Atmospheres of Exclusion: Dante’s Inferno and the Mathematics Classroom

Abstract

This paper employs allegory to examine how pupils experience exclusion in mathematics education. Using Dante’s Inferno as a structural frame, I present nine fictional narratives aligned with the nine circles of Hell. These depict recurring learner experiences: displacement, disorientation, mechanical drill, grade-chasing, resistance, doubt, internalised failure, performance without understanding, and withdrawal. The narratives are not verbatim accounts but constructed stories synthesising themes from research, classroom practice, and observed discourse. Through narrative inquiry, each story reframes issues such as language barriers, high-stakes assessment, proceduralism, and stereotype threat—not as individual shortcomings but systemic conditions shaping learner identities. The allegorical mode makes these conditions vivid, positioning mathematics education as a moral landscape where inclusion and exclusion are continually negotiated. The analysis yields three insights: first, forms of exclusion are diverse yet interconnected, often drawing pupils into cycles of silence, resistance, or performance; second, metaphor and fiction can serve as rigorous research tools, allowing affective and structural dimensions of schooling to be understood together; and third, teacher education and policy must confront the hidden costs of privileging narrow forms of knowledge. Reimagining classrooms through Dante’s allegory, this paper calls for pedagogies that disrupt exclusion and open pathways to belonging and mathematical meaning.

1. Prologue

I write this article as a mathematics teacher educator and researcher whose professional and personal trajectory has been shaped by repeated movement across cultural and linguistic boundaries. I am originally from Cyprus, where I grew up and completed my undergraduate studies, before moving to the United Kingdom for my master’s and doctoral degrees. I later returned to Cyprus to work as a schoolteacher and then as an academic, and after several years I relocated to the UK to take a university position in Scotland. Since 2021, I have been living and working in Norway, where I am currently a professor of mathematics education. Across my academic appointments in Cyprus, Scotland, and Norway, I have observed a wide range of mathematics classrooms in both primary and secondary schools, which has deepened my understanding of how systemic arrangements, cultural expectations and pedagogical practices shape pupils’ opportunities to learn and to belong. These relocations have been tied to the pursuit of academic career developments, but they have also challenged me with complex ideas of belonging, privilege, and exclusion in education. As a cultural and linguistic outsider in different contexts, I have experienced first-hand how language hierarchies, assessment regimes, and institutional norms shape who is recognised within mathematics classrooms and universities. I also acknowledge that my mobility within Europe has afforded me forms of social and economic capital not available to many migrant teachers and learners whose stories I often draw upon in my writings. My research focuses on the social, cultural and political dimensions of mathematics education, particularly in relation to teacher education and the experiences of marginalised learners. This work is inseparable from my lived perspective, as I approach questions of equity and exclusion not only through scholarship but also through everyday negotiations of navigating different educational systems as an outsider within a new system. These experiences have put me in a position to now engage with allegory as both a methodological and ethical practice, one that allows me to surface structures of exclusion without reducing them to individual failure, and to reimagine mathematics education as a space where belonging, recognition, and making meaning are not only possible but fostered.

2. Part I—(Re)Framing the Problem: From Individual Emotions to Affective Atmospheres

Mathematics education has long been concerned with questions of inclusion and exclusion (see, e.g., [1,2,3]), by problematising, among other things, whose voices are privileged and whose are silenced at different stages of the learning process. Pupils’ opportunities to learn are shaped not only by access to content but also by their affective experiences: the emotions, identities, and beliefs that infuse classroom life [4,5,6]. Anxiety, shame, and resistance emerge alongside curiosity, enjoyment, and persistence. These dynamics are now recognised as central to how pupils come to see themselves in relation to mathematics [7,8]. Learning experiences are also framed by language and cultural identities, particularly for multilingual and migrant pupils who navigate linguistic hierarchies and assessment regimes that heighten feelings of marginalisation [9,10].

Despite this substantial body of work, much research still frames affect as an individual trait such as anxiety, motivation, or confidence. This view overlooks the ways affect also emerges as a shared atmosphere shaped by institutional, material, and discursive arrangements. The concept of affective atmospheres [11,12,13] refers to shared feelings that circulate in a space, felt collectively but not reducible to the individual, that give rise to urgency, unease, or belonging. In mathematics classrooms, such atmospheres may be generated by the press of timed tests [14], the precarity associated with high-stakes grading [15], the unease created through language policing [16], or the belonging fostered through collaborative work [17]. With their emphasis on speed, correctness, and narrow epistemic norms, mathematics classrooms are especially powerful sites for such atmospheres. Yet atmospheric analyses in mathematics education remain uncommon.

To illuminate these atmospheres, this paper adopts an allegorical approach. Drawing on traditions/practices of arts-based and narrative inquiry, I weave theoretical insights and composite classroom experiences into crafted narrations. These are not literal accounts of individual pupils but stories that convey the affective textures of exclusion and reveal the structures from which they arise. As an organising metaphor, I turn to Dante Alighieri’s Inferno, the opening part of his fourteenth-century epic The Divine Comedy [18]. In Dante’s poem, a descent through successive ‘circles’ of Hell symbolises different categories of sin. Here, the allegory is not used to suggest that pupils who struggle in mathematics are culpable or flawed. On the contrary, it reveals how schooling and society often cast children as deficient, failures, or “out of place”. By adapting Dante’s allegorical structure of Hell, I draw attention to how social, linguistic, and institutional arrangements create affective atmospheres of exclusion. The metaphor shows how learners are rendered outsiders, not due to their own “shortcomings”, but through environments that judge and constrain them.

Having situated this approach within existing research on affect, identity, and exclusion in mathematics education, in Part II I adopt allegory as a methodological tool. Part III presents nine allegorical ‘circles’ that synthesise findings across studies and experiences, which are then grouped in Part IV into three constellations of atmosphere. Finally, Part V discusses implications for mathematics pedagogy and policy, arguing that shifting affective atmospheres, rather than narrowly targeting individual traits, is key to creating more inclusive classrooms.

3. Part II—Allegory as Critical-Creative Inquiry

The Cambridge Dictionary (https://dictionary.cambridge.org/dictionary/english/allegory (accessed on 21 September 2025)) defines allegory as “a story, play, poem, picture, or other work in which the characters and events represent particular qualities or ideas that relate to morals, religion, or politics”. Allegory has long been recognised not only as a literary device but also as a way of organising knowledge across disciplines. In anthropology, and specifically in ethnographic studies, it has been described as a mode of layered interpretation [19]; in organisational studies, as a means of rendering cultural dynamics perceptible [20]; in psychology, as a framework for articulating complex emotions [21]; in management, as a cognitive process that enables foresight [22] and in education, as a tool for reflection and dialogue [23]. Taken together, these perspectives indicate that allegory functions methodologically by dramatising structures, surfacing tacit values, and connecting lived experience with broader systemic conditions. As a methodological approach, allegory shares affinities with case study, narrative inquiry, and metaphor analysis, yet departs from each. Whereas a case study seeks depth within bounded instances, whether single or multiple [24,25], allegory broadens across them; where narrative inquiry privileges participants’ accounts of lived experience [26,27], allegory deliberately layers fictional construction with empirical resonance; and where metaphor analysis maps cognitive domains [28,29], allegory extends such mappings into narrative worlds that make affective and structural forces perceptible. Its distinctive contribution lies in refracting experience through storied architecture, allowing systemic conditions and affective atmospheres to be apprehended together.

Rather than inventing a new framework, for the purposes of this article, I mobilise Dante’s Inferno as an organising allegory. The circles of Hell operate metaphorically: not to blame or judge pupils, but to dramatise how educational practices cast certain learners to the periphery or silence them. In this way, the allegory operates as an interpretive lens that reconfigures mathematics classrooms as affective and moral landscapes. Overall, allegory functions here as a critical-imaginative methodology: critical in interrogating structures of exclusion [30], and imaginative in opening corridors through which possibilities for belonging and recognition in mathematics might become visible [31].

The vignettes presented in Part III are composites, inspired by three sources: research literature on mathematics-related affect, identity, and exclusion; classroom observations from my professional experience as a mathematics teacher educator in three different countries; and practitioner narratives, revoiced and resituated in allegorical form. Although fictional in voice, these vignettes remain anchored in empirical evidence. Their purpose is not to reproduce literal accounts but to evoke atmospheres and structures that recur across contexts. My aim is to offer readers recognisable narratives, much as Gonzalez Thompson [32] does in illustrating the stories of three mathematics teachers, prompting the response: “oh, I know someone who could be this person”. This practice resonates with arts-based and narrative inquiry traditions, which affirm the legitimacy of imaginative reconstruction in research [26,33], and with critical fabulation, which treats fictionalisation as a means of surfacing structures and silences that conventional data cannot fully capture [34]. In this sense, allegorical narration is not a departure from rigour but a mode of inquiry attuned to both the affective and structural dimensions of schooling.

The adequacy of allegory as method can be considered through three interrelated criteria. First, coherence with literature: each vignette is aligned with established findings on mathematics-related affect, identity, and exclusion, reflecting Tracy’s [35] call for meaningful connection between data, analysis, and existing scholarship. Second, explanatory reach: the allegory highlights how institutional practices such as assessment, language policing, and proceduralism generate shared atmospheres, echoing Lincoln and Guba’s [36] emphasis on credibility and the illumination of systemic processes. Third, transferability: rather than generalisability, the goal is resonance—narratives are written to invite recognition across diverse contexts, fostering dialogue in line with Riessman’s [27] and Ellis et al.’s [37] argument that qualitative adequacy lies in whether accounts evoke understanding and identification among readers.

4. Part III—Nine Allegorical Atmospheres of Exclusion

At the threshold of this allegory, I clarify how Dante’s architecture is used. The nine circles of the Inferno provide a scaffolding, but here they are translated from moral categories into affective conditions of schooling. Each retains its original name (Limbo, Lust, Gluttony, and so on) because the imagery of each circle evokes a particular atmosphere [11,12,13] of exclusion: waiting at the edge, being swept by turbulence, weighed down by repetition, silenced by anger, or frozen into isolation. These names therefore operate metaphorically rather than morally, distinguishing the nine cases through the specific emotional and structural textures they illuminate. The circle offers the frame; the atmosphere conveys its weight. In what follows, each vignette inhabits a circle as an allegorical setting, while also evoking the atmosphere that learners experience within it.

The immersion begins here. Voices surface in fragments of memory and struggle, carrying traces of classrooms, corridors, and conversations that echo across contexts. Their words are fictional yet familiar, evoking what it feels like to wait at the edge, to be swept along by pace, to labour without recognition, to turn anger inward or outward, or to walk away. The aim is not to catalogue experience but to enter its texture, to feel how exclusion in mathematics education takes form and substance.

4.1. Circle 1: Limbo

“And this arose from sorrow without torment,

Which the crowds had, that many were and great

Of infants and of women and of men.”

(Canto 4, p. 24 in [18])

Dante’s Limbo holds the virtuous who are guiltless yet excluded from salvation; this image of blameless deprivation frames the first classroom atmosphere, where belonging is withheld not by failure but by circumstance. The first circle is not a place of torment but of exclusion, writes Dante. Here dwell the virtuous pagans and unbaptised infants: souls who are blameless yet barred from Heaven, denied entry not through fault but through lack of access to salvation. A parallel emerges in the classroom, where a refugee child, bringing their own forms of mathematics, is judged to be “behind others” because they did not arrive with the sanctioned language or prior schooling of their peers. Like the inhabitants of Limbo, they wait at the edge of belonging, excluded not through failure, but because the boundaries of “being successful” as a mathematics learner have been constituted to leave them out.

4.2. Narration 1: The Forgotten

They say I do not try hard enough, that I am always behind, but they do not know where I started. When I was eight, I left my country as a refugee. We spent months in camps, where numbers were not written on chalkboards but on ration cards and bus tickets. We counted food parcels, not fractions. When we arrived here, the first worksheet I was handed asked me to divide 487 by 23. I had not even seen the symbol/they used. The teacher stood by my desk and tapped her pen as if the answer was obvious and I just refused to see it. That is the thing about being “behind” in maths: it clings to you. Each test confirmed that I had missed something essential—long division, fractions, negative numbers. Concepts everyone else carried forward, I had never been given. I was placed in the “support” group, where we filled pages with basic multiplication tables. It felt like circling endlessly at the edge of something greater, always kept apart while others hurried ahead into algebra and geometry. It is not that I do not see patterns. Back home, in my parents’ shop, I used to calculate change faster in my head than the till. I could work out prices, discounts and how many cartons fit on a shelf. But that type of doing mathematics does not count here. When I try to explain how I think about numbers, breaking them into tens and using mental shortcuts, the teacher frowns. “Show your working”, she says. My way of seeing does not belong. So, I was taught how to be quiet, to stand aside with the others, not guilty of anything but treated as if belonging was never ours to claim. We wait in that still place with the type of mathematics we brought with us, knowing it is valuable even if the classroom does not believe so. People like to say maths is a universal language, but it is not, not when the symbols, the words and even the ways of thinking are strange to you. Some of us arrive without that vocabulary, and by the time we start to learn it, the conversation has already moved on. I have not intentionally disengaged. I am not hopeless. The only reason I am outside is because the door was closed before I could even knock.

4.3. Circle 2: Lust

“I came into a place mute of all light,

Which bellows as the sea does in a tempest,

If by opposing winds ’t is combated.”

(Canto 5, p. 31 in [18])

In Dante’s vision, the lustful are swept forever by a furious storm, denied rest and control; this turbulence becomes an allegory for the classroom where learners are driven by the relentless winds of pace, rules, and assessment. The second circle is a place of endless storm, where souls are driven by violent winds, never allowed to rest or stand on solid ground. The turbulence is not of their own making but besieges them and tosses them around without pause. In the classroom, a child experiences a similar storm of schooling. Each lesson, each test, each rule about how mathematics must be shown sweeps their efforts away before they can take hold. Their own methods and insights scatter like paper in the wind, dismissed as distraction or failure. Just as Dante’s souls are carried endlessly by forces beyond their control, so too is this child, borne along by the demands and judgements of the classroom, never permitted to find calm in the mathematics they already know.

4.4. Narration 2: The Distracted

The numbers blur when I look at them. 478/7 looks simple to everyone else, but to me it feels like chasing something racing ahead of me, always out of reach. By the time the class has worked through the steps of long division, I am still at the first subtraction, struggling to hold on. I try to break the problem apart: 420 and 58, sixty sevens in the first, eight in the second, 68 with 2 left over. To me that feels steady, like I have just managed to grab the last carriage, while everyone else is already far ahead. But the teacher frowns and says, “That’s not how we do it. Show the algorithm”. The algorithm is a maze where I lose myself every time. Digits fall, remainders slip away, the steps scatter like papers caught in the wind. I use fingers to keep track or draw little boxes to anchor myself, but that brings laughter from classmates and warnings to stop being messy. I ask to use a calculator, but that is treated like a shortcut that ought to be forbidden, even though outside this classroom it is part of real-life mathematics. Tests are the worst. The clock ticks like thunder and my mind spaces out. I stare at the page as if the symbols are written in a language I almost understand but cannot hold long enough to read. Teachers think I am distracted and unable to focus, but that is not the truth. What unsettles me is the storm of rules, steps, and time limits that prevent me from demonstrating what I know. Even so, I notice things others do not. I see the rhythm in the multiples of nine, digits falling 9, 8, 7, 6, circling back to zero like hidden music. But when I mention it, the teacher waves me off: “Memorise the facts. Don’t waste time with patterns”. I am not avoiding mathematics. I am inventing paths into mathematics through a different way of understanding its process. I use every tool I can find—fingers, sketches, patterns, calculators—to make the numbers stable. But here, those paths are mistaken for weakness, and so I am swept into the same category again and again: the pupil who cannot focus, who will never do maths the proper way.

4.5. Circle 3: Gluttony

“In the third circle am I of the rain 80

Eternal, maledict, and cold, and heavy;

Its law and quality are never new.”

(Canto 6, p. 38 in [18])

Dante’s gluttonous souls endure an eternal, filthy rain, a symbol of excess that turns nourishment into burden; this imagery resonates with the classroom where endless drills and mechanical repetition saturate learning until effort itself becomes oppressive. The third circle is a place of endless rain, cold, heavy and foul, where souls are pushed into mud and prevented from rising. Their punishment is a weight that seeps into everything, holding them down. In the classroom, a similar pressure falls on children whose learning has been reduced to repetition and drilling. Their effort is real, their persistence undeniable, yet these are entirely overlooked, as if processes that are not expressed in identical vocabulary carry no value. Like the souls under rain, these pupils are weighed down by expectations that never relax and confined to tasks that are consistently repeated without opening into more inclusive approaches. However much they endure, they are told that what they know is never enough, and their mathematics capacities are buried under Eurocentric demands.

4.6. Narration 3: The Mechanical

I still remember the first time a teacher smiled at me in maths class. I was six, and I could recite the multiplication table faster than anyone else. Two times two, four. Two times three, six. My voice rattled off the rhythm and the class clapped. In that moment, I thought I was good at maths. For years, that was what maths meant to me: drill, repeat, answer. My notebooks filled with long pages of numbers, hundreds of practice problems, each solved with the same neat steps. It felt safe. If I just followed the rules exactly as shown, the answer would always appear. I liked the certainty. But when I came here, maths looked different. The first problem I was given asked: “A farmer has 12 cows and sells 4. How many are left?” I knew how to subtract 4 from 12, but the words confused me. Was it subtraction, or something else? The teacher wanted me to explain my reasoning. I froze. Reasoning? I had never been asked to put mathematics into words. Later, they asked me why long division works. I could show the steps quickly and accurately, but when pressed to explain I stammered, “Because… that’s the way.” My answer was dismissed. Suddenly, the very skills I had been praised for—the speed, the memory, the discipline—were treated as meaningless. I began to feel like a machine: give me numbers and I will give you answers. But when the problems changed shape, fractions in word problems, geometry proofs, questions with no single correct answer, I did not know what to do. It was as if the ground I had been standing on turned to water. Now I sit quietly, working through problems in the margins, careful to get every step right. I rarely speak up, because whenever I do the teacher asks, “But why?” I do not know how to explain why. All I know is the rhythm of the procedures I was taught. Sometimes I wish they could see that memory and repetition are not devoid of meaning. They represent effort, persistence, and a functional part of mathematics. But here my way of doing mathematics is treated like an empty shell, suppressed and jeopardised for what is considered “mathematical”. I once thought I belonged to maths. Now it feels as if maths has moved on without me.

4.7. Circle 4: Greed

“Here saw I people, more than elsewhere, many,

On one side and the other, with great howls,

Rolling weights forward by main force of chest.”

(Canto 7, p. 45 in [18])

The endless struggle of Dante’s fourth circle—bodies straining against heavy weights only to collide and begin again—echoes the futility that some pupils feel when effort brings no progress. This circle holds the souls of those who hoarded and squandered. They strain against great weights, pushing and pulling in endless opposition, their labour exhausting yet never leading anywhere. The struggle continues without end, each side blaming the other for what was lost. In school mathematics, some children are equally burdened. They push through drills and remedial tasks yet feel no progress. Their energy is real, their effort constant, but it always brings them back to the same place. Teachers and peers accuse them of carelessness or laziness, but what holds them down is the cycle itself, heavy with low expectations that they cannot fulfil. Like Dante’s souls, they are condemned to labour without release, their strength consumed by tasks that never let them move forward.

4.8. Narration 4: The Grade-Chaser

The red number at the top of the page is the first thing I see. Ninety-two. It means I can breathe today. It means my parents will nod with relief when I show them. It means I am still on track. For me, mathematics has always been about these numbers in the corner of the paper. Each mark is a step closer to scholarships, university and the life my parents want for me—the life they left behind for me to have. I do not have the luxury of liking maths. I need maths. When the teacher explains a new concept, say quadratic equations, I do not wonder about the history or the beauty of the parabola. I want to know: how many marks will this be worth on the exam? What kind of question will appear? I practise past papers until my hand cramps. I memorise the exact way to set out the solution so that no point is lost. Sometimes I hear teachers complain about students like me. They say, “They only care about grades, not about mathematics”. They speak as if chasing marks is a sin. But what they do not see is that grades are my ticket out. My parents remind me of this every day: a high score means opportunity; a low score means closed doors. I cannot afford to slip. I do sometimes find patterns interesting. I notice how the graphs of related functions reflect across an axis, or how certain numbers repeat in cycles. But whenever I start to wonder, I stop myself. Curiosity does not win exams. Efficiency does. There is no room to wander when the stakes are so high. So, I chase. I chase every point, every rubric, every past paper question. And when I get a good score, I feel proud, but also empty, because I know the pride belongs more to the number than to me. Perhaps one day I will have the freedom to slow down, to explore the parts of maths that are not on the test. For now, mathematics is a currency, and grades are the only language I can afford to speak.

4.9. Circle 5: Wrath

“Beneath the water people are who sigh

And make this water bubble at the surface,

As the eye tells thee wheresoe’er it turns.”

(Canto 7, p. 49 in [18])

In Dante’s fifth circle lies the river Styx, where the wrathful battle on the surface while the sullen sink beneath, trapped in mud. Fury and silence coexist here: some souls thrash in rage, others turn their anger inward and disappear below. This duality captures the tension of many classrooms, where frustration may erupt in defiance or fade into quiet withdrawal. In both cases, pupils are consumed by emotion and isolation, unable to rise above the atmosphere that holds them. In school mathematics, a similar river runs through the classroom. Some children are perceived as angry or disruptive, their frustration spilling out in visible ways. Others sink into silence, suppressing their feelings and refusing to raise their hand or speak. Both are judged in equally harsh terms for responding to the same conditions within a system that denies them the capacity to belong. Like the souls of the Styx, they are caught between struggle and despair, unable to escape the waters that surround them.

4.10. Narration 5: The Resistant

“Come up and solve it on the board”, the teacher says, and I feel every eye in the room turn towards me. The problem is written in chalk: fractions stacked on fractions, like a tower waiting to collapse. I know the rules for multiplying them, but my chest is already tight. If I get it wrong, everyone will have noticed. “I don’t want to”, I say. My voice comes out sharper than I intended. A few classmates snicker. The teacher sighs. “You need to try. Don’t be lazy”. And that is the word that always sticks: lazy. But they do not know how many hours I spend at home, trying to untangle long division or checking my answers again and again to make sure I have not accidentally swapped digits, like writing 78 instead of 87. They do not see how I count silently on my fingers under the desk, or how my notebook is full of scribbles from problems I almost solved before time ran out. What they see is my anger, my refusal. I admit that sometimes I slam my book shut when problems do not make sense. Sometimes I mutter that maths is stupid. It is easier to be angry than to admit how trivial and exposed I am made to feel. Anger is armour. When I raise my voice, people do not hear my confusion, only my defiance. That suits me. Better to be the pupil who does not care than the one who keeps trying and still fails. Yet I do care. I notice patterns, even when I pretend not to. When we learn about negative numbers, I think of them as walking backwards on a number line. That makes sense to me. When we study equations, I like seeing how they balance, like scales. But the moment I speak, it feels like stepping into a trap: one word wrong, and everyone knows I am not good enough. They call me resistant, difficult, even hostile. They do not realise resistance is the only way to protect myself. I am not refusing maths. I am refusing humiliation. If someone listened openly, without prejudice, if someone showed me that mistakes are not proof of failure, I think I would do better. But for now, it feels safer to scowl and cross my arms. At least then I get to decide how they see me.

4.11. Circle 6: Heresy

“For flames between the sepulchres were scattered,

By which they so intensely heated were,

That iron more so asks not any art.”

(Canto 9, p. 62 in [18])

The sixth circle is the city of Dis, where the heretics lie in burning tombs. Their punishment is to be sealed away from truth, locked in fire and silence for questioning what others held sacred. Flames rise from sealed tombs, each one holding a soul that dared to think differently. The heat of these fires speaks of ideas forbidden, voices locked away. In the classroom, children who doubt mathematics are placed in a similar position. To ask why or to wonder aloud what it all means is treated as dangerous, even disrespectful. They are told to stop questioning and simply obey the rules. Their marks may be good, their effort real, but their curiosity is buried, confined as if in a tomb. Like Dante’s heretics, they are not condemned because they lack knowledge, but because they refuse to accept anything without first asking. Their voices are silenced, their questions sealed, leaving them present yet unheard and unseen.

4.12. Narration 6: The Skeptic

“When will I ever use this?” I asked once, and that was the last time I dared to ask it aloud. It was during algebra, solving for x. The problem said something like 3x + 7 = 19. I could do it—I moved the 7 across, found 3x = 12, then x = 4. But it felt like a game without purpose, so I asked. The teacher stopped mid-step, marker frozen in the air, and gave me the look. “You’ll need this one day. Don’t question it. Just do it”. Since then, I have kept questions in my head. Because here, mathematics is not something you are allowed to doubt. It is sacred, the subject that is supposed to prove you are smart, disciplined, worthy. If you do not bow your head and accept it, you are treated as a heretic. But the truth is I want mathematics to make sense, to touch the world I know. I want it to explain why the moon pulls the ocean, or how to measure the angle of a tree’s shadow. Instead, we spend weeks on factoring polynomials, filling page after page with symbols that feel like spells I will never cast again. My friends sometimes tease me: “You’re good at maths, so why complain?” It is true—I get decent marks. I can memorise steps, I can pass tests. But being able to do it does not mean I believe in it. For me, mathematics often feels like a locked box I am asked to carry everywhere, without ever being allowed to open it and see what is inside. I do not hate maths. I hate the way it is treated as unquestionable. I hate that when I wonder aloud whether there are other kinds of knowing—like the way my grandfather tells time by natural light and wind, or how my aunt measures by taste when she cooks—I am told that is “not real maths”. Only what is on the board counts. So, I stay quiet. I play the part of the good student, but I keep asking those questions to myself. Not because I want to escape maths, but because I want it to mean something.

4.13. Circle 7: Violence

“We with our faithful escort onward moved

Along the brink of the vermilion boiling,

Wherein the boiled were uttering loud laments.

People I saw within up to the eyebrows”

(Canto 12, p. 81 in [18])

In the seventh circle, violence takes many forms: some turn their fury outward, others inward, and some defy the world itself. Dante’s rivers of boiling blood and burning sands render the pain of harm that has nowhere safe to go. Their punishments are fierce, with rivers of blood, trees torn apart, and deserts burning with fire. In mathematics classrooms, violence appears not as blood or flame but as the slow damage of humiliation, exclusion, and fear. A child’s mistake becomes a public spectacle; another’s silence is read as defiance. Some lash out, unable to bear the weight of exposure. Others implode, turning anger against themselves. Still others are crushed by the structures of schooling itself: the tests, the rankings, and the quiet erasure of what they know. Like Dante’s souls, they inhabit a landscape of punishment that mistakes survival for sin, pain for failure, and silence for peace.

4.14. Narration 7: The Self-Doubter

Before the teacher even asks the question, I already hear the answer in my head: you will get it wrong. So, I keep my hand down, even when I think I might know it. The silence feels safer than the risk of proving, once again, that I do not belong here. It was not always this way. In primary school I liked maths. I liked puzzles, patterns, the way numbers fitted together like pieces of a picture. But as the problems grew harder, the mistakes came faster. Every red cross on my test felt heavier than the last, and each time someone else shouted out the answer before I had even finished reading the question, I sank further into the background. Little by little, I started believing what the world whispered: some people are just not maths people. Maybe that was me. Maybe I was never meant to be here. When I sit with a problem now, for example, simplifying fractions, I already feel defeated. I see 12/18 and 6/9 and know they are connected, but when the teacher asks me to explain why, the words get stuck in my throat. My classmates look so confident, moving through algebra as if it is a language they have spoken all their lives. I feel like a guest in a country where I will never be fluent. I have heard the stereotypes enough times to carry them inside me: that girls are not expected to be as strong in maths, that children like me do not usually go into science. No one has to say it outright anymore. I repeat it to myself. I wear it like armour, though it cuts me, too. The strange thing is, I still notice beauty sometimes. When we drew parabolas on the graphing calculator, I loved the symmetry, the way the curve mirrored itself. But I did not say anything. It felt as if I was not entitled to feel admiration, as if I was claiming something that did not belong to me. So now, when people ask me about maths, I shrug and say, “I’m just not a maths person”. It is easier than explaining the years of doubt, the way exclusion has settled into my bones. Maybe there is a part of me that still wants to raise my hand, to step back into the conversation. But the voice inside is louder: Don’t. You will only prove them right.

4.15. Circle 8: Fraud

“There is a place in Hell called Malebolge,

Wholly of stone and of an iron colour,

As is the circle that around it turns.”

(Canto 18, p. 116 in [18])

The eighth circle, Malebolge, is the realm of fraud, a landscape of false brightness and concealed pain. Here, flatterers are sunk in filth, hypocrites bend under cloaks of lead that glitter with gold, and false counsellors speak from within flames. Each punishment exposes the distance between appearance and truth. In the mathematics classroom, a similar distance emerges when understanding is replaced by performance. Some children learn to display certainty by memorising steps, while inside they remain unsure. Others act indifferent, because caring too openly risks humiliation. They are told to “show the method” even when their reasoning is sound, so what they know cannot be revealed in the approved way. When they use tools or share ideas, they are accused of cheating, hiding practices that are valued elsewhere. Like the deceivers of the eighth circle, they are judged for dishonesty, yet their pretence is not born of malice but of a system that prizes conformity over truth.

4.16. Narration 8: The Pretender

I nod when the teacher explains. I copy the example from the board, line by line, and everyone thinks I understand. When the homework comes, I write down the same steps again, even if I do not really know what each one means. If the problem looks like the example, I can match the shapes: formula here, subtraction there, answer at the bottom. It feels like making a puzzle where the pieces do not quite fit, but if I press hard enough, they will get stuck in the blanks. Sometimes I memorise whole solutions. If the teacher shows how to solve for x when 2x + 5 = 11, I store it in my head like a script: subtract 5, divide by 2, x = 3. Next day, when the numbers are different, I just swap them and follow the same performance. I do not know why it works, but I know that it is the part I am expected to play. It is dangerous, though. When a problem looks different, like a word problem about trains leaving stations or a geometry proof, I freeze. My mask falls. The teacher calls me out: “Did you even study? You are just copying”. My classmates laugh. They do not know how hard I work to keep up this act. The truth is that the only way to stay in the room is by pretending. When English words wrap around the numbers, I get lost. When the lesson moves too fast, I grab whatever I can and hold onto it. If I do not fake it, I disappear completely. I live with the fear of being found out. Every test feels like a spotlight ready to expose me. I circle answers with shaky hands, hoping the teacher will not notice that my work is just a rearranged version of something I have seen before. Yet pretending is also a kind of persistence. It means I have not given up. I keep showing up, keep writing, keep finding ways to look like I belong. Sometimes, in the middle of mere copying, something clicks—like when I realised that subtracting both sides of an equation is about keeping things balanced, like a scale. In those moments, I feel as if I could do more than pretend. Still, most days, the mask stays on. It is the only way I know to survive mathematics.

4.17. Circle 9: Treachery

“Whereat I turned me round, and saw before me

And underfoot a lake, that from the frost

The semblance had of glass, and not of water.

So thick a veil ne’er made upon its current”

(Canto 32, p. 216 in [18])

The ninth circle is a frozen lake, where traitors lie locked in the ice. The deeper the treachery, the deeper the entombment, until some are buried completely. The cold seals every gesture, silencing movement and severing souls from one another. In school mathematics, some children experience a similar freezing. They are isolated by labels, silenced by fear, immobilised by years of exclusion. The betrayal is not of their making but the system’s: a betrayal of their potential, their creativity, and their right to belong. Like Dante’s souls in the ice, they remain present but unheard, waiting for a warmth that never arrives.

4.18. Narration 9: The Exiled

I used to be good at maths. At least, that is what I was told before I walked away. In primary school I enjoyed it, the neatness of multiplication tables, the way a problem had a definite answer. Teachers praised me for being quick. My parents beamed when I brought home full marks. For a while, maths felt like a door opening. But as I moved on, the door became less ajar. By the time I reached secondary school, the advanced maths class was full of pupils who did not look like me. Their parents could afford tutors. They spoke the language of textbooks as if they had been raised in them. When I hesitated over a problem, they leapt ahead. I felt the space closing around me, the air icier. I persisted. I studied for hours, worked through thick revision books, practised equations until the numbers blurred. But every mistake seemed to confirm what others already assumed: that I was not really a maths person, after all. Guidance counsellors suggested I focus on practical subjects. A teacher once told me, kindly but firmly, “Not everyone is cut out for higher-level maths”. Eventually, I believed them and started acting the way they expected me to. I dropped the advanced course. At first it felt like betrayal, to my parents, to my younger self who once loved the orderly certainty of arithmetic. Later it felt like relief. No more pit in my stomach when someone asked me to solve an equation on the board. No more silent comparisons. No more shame. But the world has not let me forget. Whenever someone hears I did not go on to study maths, they shake their head, saying: “You are limiting your future”. It is as if I turned my back on progress, as if choosing another path made me disloyal. They call it wasted potential. What they do not understand is that I did not abandon maths. Maths discarded me. The classrooms where I once belonged became places where I was tolerated, not welcomed. The subject that promised universality became a gate I was not allowed to pass. I still notice mathematics everywhere: in the way bus schedules overlap, in the symmetry of a woven basket, in the rhythm of a song’s beat. But that kind of noticing does not earn you a certificate. It does not count as proof you are mathematical. So yes, I defected from the weight of exclusion before it froze me completely. If that makes me a traitor in their eyes, so be it. I know the truth: leaving was a matter of survival and not betrayal.

5. Part IV—From Atmospheres to Constellations

The allegorical vignettes in Part III illustrate what exclusion may feel like from the standpoint of learners. In this section, I step back from those ‘individual’ voices (even though, in reality, they are composite voices) to consider how they cluster into broader affective conditions. I group the nine circles/atmospheres into what I call three constellations: Edges, Storms, and Weights. This move from atmospheres to constellations shows that exclusion is not a collection of isolated struggles, but a patterned set of exclusionary features generated by institutional practices and discursive norms.

The first constellation, Edges, combines Limbo (the Forgotten) and Treachery (the Exiled). Both evoke pupils positioned at the threshold of mathematics education: they are present in the classroom but never fully recognised as belonging. The Forgotten describes a refugee child whose informal mathematical knowledge is dismissed because it does not align with sanctioned language or curricular sequences, while the Exiled portrays a learner gradually pushed out of advanced mathematics through tracking, stereotypes, and discouraging advice. Research on multilingual and migrant pupils demonstrates how school transitions and language hierarchies actively construct students as being ‘behind’ [9,10], while identity studies show how such positioning becomes internalised through learners’ own narratives [7,8]. Roos [6] reconceptualises inclusion as processes of participation, and the allegories of the Forgotten and the Exiled make clear what happens when such participation is withheld. Belonging thus emerges not as an incidental outcome but as a pedagogical project requiring institutional flexibility, recognition of diverse repertoires, and porous thresholds between tracks.

The second constellation, Storms, gathers Lust (the Distracted), Wrath (the Resistant), and Fraud (the Pretender). These narrations convey the turbulence of pace, exposure, and surveillance. The Distracted is overwhelmed by the speed of lessons and by the dismissal of personal strategies as “improper”. The Resistant faces public performance at the board, where humiliation is warded off through anger. The Pretender conceals uncertainty beneath memorised algorithms, maintaining a mask of competence in order to survive constant monitoring. Research on mathematics anxiety has shown how timed testing and performance pressures trigger stress [14,15]. Yet, as Hannula [5] points out, affect cannot be reduced to stable traits found in individuals; it must be understood as multidimensional and relational. Extending this view, Storms shows how anxiety and shame are generated atmospherically circulating through clocks, gazes, and method-policing practices. Anderson’s [11] theorisation of affective atmospheres and Zembylas’ [13] account of pedagogical climates both support this interpretation. What appears as distraction, resistance, or pretence is thus not individual weakness, but turbulence cultivated by systemic arrangements that privilege conformity to speed, standard methods, and already-familiar schooling trajectories, while casting others into distraction, resistance, or pretence. Interrupting the storm requires classrooms slow down their tempo, value multiple strategies, and reframe mistakes as opportunities rather than humiliation.

The third constellation, Weights, brings together Gluttony (the Mechanical), Greed (the Grade-Chaser), Heresy (the Skeptic), and Violence (the Self-Doubter). Here, exclusion is experienced as heaviness. The Mechanical recalls the comfort of repetition and drill, which later prove inadequate when deeper reasoning is demanded. The Grade-Chaser portrays mathematics as currency for mobility, where marks matter more than meaning and curiosity is displaced by efficiency. The Skeptic shows how questioning is treated as illegitimate, producing silence rather than inquiry. The Self-Doubter reveals the long-term effects of stereotype and repeated failure, in which exclusion settles into self-blame. Scholars have long warned that proceduralism and high-stakes assessment risk narrowing what counts as mathematics [38,39,40]. The Skeptic’s silenced voice exemplifies epistemic injustice in Fricker’s [41] sense, while the Self-Doubter’s internalisation of stereotype reflects the cumulative harm documented in studies of stereotype threat [42]. Weights therefore illustrates how drills, grading, silencing, and self-blame sediment over time into atmospheres where participation itself feels burdensome. Designing against such heaviness requires assessments that foreground reasoning alongside procedure, pedagogies that welcome questioning as legitimate, and classroom cultures that contest the myth of the “maths person”.

Across the three constellations, common mechanisms of exclusion become visible. Public performance scripts generate shame, timed surveillance raises anxiety, language ideologies erase diverse repertoires, and assessment regimes reduce mathematical worth to grades. These are not isolated hindrances but institutional arrangements that invariably shape the atmospheres of classrooms. Learners may also shift across constellations: a pupil who begins as a Pretender within the turbulence of Storms may become a Self-Doubter under the accumulated Weights of stereotype and failure, and later find themselves Exiled at the Edges, stepping away from mathematics altogether. Such trajectories demonstrate both the cumulative force of exclusion and its contingency, since interventions that interrupt pacing, broaden access, or legitimise diverse reasoning alter atmospheres and open pathways toward recognition and belonging. In this way, the constellations of Edges, Storms, and Weights extend equity frameworks in mathematics education [2,5,6] by reframing exclusion as an atmospheric phenomenon. Allegory renders these dynamics perceptible, showing how routine practices such as testing, tracking, and method policing acquire moral weight in pupils’ lives, and stress how the challenge is not to correct cognitive deficits in individuals but to transform the atmospheres cultivated whenever mathematics is encountered in classrooms.

6. Part V—Designing Corridors of Belonging

If exclusion in mathematics classrooms is atmospherically produced, then belonging must be deliberately designed rather than left to chance. Corridors of belonging are not ornamental metaphors but structured pathways that allow learners to re-enter participation and reshape their relation to mathematics. The challenge for pedagogy, assessment, teacher education and policy is to recognise how routine practices generate environments of exclusion, and to reconfigure those practices so that mathematics becomes a space of recognition rather than rejection, marginalisation, and exclusion.

6.1. Pedagogy: Valuing Diverse Repertoires

At the level of pedagogy, exclusionary atmospheres are disrupted when teachers create opportunities for pupils to work in multiple ways and see their approaches treated as legitimate. Tasks with several entry points communicate that participation is possible even for those who have not yet mastered dominant procedures, and classroom discussions that explicitly compare strategies encourage pupils to recognise value in both informal reasoning and formal algorithms [43,44]. The treatment of error is equally significant. When mistakes are displayed as evidence of incompetency or shortcoming, they foster shame and silence, but when examined as partial insights, they affirm that error is intrinsic to mathematical inquiry [45,46]. Such pedagogical choices recalibrate the classroom environment from one of surveillance to collaboration and recognition, supporting the development of identities in which students see themselves as legitimate mathematical participants [47,48].

6.2. Assessment: Broadening Recognition

Assessment practices shape the atmosphere of mathematics as powerfully as pedagogy. Conventional systems that reward only speed, accuracy, and written form reinforce exclusion, particularly for learners from diverse linguistic and cultural backgrounds, including pupils with disabilities and those learning mathematics in a language other than their home language [49,50]. Corridors of belonging open when assessment is broadened to include oral explanations, collaborative problem solving, digital modelling, and reflective portfolios, which allow students’ reasoning and creativity to be recognised alongside procedural accuracy [51,52]. Formative approaches such as iterative drafts, low-stakes quizzes, and ongoing feedback reduce the anxiety of one-off high-stakes testing while helping teachers respond to learner diversity [49,53]. By diversifying assessment formats, schools create atmospheres in which pupils are acknowledged as mathematical thinkers rather than judged solely by their ability to complete timed exercises [54].

6.3. Teacher Education: Cultivating Awareness

Teacher education plays a pivotal role in equipping practitioners to notice and shift classroom atmospheres. Pre-service teachers benefit from learning to attend not only to lesson planning and curriculum coverage but also to the affective air that circulates in their classrooms. Silences after mistakes, discernible anxiety during timed tasks, or resistance in response to method policing all provide atmospheric cues that can be interpreted and addressed, therefore cultivating teachers’ capacities to pay closer attention to responsive variation and become acutely aware of them is central to this work [55]. Teacher education can also model methodological pluralism by requiring future teachers to engage with pupils’ invented strategies alongside canonical methods, or by designing assignments that draw upon multilingual repertoires, thereby valuing diverse ways of reasoning as legitimate contributions [56,57]. Reflexivity is equally important. Teachers’ own cultural, linguistic, and disciplinary trajectories shape how they interpret participation, and so a reflective engagement with these positionalities can enhance levels of sensitivity in relation to more exclusionary dynamics they might otherwise reproduce [58,59].

6.4. Policy: Shifting Institutional Climate

Atmospheres of mathematics classrooms are also sustained by broader institutional arrangements. Practices such as rigid tracking, public ranking and the proliferation of digital dashboards promote spaces of competition, anxiety and comparison [60,61]. Policy frameworks that reward efficiency through standardised testing intensify these conditions [62]. By contrast, policies that delay or reduce tracking, that support project-based and collaborative assessments, and that reframe data use around recognition of growth rather than surveillance foster settings more conducive to belonging [61,63]. These changes are not beyond reach. Pilot programmes and alternative assessment systems already exist, demonstrating that it is possible to imagine and enact policy frameworks that resist reproducing exclusionary atmospheres [62]. What is required is the determination to support/advocate building school systems based on justice that will privilege recognition, visibility, and real participation over competition, standardisation, and surveillance.

6.5. Concluding Reflections

The allegory of Dante’s Inferno has been activated here not to dramatise the shortcomings of pupils but to illuminate how ordinary practices such as timed tests, method policing, grade hierarchies and linguistic borders function as circles of exclusion. Dante’s journey, however, does not end in perpetual descent. His passage through Hell concludes with an upward movement, reminding us that transformation is possible. If the nine circles represent atmospheres of exclusion, then the pedagogical and policy task is to construct corridors of belonging: routes through which learners may move, re-enter participation and encounter mathematics as a site of recognition rather than exclusion.

Exclusion in mathematics education is simultaneously affective and structural. It resides in shame, silence, and self-doubt, but it is also organised through institutional architectures of judgement and refusal. Designing corridors of belonging therefore requires attention to both registers. The pressing question is whether mathematics education will continue to replicate spaces/environments of exclusion or whether it will, indeed, take on the responsibility of constructing architectures through which belonging, recognition, and mathematical meaning-making can flourish.