Mathematics Education (GPIMEM) for the academic debates and dialogues. We also thank CNPq, Brazilian funding agency, for partially supporting this research.

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• Data Availability:
  The data generated or analyzed during this study are included in this published article.
• 1
  Doctoral thesis entitled Festival de Vídeos Digitais e Educação Matemática Crítica [Digital Video Festival and Critical Mathematics Education] (Carvalho, 2023), which investigates videos from the 3rd and 4th FVDEM from a critical perspective, linked to the semiotic landscape. Developed in the Postgraduate Program in Mathematics Education (PPGEM) at the São Paulo State University “Júlio de Mesquita Filho” (UNESP), Rio Claro (SP) campus.
• 2
  There are three broad categories of functions that language performs simultaneously to create meaning. These functions are general enough to organize the language as a whole, differentiating themselves from the countless specific functions that a text can have, such as convincing or narrating. Metafunctions are fundamental to understanding how language operates in different contexts and how it constructs meaning in a structured and interactive way.
• 3
  Available at: https://www.youtube.com/watch?v=rGx4ia7iPt4. Access on 08 Dec. 2023.
• 4
  Available at: https://www.voxeldigital.com.br/blog/styleframe-de-videos/. Access on 08 Dec. 2023.
• 5
  TN: The intended pun in the Portuguese language is that, in the context, the word “laranja” (orange) in Brazilian political slang means a person who lends politicians or businesspeople their names and bank accounts for suspicious financial or influence transactions.

• Editor-chefe responsável:
  Prof. Dr. Marcus Vinicius Maltempi.

• Editor associado responsável:
  Prof. Dr. Maurício Rosa.

Data availability

The data generated or analyzed during this study are included in this published article.

Publication Dates

• Publication in this collection
  05 Dec 2025
• Date of issue
  2025

History

• Received
  07 Aug 2024
• Accepted
  09 May 2025