It’s Understandable If It Destroys You, Right?—Grades, Students’ Self-Images, and Quantification

Human life is increasingly quantified. From blood pressure to body mass index, from likes and retweets to performance metrics at work, from IQ results to facial attractiveness scores issued by smartphone apps. Many of these numbers have the potential to substantially shape how individuals view themselves, and yet the link between quantification and self-image is to date not well understood. My window into this phenomenon is one of the most ubiquitous and influential metrics worldwide: the school grade. Based on ethnographic fieldwork in a German comprehensive school, I explore how students’ self-images are shaped by their numbers. Comparing students’ official and unofficial remarks reveals a striking contrast between a seemingly detached stance toward marks and a powerful feeling of being defined by them—notably with regards to “intelligence.” Nevertheless, rather than passively identifying with their grades, especially low-performing students draw on a wide range of strategies in an effort to negotiate their self-image in light of their numbers.

The school's meeting room was an oddly shaped little space that looked as if it had been squeezed in between a biology classroom and a staircase. It was filled almost entirely with an octagonal table, surrounded by eight chairs. A flipchart and a ventilator stood in the corner, and the blinds had fallen off onto the window sill. Whenever I could, I co-opted this room for my interviews with the final-year Abitur (A-level equivalent) students in a German comprehensive school. To my surprise, Enes turned up punctually to the minute. He was Turkish-born, 20 years old, tall, and with a broad, somewhat overweight build; he had short black hair and a matching beard. Overall, Enes looked too old to still be in school, and at first sight, he appeared slightly threateningan impression that was however quickly dispelled by his kind face. Before long, Enes and I started talking about his school biography. He spoke about trouble concentrating in primary school, going to the comprehensive for his envisaged Abitur and finally having to repeat the previous school year after he had been retained due to low grades. Thanks to the school's central database, I already knew that Enes still had very low marks, even though he did not quite tell me so. In fact, several months after our interview, it was because of his results that he was not admitted to sit the final Abitur examinations and had to leave school without the diploma. I asked Enes about his favorite ever teacher, and he named his former music teacher who had thought that Enes was a choir talent even though he had never joined because it "wasn't for him." As his least favorite teacher, he cited a woman who, as he said "told me relatively often that nothing would become of me and that I couldn't speak German." After some time, I posed one of my classic questions: "What do you think grades measure? What do they refer to?" Enes grinned and rubbed his face with his hands, he sighed and then said earnestly, "Well firstly there's the oral 1 and the written. . .the oral is, I suppose, made better through sympathy points (Sympathiepunkte). But also through your own performance. How you behave in school, how you behave with the teacher." He broke off. I went a step further by saying: "Sometimes you hear people say that grades correlate with intelligence. ('I see!') What do you think of that?" Within a heartbeat, Enes answered: "I don't think so. It's more that the grades correspond to. . . studiousness. I would say that good grades are the result of a student who shows a lot of studiousness." I dropped the subject and after a while talking about related issues, I tried a thought experiment with Enes. "Imagine a pupil who continuously has very low grades. Do you think that does something to the student?" Enes hesitated but then said: "I think the person who gets very bad grades, or rather only gets bad grades. . .would ask themselves the question if that person was stupid or not, I assume. And whether. . .it makes sense to still go to school if you already get bad grades anyway."

Introduction
Human life in the twenty-first century is many things-it is also quantified. From the first in utero measurements of the embryo to those tracking a child's development, from school grades to IQ scores and performance ratings at work, from body mass index (BMI) to blood pressure, from salary to screen time-numbers 2 now accompany individuals from the womb to the tomb. Many of them have the potential to inform how we think about ourselves, for instance, when they seem to indicate whether we are healthy or unwell, fit or lazy, successful or failing, and clever or not so much. Despite a blossoming academic interest in quantification, the link between numbers and self-image has to date largely escaped scholarly attention. In this article, I begin to explore the relation through an ethnography of one of the world's most influential social metrics: the school grade.
During extensive ethnographic fieldwork in a disadvantaged German comprehensive school, it became apparent that, even though students often denied this being the case, grades had a significant impact on how they perceived themselves. In particular, the pupils often treated grades as a reliable measurement of their intelligence. My fieldwork, however, also illustrated that especially low-performing students did not straightforwardly internalize their grades, as educational research can sometimes make it seem. My informants rather drew on a variety of strategies designed to protect their selfimage from the potentially corrosive effects of "bad" grades. The most common tactics were highlighting achievement outside of school, explaining "bad" grades away, emphasizing "good" grades, and engaging in self-deception. I offer an analysis of how each of these strategies answers particularly to the quantificational nature of grades, but also why it is this very nature which makes grades difficult for students to erase as a source of identification.

Context and Methods
The ethnographic fieldwork underpinning this article was conducted during 12 months in a German comprehensive school in the federal state of North-Rhine Westphalia. The German school system is a particularly intriguing one for exploring the question at hand since it heavily quantifies its attendees. High-stakes testing and formal assessments have increased noticeably over the past two decades (Grek 2009) and, as oral participation in class is graded, essentially every day of school "counts." As a result, secondary school students receive between 100 and 120 marks per school year. The grading system is based on a six-point scale, on which each number can be modified with a plus or minus. The very highest result is a 1+, followed by a 1, 1-, 2+, and so on, down to a 6.
Grades play a pivotal role in the lives of German students and are often the sole determining factor in institutional decisions of the most far-reaching kind. Grades are the basis of primary school teacher recommendations as to which secondary school type a student should attend, they are also decisive for retentions, and for admission to the Abitur or university. While the importance of grades may create the impression of a meritocratic education system, empirical research does not support this conclusion. In fact, among OECD countries, Germany has one of the highest correlations between an individual's background and their school success (Quenzel and Hurrelmann 2010, 20, 28). One of the many ways in which educational injustice is cemented is in the early "tracking" of children into secondary school types of varying prestige, at the age of 10 or 11 (Letendre, Hofer, and Shimizu 2003). The two most common types of secondary schools are the reputable Gymnasiumsometimes likened to British grammar schools-and the less well-regarded comprehensive school. For reasons which include prejudice, barriers to learning, and lower parental ambitions (Quenzel and Hurrelmann 2010, 14), the likelihood that the child of a skilled worker is recommended for and attends a Gymnasium is four times lower than for a child from the educated middle class (Hußmann et al. 2017). For many of my informants at the comprehensive, their own school type was thus considered "second best"-an option for those whose primary school grades were (for whatever reason) not high enough to attend the Gymnasium or who felt that they did not fit in there.
My fieldsite school was a large institution with approximately 1,200 students and was located in a socioeconomically disadvantaged area in a medium-sized city. The student body was certainly diverse in terms of its backgrounds, but a large proportion of pupils lived in the little reputable area surrounding the school and had experiences with poverty, precarity, or parental unemployment. A great deal of students-though by no means all-had a migration background. The degree of variety was large also in this regard, including recently arrived refugees from Syria, first-generation migrants from Afghanistan, Iran, or Iraq, but also second-or third-generation Turkish-Germans, Russian-Germans, or Polish-Germans.
Participant observation and qualitative interviews formed the backbone of my research, and I focused on three classes, following a maximum variation sampling strategy (Given 2008, 697). The cohorts were a final-year biology major (students aged 18 to 20), a year nine philosophy class (ages 14 to 15), and a year five class (ages 10 to 11). I presented myself as a researcher interested in what students think about grades and gathered informed consent either from students or additionally, where required, from parents. Being roughly at the age of a trainee teacher and looking relatively young, I acquired a liminal status vis-á-vis the students. While some of the older pupils approached me, for example, about scholarship applications, the younger children often compared me to their older siblings in terms of age or looks. On one occasion, an 11-year-old student jokingly presented me to a friend with the words "she's one of us, she's just long." I sat in class with the students, often in the seat of someone missing that day, spent the breaks with them, shared part of the way home, and accompanied the pupils to a wide range of events including away days, career fairs, results, and exam days. The data gathered this way was complemented with a large corpus of qualitative, semi-structured interviews with my informants throughout the year. I also interviewed teachers and parents, even though the results are less relevant for the question discussed in this article.
By means of ethnography, I sought to explore how students navigate a context in which an important and large part of their lives is routinely quantified. In the following, I investigate one aspect of this lived experience in greater detail, namely the relation between grades and students' self-images.

Grades, Quantification, and Self-Image
That marks can have an effect on students' self-images even beyond school is a well-represented point in the academic literature on education. Jörg Ziegenspeck, for instance, states in his extensive treatise on grades and reports in Germany, that the broad-brush distinction between "good" and "bad" pupils is a "global valuation which can hardly be taken by the student and their parents as restricted to the concrete and bounded school and learning setting. Rather, performance judgments are taken 'personally'" (Ziegenspeck 1999, 31, own translation. See also Quenzel and Hurrelmann 2010 for a more current reiteration of this). The philosopher of education Robert Paul Wolff (1969) argued as early as 1969 in an essay on grading in the United States that "the American student lives, breathes, grows and defines himself in a world of grades" (ibid., 459). That grades can influence how students view themselves as a person is also a premise of some of the most well-known classic studies of school cultures, including Reproduction in Education, Society and Culture (1990) by Bourdieu and Passeron and Learning to Labour (1977) by Paul Willis. Explicit attacks of grading by scholars and public intellectuals alike also frequently reiterate the point (see, e.g., Bower and Thomas 2013;Illich 1973;Kohn 2013;Monbiot 2022;Schinske and Tanner 2014). Some quantitative work exists as well, for example illustrating an impact of marks on self-esteem (Klapp 2015;Owens 1994).
Even though ethnographies focusing specifically on grades are rare, ethnographies of schools constitute a lively genre. Some of the works in this tradition at least touch on grades and lend further support to the relevance of marks for students' identities (Bittencourt 2021;Everhart 1983). One of the few qualitative studies to foreground student perspectives on grades is Becker et al.'s work (1968) on US college students and the "GPA perspective." The central argument is that where marks are the primary means of acknowledgment, students necessarily prioritize the GPA over other things in their lives. Grades hence "come to be a measure of personal worth, both to others and to one's self" (ibid., 55). Rabow et al. (1998) continued work on the GPA perspective and argue that it does not originate in the students' time at university but instead has its roots in early school experience.
The identity-defining power of grades is also alluded to within anthropology. In an aside to her work on indicators and quantification, Engle Merry mentions that "in some of the most successful examples of responsibilization, such as grades in school, the indicator comes to shape subjectivity, defining for the individual his or her degree of merit" (2016,33). Scholars have also pointed to the fact that this effect is not limited to the Global North. For instance, Kawanishi notes on the Japanese standardized rank score for pupils-the Hensachi-that "[it] painfully suggests to many students that they are inferior to others. Its impact on them and on their attitude to life is so strong that it often lingers throughout their lifetime" (Kawanishi 2009, 79).
The impact of quantification generally-rather than grades-on individuals' self-image is to date not well researched. Quantification is here understood as the transformation of a quality into a measurable size, a quantity (Ritter and Gründer 1989). Quantification translates an aspect of the empirical world into symbolic language, often using numbers, but possibly also letters (think of the US or UK grading scales), or other symbols such as smileys or stars. Two distinct types of quantification are to be distinguished, as delineated in a foundational article by Espeland and Stevens (2008). Where quantification is used in lieu of a name or signifier, the sociologists speak of "numbers that mark." Examples are postcodes, telephone numbers, or the digits on football players' shirts. These numbers do not carry any mathematical meaning and do not allow for sensible comparisons between entities. "Numbers that commensurate" on the other hand, do just that. School grades, but also almost all other social metrics such as the IQ, BMI, university rankings, and so forth belong in this category. Commensuration makes entities comparable by imposing the same unit on them. Quantification of the commensurative type thus introduces a spectrum or scale, upon which entities can be placed and thus compared with one another. As Espeland and Stevens put it, commensuration "transforms all difference into a quantity [. . .]. Difference or similarity is expressed as magnitude, as an interval on a metric, a precise matter of more or less" (2008,408). It is this commensurative type which I refer to when using the term "quantification." The scholarly literature on the social effects of quantification has grown rapidly in the past two decades (Berman and Hirschman 2018;Mennicken and Espeland 2019). Works that speak to the issue are widely dispersed across disciplines and cover topics such as classification, commensuration, indicators, metrics, or rankings-to name just a few. The connection between quantification and perceptions of self is, however, not an explicit research focus in quantification studies broadly construed. A notable exception is an article by Charles Stafford (2009), detailing ethnographically how a Taiwanese tradeswomen uses numbers to portray a certain image of herself. An area of scholarly research that lends further robust, if indirect, support to the identity-defining power of numbers is that dedicated to practices of selftracking. The term refers to the "monitoring, measuring, and recording [of] elements of one's body and life" (Lupton 2016, 1), usually with the help of digital devices such as smartphone apps or wearable sensors. The vast majority of trackable parameters, such as daily steps, productivity, calorie intake, etc., are displayed to the user in the quantified form, for example as levels, scores, counts, or percentages (Lupton 2013(Lupton , 394, 2016Schüll 2016, 5). While there exists a variety of reasons why people engage in self-tracking (see Berman and Hirschman 2018, 257;Mennicken and Espeland 2019), by far the most commonly cited motivation is gaining knowledge about oneself. The slogan "Know Yourself. Live Better" with which the Jawbone Up Sensor was marketed (Crawford, Lingel, and Karppi 2015, 487), epitomizes this. Similarly, the Quantified Self-movement, a worldwide network of particularly avid self-trackers, operates under the motto "self-knowledge through numbers" (Quantified Self 2022). Ethnographic work on self-tracking shows that hitting a quantified goal can elicit powerful feelings of accomplishment and personal worth (see, e.g., Lupton 2017;Pink and Fors 2017). On the other hand, especially patients with multiple chronic conditions frequently avoid (medical) self-tracking because their "bad" numbers can mean that "you get reminded you're a sick person" as one informant put it (Ancker et al. 2015, 1). A powerful example of the potential of numbers to figure centrally in one's sense of identity is a poem by former Quantified Self member Alexandra Carmichael (2010quoted in Lupton 2016, in which she explains why she stopped tracking: Each day my self-worth was tied to the data. One pound heavier this morning? You're fat. 2g too much fat ingested? You're out of control. Skipped a day of running? You're lazy. Didn't help 10 people today? You're selfish. It felt like being back in school. Less than 100% on an exam? You're dumb.
The existing work on self-tracking hence indicates that for those logging and analyzing aspects of their life, numbers promise to offer deeper insights into who, or how, they are.
To recapitulate, research by education scholars from different traditions strongly suggests that grades can significantly shape the way students perceive themselves. Ethnographic engagement with the phenomenon is rare, however, and as a result, the specific mechanisms of identity formation through grades remain largely in the dark. Much of the existing literature creates the impression that students simply adopt an image of themselves, which corresponds to their marks-perhaps along the lines of "good," "bad," or "mediocre." This model of passive identification was not supported by my fieldwork. Most importantly, none of the existing studies consider grades as a technology of quantification and query the significance of their numerical nature. As will become clear, the way in which students think about and engage with grades is very much shaped by the fact that the latter present themselves to the pupils as numbers.

Graded Identities
A consistent finding during my fieldwork was that many students stated, contrary to the widespread hypothesis in the scholarly literature, that grades did not influence how they saw themselves as a person. When I asked 18-year-old Leila, what she thought grades reflected, she replied "just my school performance in the subjects. Not what kind of a person I am, but just my school performance. They don't say anything about my character, but just. . .well school." In response to the question whether grades shaped the way he viewed himself, Malte (18) answered similarly: "Not as a human. . .because for me that doesn't have much to do with school. But as a student, yes, of course." The 11-year-old Jamil asserted: "Grades don't mean how good you are. I think grades only mean if you revised or not." Final year student Teresa (18) lamented about her school experience that "everything is judged in grades. I'm not a grade. . .you know?" Based solely on the official convictions uttered in the interviews, it appeared as though students at best interpreted grades as a reflection of their school-related behavior, but never as a testament to their overall character. However, my ethnographic work also revealed a striking discrepancy between assertions in interviews, and more heedless remarks as well as comportment during school life. One example of this divergence, in my interview with Enes, was described in the introductory vignette. Another instance when grades were read as a reflection of who one was, was when 11-year-old Nasir received back a maths exam sporting a big red 5-. He muttered "I revised and I got a 5-. [. . .] I'm just too stupid. I am so stupid. Nothing will ever become of me, I'll never achieve anything in life." Maria, the valedictorian from the final Q2 year argued that she wanted to get a good Abitur result in order to boost her confidence later on in life. As she put it: "[. . .] later one can maybe look back at the Abitur and say 'Oh, I had these good grades once,' when you're not feeling well. And 'I can do it again. I can reach this standard again.'" In other words, the reports here served as a reminder of who one could be.
A particularly intriguing source of insight was a thought experiment that I conducted in the interviews. I asked students to imagine a different pupil who had so far only received very low grades in their school career. I then posed the question whether and in what way this would affect the student. As the informants whose answers I have reproduced below all dealt with low grades on an almost weekly basis, it is reasonable to assume that their answers were shaped by their own experiences: Sad. He wouldn't show the whole world when he would get something like that but yes, he would just feel really sad. He would think about himself "I am bad. And. . .yes I am bad." (Dennis,11) [He would think] I'm fucked. I'm fucked! (Jamil, 11) Well, if he's not completely stupid then he would be ashamed of himself. (Daniel,14) I would even, I think, believe that he thinks about himself that he is. . .useless, I'd say. Because I too have. . . I. . .know a few of those people. (Alex, 15) I think he would become very self-critical. Would, let's say, look in the mirror more often and think: "What kind of a person is standing in front of me? Somehow, I don't recognize myself in him." Because he wouldn't live up to his own expectations. (Ilja,18) The replies suggest that grades shape students' self-perception far more deeply than their assertions in the interviews would make it appear. Rather than being strictly limited to school-behavior, grades here appear as an indication of personality ("I am bad") and general worth ("he is useless"). Highperforming students interestingly expressed very similar views: [One would think that] one has failed. I mean that one is, on a social level, just not worth anything. And then also with this big fear of social decline, that one won't find a good job later or that one cannot keep up one's living standard. I do think that it would be a very severe issue. (Jarek,18) When grades signal to you that you know. . .that you are bad, then one also feels bad. And at some point, we also had this in economics, if. . .if a person does not find a job afterwards, they feel worthless. (Jonas,14) A particularly strong connection between grades and self-perception was to be observed with regards to the notion of intelligence. The great majority of my informants linked school marks with intelligence, in one way or another. Some students, such as Nayla, the 5c star student, expressed the view directly in our interviews. When I asked Nayla if she thought one's grades were related to one's intelligence, she replied: "Yes, well. . .it does have something do to with being smart. If you, for example, always write 1s or 2s, then it is just true that you must be smart. But if someone, for example, only writes 5s or 6s, then you can also say that they are not so smart." In response to the same question, the 18-year-old Julia stated that in school "you grade how clever the person is." Enes was one of the students who explicitly denied that intelligence was related to one's grades, but nevertheless later mused that someone with consistently low grades (like himself) would inevitably wonder if he was "stupid." The close perceived connection between grades and intelligence was also borne out in responses to the abovementioned thought experiment: One will think. . .he will always think that he is. . .stupid. That he cannot do anything. That he just doesn't accomplish anything. That he is a failure. And. . . (Pause). Yes. (Valentin,11) I think that that would change something about the self-image. Because, in today's system you're being told that grades reveal everything. How smart you are in maths, how good you are in English and so on. But it's not that which counts in life. Good grades, I think. . .you shouldn't let this destroy you. But it's understandable if it destroys you, right? You know, that you lose a little confidence. (Sonia, 18) I believe that the child wouldn't get such good self-confidence and would just think that one is stupid and can't do anything. (Julia,18) Again, the view extended to high-performing students like Natasha (14), who stated: I would say that the word "intelligent" would for this person really be thought in a bad area. That she would think that one is not really. . .that the person is not really intelligent. She would think of herself: "Well, I can't do anything. I am not competent enough. I will not accomplish anything in my life." That grades could be a straightforward indicator of a student's intelligence is strongly contested by educational research. A myriad of factors, which are unrelated to cognitive capacities, have been shown to influence which grade is issued. For instance, teachers' grading styles and prejudices, but also students' socioeconomic background and parental ambitions play significant roles (Ingenkamp 1976;Maaz, Baeriswyl, and Trautwein 2011;Oelkers 2002). Even pupils' first names (Bonefeld and Dickhäuser 2018), handwriting (Hauschild 2014), and looks (Bull and Stevens 1979) can be relevant. And yet, many of my informants treated grades not so much as appraisal or feedback by their teachers but rather as objective measurement. In other words, they assumed an indicator-feature relationship between grades and intelligence. One of the most consistent findings in quantification studies since the days of Porter's seminal Trust in Numbers (1995) is that numbers are closely associated with the notions of objectivity, rationality, and ultimately truth. Several students were in fact convinced that grades were much superior to written evaluation for gauging "how one is." Eleven-year-old Nelly argued that "if you don't get grades then you don't know how good you are and when you get grades you can evaluate yourself better." Her classmate Angelika stated: "The text can't really explain if you've done it really well or badly. But the grades. . .show. . .really show it." Beyond suggesting to students the presence of measurement, grades had additional effects on how they viewed intelligence. Grading entails subjecting all students to the same metric-the marking scale-and thereby orienting these different entities along a shared scale. One of the repercussions of this perceived commensuration was that intelligence appeared as a single, clearly delineated feature, such as height, rather than as a multifaceted phenomenon, like, say, creativity. When I asked 11-year-old Dennis if he could imagine that everyone was equally clever in their own way, he replied as if he thought me insane: "No. Doesn't work. No. I think. No! Never in a million years!" When I asked students who they thought the smartest kids in their class were, they usually named those with the top marks. The idea that different types of intelligence could exist-a theory which is seriously discussed in the scholarly discourse (see, e.g., Aspara, Wittkowski, and Luo 2018; Gardner 2006; Mayer, Salovey, and Caruso 2008)-was hardly ever referenced. A notable exception was Maria, who stated that "you can be intelligent on different levels than on a grade level [. . .] socially, for instance, that you can deal well with others." Also, Enes departed slightly from the predominant view when he said that a friend of his brother had served as a deterring example for him because he had been "very stupid in school terms." Apart from these rare exceptions, students usually interpreted intelligence as that which is "measured" by grades-a single feature, picked out by a metric like temperature in degrees Celsius.
Closely connected to the singular entity view of intelligence was the widespread belief that the feature behaved in a linear fashion-a belief which, in turn, fostered comparison among students. My informants often talked about intelligence as if it were a matter of more or less as if there existed a "smartto-stupid spectrum" upon which each person occupied a definite locus. This transformation of individual difference into magnitude is a classic effect of commensuration and allows for entities-in this case students-to be placed in a competitive relation with one another. For instance, when Enes heard about a classmate's grade in a recent exam, he exclaimed: "Wow, you're even worse than I am." Eleven-year-old Milad shouted, when I aided a high-performing classmate of his with a task: "Don't help him, he's smart. Help me!" One of the widely recognized best students in the final year, Jarek, summarized the issue succinctly when he talked about the pressure he felt about the fact that fellow students sought to compare themselves to him: Students were not the only ones to draw on grades in order to ascertain their relative "cleverness" or "being good"; the phenomenon also extended to parents. During a thought experiment, when he was asked to explain how he would react to a 2 in an exam, Jamil stated: With a 2, I'd be happy. . .would show it to my parents. And my parents would ask me: "What grade does Mehmet have?" When Mehmet has a 6, they'll say "Well done." And she [Jamil's mother] says like: "Who wrote the best grade in class?" And as always it has to be Nayla! When I say it's Nayla. . .she [his mother] says "Get better. Do a 1 yourself!" The Leila worried that both her parents and her teachers could think of her as stupid because of her low grades. She also explained that it was painful for her to hear her parents' responses to low grades: "For example, 'This can't be, you can't always be mediocre.'" The term "mediocre" in itself implies that this is not an absolute judgment but rather one which is based upon the comparison.
In the context of my research then, students routinely drew on grades as a reliable source of information about themselves, especially with regards to intelligence. The quantificational nature of grades implied the presence of measurement to the students, many of whom assumed a clear indicator-feature-relationship between grades and intelligence, sometimes even despite official statements to the contrary. Grades not only significantly shaped the students' views about their own degree of "cleverness" but also about the concept more generally. Intelligence emerged, much in line with Jo Littler's observation of contemporary discourse (2018, 4), as a solitary and linear feature. Moreover, grades commensurated students and thus enabled them and their teachers or parents to make comparative judgments about different pupils.
My fieldwork, however, also showed that especially those students who have the most to lose by handing over their self-image to their marks do not simply surrender to their results. In the following, I detail the four most common strategies which low-performing students drew upon to negotiate and protect their identity. I observed any of these strategies in many different pupils but, for the sake of clarity, I will here mainly concentrate on the case of one particular student, Milad, who strikingly exhibited all of them. I also discuss why the quantificational nature of grades makes the latter difficult for students to contest, despite the resourceful application of counter-measures.

Negotiations of Self in a Marked World
Eleven-year-old Milad had been born in Germany and was the second eldest of four boys. With his parents, who had migrated from Afghanistan and who were then both unemployed, he lived in close proximity to the school, in the little reputable area of town, locally associated with poverty, crime, and "migrants." Milad was skinny, had short dark-brown hair, hazel eyes, and fine features. Lively, and with a propensity of silliness, he was soon taken in by a group of Syrian boys in his class, together with whom he often got into physical fights during the breaks. Milad's school grades were quite low-a 4 in almost every subject-a fact which the other boys teased him with on a regular basis. Statements along the lines of "You're so dumb" or "Can't you think?" were frequent, as were ironic comments such as "Wow, Sherlock Holmes" or "You genius" when Milad said something correct in class.
Despite the official reminders of his education "failure" in the form of school grades and the daily mocking of his allegedly low intelligence by his friends, Milad did not seem to simply adopt the image painted of him. Rather, he drew on a range of strategies, all of which had as their aim to maintain at least a somewhat positive self-image. The first strategy Milad employed was to stress achievement outside of school. On a hot summer's day in the middle of a peculiar type of schooling shaped by governmental decisions around Covid-19, I was sitting in a classroom with half of the 5c class which had been split up. Each of us tethered to their desk with at least 1.5 meters distance in between, the children were shouting across the room to communicate with one another and myself before the arrival of the teacher. Jamil began to tell me about his successes in mathematics. As his story about a maths competition unfolded, I noticed Milad starting to fidget at his desk in the corner. Suddenly, he yelled across Jamil's talk: "Yes, shut the fuck up now!" He continued shouting over him: "We had clubs in primary school, we had clubs and I was in the football club!" Milad here drew on football as something he succeeded at in order to stress that he too had achieved something. Sensing perhaps that he could not compete with Jamil's widely acknowledged cleverness, Milad emphasized a quality which both was distinctly located outside of the school context and also unmistakably physical as opposed to cerebral. In the interviews, this strategy of stressing alternative kinds of achievement was employed by students of all ages. Pupils often told me that "school isn't everything" and talked about a range of other things that they were good or successful at. The list of cited examples ranged from dancing to gaming, from drawing to having a girlfriend.
Numbers not only serve to represent value, for example in the case of prices but can also create it in the first place. The very fact that quantification is applied to a phenomenon or entity often indicates that it is of some importance (Adams 2016;Stafford 2009). In other words, what is counted, countsat the risk of excluding the unquantified or unquantifiable (for further discussion, see the literature on the McNamara fallacy, Cook 2019; Hendrick 2015; O'Mahony 2017). Highlighting achievement outside of school allows students to assert an individual conception of value, and to uphold a positive self-image beyond the predominant metric of the school grade. Nevertheless, it has to be acknowledged that the students' leeway in defending alternative ways of valuing is restricted in the epistemic context they navigate. Grades not only take center stage because they purport to represent one of the key values of meritocratic societies, performance (Waldow 2011, 485), but also because they do so in quantified form. As Engle Merry notes, "the indicators that make the greatest impact are ones with strong institutional support and funding, a coherent and attractive narrative, and a composite indicator that allows for ranking" (2016,211). Faced with a metric as simple and institutionalized as the grade, it is difficult indeed for low-performing students to maintain an overall positive image of themselves, even if they underline other ways in which they excel.
The second strategy I witnessed was explaining "bad" grades away. Most of the students with low marks tended not so much to question the accuracy of the latter, but rather created a range of explanations for them. By far the most common reasons for low grades were, "I am lazy," "I have no motivation," "I didn't revise," or "I'm no good at this subject/topic." Some of the older students, like Enes, also mentioned likeability and argued that a particular teacher disliked their personality or behavior, such as chatting in class. When I asked Milad about his recommendation for secondary school, he told me that he had wanted to go to the Gymnasium. He added: "But doesn't matter. Because Gymnasium was too far, because I live here. . .like two minutes from here." In truth, the fact that Milad attended a comprehensive school would most likely not have been a result of geographical considerations but rather of his low grades in primary school-whatever the reasons might have been for these. Students not only explained away their own "failures" but sometimes also the "successes" of others. Jamil, in particular, was often in the grip of a hot envy of other pupils' good grades. For example, he told me that one of his classmates received better grades than him "only because she's German," and mused about a different girl that "she gives money to get good grades." High-achieving students themselves would also sometimes, though rarely, explain away their achievements. Jarek, for instance, argued that his stellar marks were to some degree the result of luck, in what might have been an enactment of due humility and perhaps safeguarding against other people's gleefulness if he were to fail one day. In her work on indicators, Engle Merry underscores that "counting things requires making them comparable, which means that they are inevitably stripped of their context, history, and meaning" (2016, 1). Espeland and Sauder argue along the same line in their study of law school rankings that "quantification can be understood as a systematic stripping away of author, protagonist, scene, and other core components of narrative [. . .]" (2016, 37). They note about their informants, law school deans, that "people find it difficult to let the numbers speak for themselves and almost invariably create narratives to explain or explain away the numbers" (ibid.). Explaining bad grades away is often an attempt to reintroduce narrative, allowing students to affirm a positive self-image by reframing the situation. Many pupils used this strategy to interpret their grades as a product of their behavior (e.g., not having revised), rather than resulting directly from the seemingly fixed and innate feature of intelligence. To endorse the belief that one is "stupid" would arguably amount to self-abandonment and quite likely, as Enes thought, in the loss of hope for any future (educational) success. Continuously low grades come perilously close to telling students that they are "stupid," and explaining them away was therefore a common attempt of defusing. Nevertheless, also this tactic has its limits. As Heintz writes, "while language always provides a Yes-and No-Version and thereby a sentence already carries its negation within it, a negation in the case of numbers needs to be actively produced" (2007, 78, own translation). Bläser adds, "this means that the simple assertion of the falsity of numbers cannot be carried out without some effort" (2017, 77, own translation). It is therefore not sufficient to simply assert the inaccuracy of a grade-and students tended not to do so-but a more complex process of reframing and retelling is required to protect one's self-image. In a context which issues struggling students with 100 to 120 reminders of "failure" per year, this is an extraordinarily demanding task, which usually does not succeed fully.
Another common strategy employed by students to defend a positive sense of identity served as a complement to explaining away "bad" grades: highlighting "good" grades, however few. In the case of Milad, this was a single 1 which he had received in engineering, mainly for doing very well in the task of building a pocket light. Whenever some of the children made fun of Milad's low grades, he would yell "And what did I get in engineering?!" At one point, Jamil came to me during a break to boast about his philosophy grade. He had received the only 1 in the class, an astonishing feat according to his teacher Mr Wegener. Jamil stood in front of me, gesticulating expressively as always, and said loudly: "Miss, I'm telling you, I'm the philosophy-BOMB." I laughed and said "Are you?" "Yes, I'm the philosophyBABA," he continued. "I'm the FATHER of philosophy!" While I was still laughing at Jamil's imaginative neologisms, Milad came running. He stopped short next to us and shouted with an expression of utmost sobriety: "I'm the father of engineering! I have a 1 in engineering!" Later in the year, I had the opportunity to observe Milad in an engineering class. I could not quite believe what I saw for there could not have been a more extraordinary contrast to Milad's usual behavior. He sat almost comically upright, and when the teacher started a short video clip, he asked permission to move his seat in order to see the screen better, in the politest way imaginable. Milad raised his hand for every single question and when he got an answer right, he turned around to his friends to say "I'm the smarty (Schlaumeier) here." When he once said something wrong, he muttered under his breath "That was wrong but I'm still the smarty." After class, Milad went up to his teacher and said: "Misses Hertel, who was the best in engineering last term? How was I in engineering?" Mrs Hertel jokingly replied: "You were awful!" They both laughed warmly and Milad asked again: "But who was the best?" "The best student is the one who knows least to begin with and most in the end." "That was me," Milad settled the question with a heartrending smile on his face. Charles Stafford has convincingly argued that when anthropologists discuss quantification, they often present it as "the hand-maiden of objectification, bureaucratisation, scientism and control" (Stafford 2009, 123). While, both empirically and historically speaking, there is indeed often good reason to do so, it is true that an one-sided approach can lead to an impoverished understanding of quantification. Based on ethnographic work in Taiwan and China, Stafford argues that quantification does not inevitably "reduce people to numbers" (ibid., 1), but that the latter can also be drawn upon to create and sustain a certain identity. When they highlighted their good grades, students too "narrate[d] the self numerically" (ibid., 108). As Espeland and Sauder have shown for law schools whose alleged quality is quantified in rankings "it becomes much harder to make status claims not supported by rankings, or to sustain identities that are not linked to rankings" (2007,20). Vormbusch argues similarly for calculative practices in human resource management that they no longer "allow actors to legitimately communicate descriptions of the field and their own actions outside of the frame for description and action created by the numbers" (2012, 222, own translation). My informants navigated a context in which, much like for ranked law schools or contemporary employees, a central part of their lives is represented by means of quantification. Having high grades is without a doubt the most potent way of convincing oneself that one is, or can be, a good student after all. For Milad, all of his efforts in this direction concentrated on the single perfect grade in engineering, and he was not the only informant to make use of this strategy of accentuation. In the interviews, all of my informants could name their best-ever grade off the top of their head, when prompted. Sometimes this particular mark even dated back as far as primary school, but the students were nevertheless able to relate in detail what, for instance, the topic of the examination had been. In an environment where one's self-image as a student is almost exclusively mediated by grades, it is crucial for pupils to continuously remind themselves of those particular marks which support their desired sense of identity-even if they are outnumbered.
The last strategy of negotiating one's self-image in the face of grades to be discussed here is downright self-deception. Its essence was captured in an intriguing interaction that I had with Milad. I was sitting next to him in an English lesson during which the children were to write their weekly vocabulary test. Milad had so far only received quite disappointing results, but on that day he was confident that it would be "a 1 or a 2" because he had known a few of the words that I had asked him before class. I was less optimistic. Mrs Sievers, the English teacher, distributed the test sheets face down and I also received one to keep me occupied. Shortly before the test started, Milad asked me: "What is sauber in English again?" "Clean," I replied. "And schmutzig?" "Dirty." He wrote both words on his left palm.
The children were finally allowed to turn the sheets around and started writing. Milad was constantly talking to himself under his breath and was hitting his forehead with his fist. On the other side of him, Sebastian was muttering "Shit, shit, shit," while Nelly was moving her lips soundlessly and staring into space. After Mrs Sievers had collected the filled-in test sheets, she revealed the answers and Milad's previous confidence was dwindling rapidly as he was counting his mistakes. "I had five mistakes," he told Nayla and Nelly, even though in truth there were many more. "That's maybe going to be a 2." During the following class, the lesson topic was reading an analogue clock, which Milad had already mastered. Instead of listening, he swiftly seized the still blank vocabulary test sheet lying before me and said "I'll do this one." He filled in as many words as he could, of course also remembering the answers Mrs Sievers had just revealed in class. For several other words, he asked me and wrote them down as I spelled them. Then, to my surprise, he handed the test back to me and said: "Can you correct this for me?" I agreed. The first two words were already wrong: "tooth" instead of "teeth" and "foods" instead of "feet." Because I hesitated to cross things out, I only wrote the correct words into the margin, but I could already see Milad's chest sinking next to me. Many other words were correct because we had of course filled in the test together. Still, others had a funny spelling (sausage = saufag). I corrected everything and gave the test to Milad. "Which grade?" he asked. I felt so sorry for him that I jokingly wrote down a 2+. I pushed the sheet back to him and his eyes widened. With an air of awe in his voice, he slowly said: "Woah, 2+!" "And how many points?" he added. I tried to make it look as if I was calculating and gave him at least half a point for every puny attempt, totaling 17,5 fictional points. But, Milad was still not done: "Out of how many?" he asked. I counted the words and wrote down 22. Finally, Milad asked "Can you sign it?" I did and wrote "for an especially nice student" over the top. "Great," Milad said with a big smile, "I'm going to show this to my parents." Now, it was presumably me whose eyes widened, for this twist caught me by surprise. In an attempt to cheer Milad up, I had just forged an official document which he was to take home and present as genuine. "Hey Nayla, Nelly, look! I had a 2+ in the vocabulary test!" Milad now called his neighbors enthusiastically, and the two girls looked with bewilderment from him to me. "Listen, you cannot show this test to your parents," I said quietly. "It's not real." Milad laughed and replied: "Yes, I will. It doesn't matter if it's real or not." A few days later, I asked Milad if he had actually taken the test home to his parents and his response was once again accompanied with a big smile; that he had and that they had been very happy.
What made this episode such an insightful one was that Milad seemed genuinely proud of his 2+ and systematically ignored how he had achieved it. Of course, he could not know that I was making the points and grades up, but the fact remained that we had completed the test together and, what is more, shortly after his teacher had announced the right answers. It was quite clear that Milad was so desperate for a good grade that he was willing to tweak his perception of reality somewhat, in order to achieve it. Selfdeception in relation to grades was not limited to Milad and I observed it on several other occasions. During my own school time in Germany, there already existed a dictum that one can now buy printed onto postcards or mugs and which pupils today still cite, albeit with tongue in cheek: "A 5 is almost a 4, a 4 is good, good means a 2 and a 2 is almost a 1." Quantification studies have repeatedly shown that numbers are closely associated with objectivity and facticity. Authors variously write about an "aura of objective truth" (Merry 2016) or describe numbers as "symbols to make truth claims" (Klausner 2018, 41) to refer to the same phenomenon. While Vormbusch argues that expert cultures, notably those which produce the numbers in question often do not believe in an "objective representational praxis" (2012, 21) of numbers, the lay perspective is nevertheless frequently characterized by profound trust in numbers (see Desrosières 2001;Mari 2003 for related discussions on statistics and measurement respectively). As Marilyn Strathern observes, those who are farthest removed from the production of a certain number, tend to sanctify it the most (2000,8). Resulting directly from the respectable epistemic status of numbers is the common presumption that they guard against self-deception. Crawford et al., for example, note in their historical analysis of body measuring that the trope of "knowing your metrics-as a precursor to self-knowledge and the good life can be traced from the first public weight scales onward" (2015,486). In fact, some of the earliest models of scales were marketed with pictures of slender women standing on the device and slogans such as "She doesn't GUESS. She KNOWS" (ibid., 489). Present-day self-tracking technologies are advertised with the same promise of insight into the frank truth of one's fitness and activity levels (ibid., 480). As was already discussed, many of my informants strongly preferred number grades to written evaluation because they felt that only marks could really offer reliable information about "where one stood" or "how one was." Low grades present such a blunt, unadorned, and painful "truth" to the students-often interpreted as a verdict on their intelligence-that it can become unbearable for some. While it may seem that numbers guard against self-deception, an ethnography of the grade shows that they sometimes necessitate it instead. Nevertheless, even this most far-reaching strategy to save one's self-image from corruption through low grades has natural limits. First, it is, much like explaining "bad" grades away, an enormously laborious and energy costly process, in particular when students are faced with almost daily grading. What is more, self-deception is by definition a reflexive process. Even though it may allow students to temporarily convince themselves, the strategy does not extend to other people, such as teachers, parents, and peers. Teasing or parental disappointment continues to remind low-performing students of the picture their grades paint.

Conclusion
Ever since their introduction to Jesuit schools in the sixteenth century, grades have developed into a truly global technology, figuring prominently in the lives of billions of young people. And yet, much remains to be learned about this most powerful metric. A barrier to fully understanding the effects of marks on students and, by extension, on society is that scholars frequently overlook their nature as a form of quantification. In this article, I have suggested that viewing grades through the lens of quantification allows us to analyze a widely acknowledged but little-understood phenomenon, namely that grades have a strong impact on student self-images. Ethnographic approaches to grading remain the exception, and yet the method offers a unique vantage point. Relying only on interviews or surveys limits the research to students' official and curated statements. In the present case, this would have created the false impression that grades have little to no influence on how students view themselves as a person. Accompanying my informants throughout a whole school year allowed a more nuanced picture to emerge and revealed that students routinely interpret marks as a reliable indicator of intelligence, assuming a process of objective measurement. In line with the marking scale, intelligence appeared as a singular and linear feature, as well as a commensurable, thus incentivizing comparison between students. Contrary to the impression created by some of the scholarly work in education, however, my fieldwork did not lend support to the hypothesis that students straightforwardly endorse their grades and incorporate them into their self-image. In particular low-performing students instead draw on a portfolio of tactics for saving their identity from the potentially undermining effects of "bad" and seemingly objective grades. Upholding alternative ways of valuing, reintroducing narrative, narrating the self numerically, and deceiving oneself must all be considered as answers to the quantificational character of grades. At the same time, it is this very nature and the resulting epistemic panache that makes grades so very difficult to challenge completely. Most of the existing work on grades is pedagogical in nature and considers marks only in terms of their usefulness (or lack thereof) for the process of learning. The findings in this paper stress that this "learnification" (Biesta 2009) does not do justice to students' lived experiences. Grades must be placed in a wider theory of quantification and its role in contemporary society in order to appreciate their significant and lasting effects on students-far beyond learning. The quantification of human life is, of course, not limited to the school context, and the results discussed therefore have broader implications. The student data unearths a strong link between numbers and self-image, suggesting that quantification is not simply a neutral technology but can rather have a substantial impact on those at its receiving end. As such, the present work provides reason to further investigate an experience that is integral to human life in the twenty-first century and which deserves more scholarly attention: being quantified.

Acknowledgments
First and foremost, I would like to thank my informants who generously shared their thoughts and experiences. I am grateful to Javier Lezaun and Morgan Clarke for our discussions on the topics addressed in this article. Finally, I thank the anonymous reviewers at the Journal of Contemporary Ethnography for their insightful comments.

Declaration of Conflicting Interests
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Arts and Humanities Research Council through the Open-Oxford-Cambridge DTP [ref. AH/ R012709/1]'. and the German Academic Scholarship Foundation (Studienstiftung des Deutschen Volkes).

Ethics Approval
The project was examined and approved by the University of Oxford's Central University Research Ethics Committee (CUREC) and the School of Anthropology and Museum Ethnography Research Ethics Committee (SAME REC) under the reference number SAME_C1A_19_004.