Abstract
Social institutions function not only by reproducing specific practices but also by reproducing discourses endowing such practices with meaning. The latter in turn is related to the development of the identities or subjectivities of those who live and thrive within such institutions. Meaning and subjectivity are therefore significant sociological categories involved in the functioning of complex social phenomena such as that of mathematical instruction. The present paper provides a discursive analysis centered on these categories of the influential OECD’s PISA mathematics frameworks. As we shall see, meaning as articulated by the OECD primarily stresses the utilitarian value of mathematics to individuals and to society at large. Furthermore, molding students’ subjectivities towards endorsing such articulation of meaning is emphasized as an educational objective, either explicitly or implicitly, as connected to the OECD’s definition of mathematical literacy. Therefore, the OECD’s discourses do not only serve to reproduce the type of mathematical instruction implied in the organization’s services concerning education, but also concomitantly provide a potentially most effective educational technology through which the demand of these very services may be reproduced.
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1 Introduction
Max Weber, one of the fathers of modern sociology, posited meaning as a category crucial to the understanding of social action. In general, Weber defined action as “human behavior linked to a subjective meaning [subjektiver Sinn] on the part of the actor or actors concerned” (Weber, 2019, p. 78, emphasis deleted). For instance, one cannot understand a community’s involvement in, say, a religious activity, without considering the meaning that people in the community assign to such activity. To do this, one could empirically investigate discourses articulated directly by the people themselves. Alternatively, one could study the discourses articulated within official or important texts adopted or followed by such people or community. Teaching and learning mathematics is a social phenomenon (cf. Lerman, 2000; Valero, 2004; Kollosche, 2016) and hence understandable in these terms. It follows that studying the meaning assigned to mathematics and to involvement with mathematical instruction^{Footnote 1} has the potential to contribute substantially to the growing branch of sociological approaches in mathematics education research (cf. Gellert, 2020).
With respect to the study of people’s discourses, for instance, Ornella Robutti, Paola Valero, and I analyzed essays written about mathematics by master’s students in mathematics preparing to become teachers (Beccuti et al., 2024). In particular, we employed the discourses articulated in these essays in order to study the process of formation of the participants’ subjectivity, which we described as analogous to that resulting from forms of religious ascetic behavior. Overall, we attempted to shed new light over part of the mechanism underlying social reproduction^{Footnote 2} with respect to mathematical instruction, which we understood as connected to the interplay between the participants’ process of becoming subjects and the meaning they ascribed to mathematics and to their involvement in it.
The link between meaning and subjectivity characterizing the latter study exemplifies a potential point of convergence existing between different streams of research in mathematics education. On the one hand, a more affectoriented branch of research concerned with meaning as assigned by individuals to mathematics and mathematical instruction has evidenced that there seems to be a relation between the latter and these individuals’ identity or subjectivity (e.g., Birkmeyer et al., 2015; Reber, 2018; Vollstedt & Duchhardt, 2019). On the other hand, researchers of a more sociological or sociopolitical tradition have discussed how the discourses or stories told about mathematics and mathematical instruction (and which confer meaning to them) are related to how subjectivities develop within institutions (e.g., Kollosche, 2016; Wagner & HerbelEisenmann, 2009). Moreover, a group of sociopolitical studies has provided insights on how specific types of students’ subjectivities develop in connection to the meaning they assign to mathematics and to their involvement in it, for instance, with respect to compulsory school students (Kollosche, 2017), undergraduate students (Bartholomew et al., 2011), and, as said, master’s students in mathematics (Beccuti et al., 2024). Other sociopolitical studies concentrating on institutional documents have further explored the connection between the implicit or explicit discursive meaning assigned to the teaching and learning of mathematics within such documents and the ideal subjectivities which are fabricated within the institutions regulated by such documents (e.g., AndradeMolina & Valero, 2017; Montecino & Valero, 2017; Kanes et al., 2014).
In the present paper, I will discuss a theoretical framework aimed at conceptualizing this point of convergence found in the literature from a sociological perspective. I will then employ these theoretical considerations in the analysis of an influential group of policy documents: the main mathematics frameworks of the Programme for International Student Assessment (PISA) of the Organization for Economic Cooperation and Development (OECD), with reference in particular to the most recent of these. My analysis will aim to explore the following two research questions.

1.
What is the meaning of the teaching and learning of mathematics articulated by PISA?

2.
Who is the (ideal) subject articulated by PISA with respect to this meaning?
By addressing these questions, the present article does not aim to provide explicit normative suggestions for the amelioration of mathematical instruction (cf. Kollosche, 2017). Indeed, given the foremost international influence of the PISA mathematics frameworks (cf., e.g., Beccuti & Robutti, 2022; Jablonka, 2015; Kanes et al., 2014), the present article primarily aims to contribute to the sociological understanding of the way in which mathematical instruction is globally reproduced. Reaching a clearer and more comprehensive picture of this phenomenon may nonetheless serve to open up or to broaden spaces of critique challenging the naturalness and the “takenforgrantedness” (Chevallard & Bosch, 2020, p. 56) of the discourses sustaining the OECD’s influence over mathematical instruction worldwide.
2 Theoretical framework
2.1 Defining meaning
Amit and Fried (2005), following Weber, remarked that the power subsumed under the types of authority associated with the functioning of educational institutions is crucially linked with claims of legitimacy of such power/authority. Concerning mathematical instruction, it is not only important to analyze this in the restricted sense of the acceptance of the legitimacy of a mathematical argument in a classroom setting, but also in the more general sense of the acceptance of the legitimacy of the discipline itself. This in turn depends on how the discipline’s overall meaning is articulated with respect to the people involved in it and to society at large.
Very generally speaking, the meaning of an activity can be understood in terms of the discourses which give reason or justify such activity. As said, Max Weber understood action as the combination of mere behavior and its associated meaning. Within research in mathematics education, in a comparable fashion, the anthropological theory of the didactics has provided a general understanding of any human activity in terms of praxeology: an understanding of the activity given in terms of its praxis (πρᾶξις) component (the activity itself) together with its logos (λόγος) component (the stories or discourses which sustain, justify and motivate such activity) (cf. Bosch & Gascón, 2014). At the highest institutional level, according to Chevallard, 2022, p. 185), a question is fundamental to ground the analysis of any activity: Why do people do it? In other words, what is the activity’s raison d’être? This question should be approached, according to Chevallard and colleagues (2015), by accounting for the stories or discourses which attempt to explain, found, justify, or support the activity itself. This should be done by delineating utterances “with a generally strong justifying and generating power. Such utterances are the things that endow our world with meaningfulness and takenforgrantedness” (Chevallard & Bosch, 2020, p. 56).
Other authors, belonging to a more sociological or sociopolitical tradition, have employed the resonating category of myth (μῦθος, mythos): a story told about mathematics or mathematical instruction which is used to make sense of people's engagement with it. Myths involve a strong explanatory and validating power, are often wellingrained in a culture, and substantially contribute to create (or shape) the subjectivity of those who are affected by them (Dowling, 2000; Kollosche, 2016; Wagner & HerbelEisenmann, 2009).
Notice that while the word “logos” carries within it an idea of rationality, the anthropological theory of the didactics rejects the idea of a universal rationality (Chevallard et al., 2015, p. 2616). Thus, logos could be interpreted in an almost neutral manner (cf. the neutral sense of “ratio” in Latin). In a similar, yet opposite way, the word “myth” retains perhaps an almost mystic or irrational flavor, but it can also be employed in a neutral sense since “calling a story a myth makes no claim about its veracity” (Wagner & HerbelEisenmann, 2009, p. 6).
Nevertheless, as an alternative to both words, I will employ Weber’s notion of meaning as a more historically neutral and general category, devoid of the aforementioned implicit connotations. Indeed, meaning for Weber is not “some kind of ‘objectively correct’ meaning, nor any such ‘real’ meaning arrived at metaphysically” (Weber, 2019, p. 79), nor is it—I add—objectively incorrect or irrational. It is instead a category which may comprise both seemingly rational and seemingly irrational discourses (cf. Weber, 2019, p. 80).
I will thus understand here the word “meaning” as simply what presents itself as being the drive as well as the cause pointing towards an action, that is, in this case, the very general action of teaching and learning mathematics. These will be the discourses which explain, rationalize, support, or sustain engagement with mathematics within institutions. I will employ the singular form “meaning” rather than the plural “meanings,” aiming to remark the attempt to unify under one conceptual category different (and potentially conflicting) discourses when they concur to legitimize the practice of teaching and learning mathematics in institutions, that is, when they generally concur to confer meaning to such activity.
2.2 Meaning, subjectivity, and power
As mentioned above, authors belonging to a sociological or sociopolitical tradition have remarked that the stories told about the discipline (and used to endow it with meaning) crucially contribute to shaping people’s subjectivities. This resonates with the conclusions of a more affectoriented stream of research which has pointed out the relationship between meaning and the subjectivity or the identity of the carrier or utterer of such a meaning.
Heine and colleagues (2006) suggested that meaning is a general need of human beings which is based on the necessity to draw connections between different domains, in particular between the self and the world. According to Vinner (2007), the search for meaningful learning is part of a general search for a meaningful life, which is a fundamental driving force for human action. Meyer (2008) argued that constructing a personal sense of meaningfulness for mathematics has to do with the constitution of the person itself. Suriakumaran and colleagues (2017) argued that meaning is a source for the generation of values producing people’s motivation to engage with mathematics. Vollsted and Duchhardt (2019) contended that “the need for meaning and a coherent system of meaning is forming the basis for the development of a coherent sense of self” (p. 142). Reber (2018) in turn referred to identity as one of the forms in which meaningfulness is delivered with respect to education. Furthermore, according to Birkmeyer and colleagues (2015), meaning in general is related to one’s identity, since when something or some practice is meaningful to someone then he or she gains orientation from this meaning.
Therefore, it seems that the general question of meaning cannot actually be disjointed from the question of the subjectivity/identity of the person who enacts and is driven (or should enact and be driven) by this meaning.
A radical and discourseoriented perspective on this issue is represented by the theory of the subject elaborated by philosopher Michel Foucault within his more general theory of discursive formations and of reproduction of social institutions, itself influenced by Weber’s scholarship (O’Neill, 1986). In Foucault’s theorization, “discourses” are “institutionalized patterns of knowledge that govern the formation of subjectivity” (ArribasAyllon & Walkerdine, 2017, p. 110). It follows that subjects can be understood as products of historicallyspecific available discursive positions which delimit the thoughts and actions of individuals and communities within institutional structures of power. As Kollosche (2016) remarked: “It is within the power relations we live in that we construct our own subjectivity, thus adjusting to and reproducing the very power relations that we live in” (p. 76).
According to Foucault, institutions work by means of the simultaneous reproduction of forms of power, forms of knowledge, and forms of subjectivity (cf. Walshaw, 2016). In particular, governing can be conceptualized as imposing various technologies of the self: ways of conducting people’s conducts or, in other words, mechanisms which govern people to govern themselves (Ball, 2017). These are evidenced particularly in discourses that individuals working and living in institutions use to make sense of (i.e., to instill meaning in) their own institutional experience and which thus serve to legitimize and reproduce institutions themselves. Various authors adopting a discursive Foucauldian stance have studied discourses articulated by people in order to investigate the identities or subjectivities of different categories of individuals involved in mathematical instruction, as said in the introduction (e.g., Bartholomew et al., 2011, Kollosche, 2017, Beccuti et al., 2024).
Importantly, following Foucault, discourses are not only available as utterances of individuals, but also crucially reside “on the surface”, so to speak, of institutions’ explicit ways of working (Olson, 2008, pp. 334–335).
The rational schemas of the prison, the hospital or the asylum […] are explicit programmes […] a set of calculated, reasoned prescriptions in terms of which institutions are meant to be reorganized, spaces arranged, behaviours regulated. (Foucault, 1991, p. 80, emphasis in the original)
As a consequence, the analysis of the discourses articulated by explicit programs regulating the functioning of institutions (e.g., those stated directly and openly in the documents which govern them) is paramount for understanding how subjectivities become constituted “from above”, so to speak.
A stream of research in mathematics education has thus employed tools derived or inspired from Foucault’s scholarship in order to explore how the discourses (“meaning” in the sense explained above) articulated within influential or official documents come to fabricate the ideal subjectivities which are apt to thrive within institutions (e.g., Kanes et al., 2014; AndradeMolina & Valero, 2017; Montecino & Valero, 2017).
In particular, Kanes and colleagues (2014) investigated how students and teachers of mathematics are fabricated as governable subjects in connection to participation to the OECD’s PISA program. As to the latter, a notion which evidences particularly well the influence of the project of subjectformation incardinated in its educational and political endeavor is the notion of mathematical literacy (i.e., the type of mathematical competence that the PISA tests aim to measure). The central relevance of this and related notions in the cultural politics of schooling was already evidenced by Apple (1992). Indeed, this notion has been identified as crucial to the aim of delimiting “a particular form of knowledge and order of meanings to be within the domain of the PISA regime” (Kanes et al., 2014, p. 155), thus serving as a fundamental discursive tool in the OECD’s project of setting a normative standard against which subjectivities have to be produced and ranked with respect to mathematical instruction. Interestingly, as we will see below, this notion does not include only reference to mathematical skills per se, but also importantly involves developing (or possessing) personal dispositional characteristics such as a good attitude to mathematics and an awareness of its importance and utility (Tsatsaroni & Evans, 2014; Jablonka, 2015; Niss & Jablonka, 2020). Thus, the notion of mathematical literacy exemplifies the interrelationship between discourses articulating meaning and connected explicit programs of formation of subjectivities. In particular, the inclusion of the aforementioned dispositional features in this notion “can be understood as the addition of an ethos that entails a commitment to behave” in a certain way (Jablonka, 2015, p. 604) which in turn would reflect “the expansion of the scope of measurement beyond cognitive dimensions of the skills of the human capital” involved in the OECD’s educational and political endeavor (ibid.). Hence, the notion of mathematical literacy has been and continues to be central in the project of establishing and reaffirming the scope of the OECD’s explicit program of influence over mathematical instruction.
Therefore, it seems to be important to provide a nuanced analysis of the PISA mathematics frameworks in terms of meaning and subjectivity focusing on the notion of mathematical literacy. This analysis would advance the latter stream of mathematics education research while also contributing to the general understanding of the social and educational impact of the PISA documents worldwide.
3 Data and method
PISA is an international standardized form of assessment conducted by the OECD aiming to test 15yearold school pupils’ performance on the main domains of reading, mathematics, and science. Starting from the year 2000, eight subsequent assessments were enacted, normally every three years, focusing in turn on one of the aforementioned main domains (see Table 1). The most recent edition, PISA 2022, tested students from more than 80 countries and economies. In all cases, normally a year after conducting the tests, the OECD published a document (called the “general framework of assessment”) which includes a section dedicated to mathematics (called the “mathematics framework”). The latter contains a definition of the type of mathematical competence that the program aims to test (called, as said, “mathematical literacy”) the motivation or justification for employing such a definition, as well as related discussion of the choices made in constructing the test questions.
The present study concentrates on the most recent mathematics framework included in the PISA 2022 general framework, which, as said, focuses on mathematics. I also compare this with the previous PISA mathematics frameworks focusing on mathematics (as well as with the first PISA framework) in cases when this will serve to discuss by contrast problematic or noteworthy issues pertaining to the 2022 framework. The data for the present study are thus the mathematics frameworks of PISA 2000, PISA 2003, PISA 2012, and PISA 2022, with specific attention to the latter.
As anticipated in the introduction, my objective in studying these documents was to explore how they articulate meaning (first research question) and, furthermore, what type of ideal subjectivities they articulate in connection with this meaning (second research question). In order to address these questions, I performed over the documents a (Foucauldianinspired) discourse analysis revolving around the notion of meaning. Following ArribasAyllon and Walkerdine (2017), this type of discourse analysis has the objective to nuance how a corpus of documents (in this case the PISA mathematics frameworks) referring to a particular body of knowledge (in this case mathematics) and set of practices (in this case mathematical instruction) accounts for a chosen object (in this case the meaning of such knowledge and practices), and for the constitution of the primary subjects involved in such practices (in this case students of mathematics), while also problematizing these dimensions from a historical or temporal point of view as well as in view of the institutional objectives of the corpus. These latter features in particular distinguish discourse analyses inspired by Foucault’s work from other types of discourse analysis (cf. Morgan, 2020) and render them particularly apt to study groups of documents impacting the functioning of institutional organizations.
Central to the analysis was the adopted discursive definition of meaning and the discussed Foucauldian idea that subjectivities come to be ideally constituted by means of explicit institutional prescriptions. In the analysis, I specifically concentrated on the notion of mathematical literacy which I identified (in view of the previous discussion and after a first reading of the documents) as a discursive focal point of the corpus, relevant to both questions and entailing (both mathematical and nonmathematical) features important to the characterization of the ideal subjectivity that these documents attempt to reproduce.
As to the first question, I preliminarily searched the PISA 2022 framework for how the document addresses the problem of the justification of the teaching and learning of mathematics. Hence, I singled out sentences containing expressions referring to relevant semantic categories (e.g., the “significance” of mathematics, the “benefits” it entails, its “relevance,” the fact that learning mathematics is or should be “critical,” “useful,” or “important”). In almost all cases, these sentences themselves contained statements articulating meaning or else were directly preceded or followed by statements articulating it and describing connected worldly contexts and mathematical areas. Concomitantly, I searched the PISA 2022 mathematics framework for enunciations of how students should become with respect to the notion of meaning there articulated. In this case, I singled out sentences containing expressions referring specifically to learners or to people in general (e.g., “individuals,” “people,” “learners,” “students,” “community,” “citizens”). Again, in most cases, these sentences contained or were directly connected to statements referring to the type of ideal student which should be the product of mathematical instruction in terms of mathematical skills, nonmathematical skills, as well as more dispositional personal characteristics (e.g., “motivation,” “views,” “attitudes,” “willingness to engage,” “curiosity,” “interest”).
I thus identified paragraphs and passages related to the first question, the second question, or both. A selection of these passages^{Footnote 3} was employed in order to construct the text presented in the next section which organizes and discusses them in view of their relevance to the argumentative structure of the framework and to its institutional objectives. Overall, in presenting and examining the passages, I attempted to refrain from valuejudgment considerations, but—when relevant—I accounted for inconsistencies or ambiguities or else for my own perception of rhetorical or logical difficulties within the document. In these cases, I then turned to searching the previous PISA frameworks for how they articulated topics related to these difficulties in order to evidence sameness, similarity, or difference between these and the most recent PISA framework (this was again done by searching the previous frameworks for expressions pertaining to both questions as well as to the problematized topic and then by selecting relevant related passages addressing them).
Overall, the next section presents an analysis of how the PISA mathematics frameworks discursively conceptualize in terms of meaning their own explicit program of governmentality concerning mathematical instruction and of how they portray the way in which students should ideally be or become in relation to such a proposal.
4 Findings
A considerable initial portion of the PISA 2022 mathematics framework is devoted to the discussion of problems related to meaning, with consistent attention to issues connected to the relevance and utility of mathematics and mathematical instruction. The document begins by endorsing considerations regarding mathematics’ increasing irrelevance and meaninglessness, while at the same time affirming the conviction that mathematics must be made to be meaningful or else that our understanding of mathematical literacy (i.e., as said, the type of mathematical competence that the PISA tests should measure) must be changed accordingly. On the one hand, it is explicitly acknowledged that mathematics is not useful in many activities or jobs because of recent technological advances.
The most used argument in defence of mathematics education for all students is its usefulness in various practical situations. However, this argument alone gets weaker with time—a lot of simple activities have been automated. Not so long ago, waiters in restaurants would multiply and add on paper to calculate the price to be paid. Today they just press buttons on handheld devices. Not so long ago, people used printed timetables to plan travel—it required a good understanding of the time axis and inequalities as well as interpreting complex twoway tables. Today we can just make a direct internet inquiry. (OECD, 2023, p. 19)
On the other hand, this problem is addressed by challenging what is narrated to be the traditional understanding of what makes an individual mathematically competent or literate.
Each country has a vision of mathematical competence and organizes their schooling to achieve it as an expected outcome. Mathematical competence historically encompassed performing basic arithmetic skills or operations, including adding, subtracting, multiplying, and dividing whole numbers, decimals, and fractions; computing percentages; and computing the area and volume of simple geometric shapes. (OECD, 2023, p. 19)
However,
This perspective on mathematics is far too narrow for today’s world. It overlooks key features of mathematics that are growing in importance. (OECD, 2023, p. 20)
Indeed, the very technological advances of society “have reshaped what it means to be mathematically competent” (OECD, 2023, p. 19). This is because
In recent times, the digitisation of many aspects of life, the ubiquity of data for making personal decisions involving initially education and career planning, and, later in life, health and investments, as well as major societal challenges to address areas such as climate change, governmental debt, population growth, spread of pandemic diseases and the globalising economy, have reshaped what it means to be mathematically competent and to be well equipped to participate as a thoughtful, engaged, and reflective citizen in the 21^{st} Century. (OECD, 2023, p. 19)
The result is a reinfusion of meaning into mathematics.
Ultimately the answer to these questions is that every student should learn (and be given the opportunity to learn) to think mathematically, using mathematical reasoning (both deductive and inductive) in conjunction with a small set of fundamental mathematical concepts that support this reasoning and which themselves are not necessarily taught explicitly but are made manifest and reinforced throughout a student’s learning experiences. This equips students with a conceptual framework through which to address the quantitative dimensions of life in the 21^{st} Century. (OECD, 2023, p. 20)
In terms of the type of claim concerning the general necessity of learning mathematics, these conclusions appear to be not very different from those expressed in previous PISA frameworks, which also polemized against traditional mathematics curricula in analogous fashions (cf., e.g., OECD, 2000, pp. 52–53; OECD, 2004, pp. 26–28). In the 2022 framework, such a claim is connected to the following skills, which are stated to be fundamental for students in order to become productive twentyfirst century citizens.

critical thinking;

creativity;

research and inquiry;

selfdirection, initiative, and persistence;

information use;

systems thinking;

communication;

reflection. (OECD, 2023, p. 42)
These are skills that mathematical literacy should encompass or else that should be assessed in connection with mathematical literacy by means of questions referring to the following four mathematical content categories.

change and relationship;

space and shape;

quantity;

uncertainty and data. (OECD, 2023, p. 34)
These or almost identical content categories have been the focus of the mathematical content knowledge tested by PISA since 2003 (cf. OECD, 2004, p. 35). According to the 2022 framework, the questions of the test should be further framed into one of the following contexts.
Personal – Problems classified in the personal context category focus on activities of one’s self, one’s family or one’s peer group. The kinds of contexts that may be considered personal include (but are not limited to) those involving food preparation, shopping, games, personal health, personal transportation, recreation, sports, travel, personal scheduling and personal finance.
Occupational – Problems classified in the occupational context category are centered on the world of work. Items categorised as occupational may involve (but are not limited to) such things as measuring, costing and ordering materials for building, payroll/accounting, quality control, scheduling/inventory, design/architecture and jobrelated decision making either with or without appropriate technology. Occupational contexts may relate to any level of the workforce, from unskilled work to the highest levels of professional work […].
Societal – Problems classified in the societal context category focus on one’s community (whether local, national or global). They may involve (but are not limited to) such things as voting systems, public transport, government, public policies, demographics, advertising, health, entertainment, national statistics and economics. […]
Scientific – Problems classified in the scientific category relate to the application of mathematics to the natural world and issues and topics related to science and technology. Particular contexts might include (but are not limited to) such areas as weather or climate, ecology, medicine, space science, genetics, measurement and the world of mathematics itself. […] (OECD, 2023, pp. 40–41, emphasis erased)
Notice that these contexts are the same as those listed in the 2012 framework (OECD, 2013, p. 37). Notice also that, despite the above reference to the irrelevance of mathematics to many unskilled jobs, the 2022 framework includes within the occupational context also unskilled work, thus potentially contradicting itself on this issue (the same can be said about problems in the personal context: it is difficult for instance to see how everyday cooking or shopping could actually involve employing mathematics). Indeed, the aforementioned doubts related to the irrelevance of mathematics are voiced in the passages shown at the beginning of the document but are not really resolved in what follows. Notice in fact that the 2022 framework states the following.
An understanding of mathematics is central to a young person’s preparedness for participation in and contribution to modern society. A growing proportion of problems and situations encountered in daily life, including in professional contexts, require some level of understanding of mathematics before they can be properly understood and addressed. Mathematics is a critical tool for young people as they confront a wide range of issues and challenges in the various aspects of their lives. It is therefore important to have an understanding of the degree to which young people emerging from school are adequately prepared to use mathematics to think about their lives, plan their futures, and reason about and solve meaningful problems related to a range of important issues in their lives. (OECD, 2023, p. 21)
Aside from minor changes, this passage is almost the same as a passage found at the beginning of the PISA 2012 framework (which comparatively overall did not stress as much mathematics’ increasing irrelevance as connected to technological changes and automation) (OECD, 2013, p. 24). In both cases, the conclusion is that mathematics is of crucial importance for young people. Thus, the above concern with the growing irrelevance of mathematics to various jobs is largely extraneous to the organization’s current conclusion, which is always that studying mathematics is indeed important as related to the very same contexts.
Notice also that the definition of mathematical literacy has likewise not fundamentally changed between the 2012 framework and the 2022 framework, except for the reference to the aforementioned twentyfirst century skills. The definition is currently the following.
Mathematical literacy is an individual’s capacity to reason mathematically and to formulate, employ, and interpret mathematics to solve problems in a variety of realworld contexts. It includes concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to know the role that mathematics plays in the world and to make the wellfounded judgements and decisions needed by constructive, engaged and reflective 21^{st} Century citizens. (OECD, 2023, p. 22)
Observe the last sentence: mathematical literacy “assists” people to know about the role of mathematics in the world. It would seem that, at a general level, the definition of mathematics literacy does not only comprise knowing mathematics or being capable of applying it, but something more: having a very specific (positive) view of mathematics and of its role and relevance in the world. Indeed, the adopted
conception of mathematical literacy recognises the importance of students developing a sound understanding of a range of mathematical concepts and processes and realising the benefits of being engaged in realworld explorations that are supported by that mathematics. (OECD, 2023, p. 21).
A further section of the text is explicitly devoted to students’ attitudes, dispositions, and emotions towards mathematics as well as to interest in mathematics and willingness to engage with it.
Two broad areas of students’ attitudes towards mathematics that dispose them to productive engagement in mathematics were identified […] These are students’ interest in mathematics and their willingness to engage in it. (OECD, 2023, p. 50)
These faculties are narrated to be something distinct from literacy itself and, it is said, they should not be measured by the PISA tests directly but from background questionnaires provided aside, which should focus
on students’ interest in mathematics at school, whether they see it as useful in real life as well as their intentions to undertake further study in mathematics and to participate in mathematicsoriented careers. (OECD, 2023, p. 50)
However, there seems to be a difficulty here in distinguishing clearly between literacy and these other more motivational or dispositional features. It is problematic to see, for instance, how a mathematically literate student (being thus “assisted” in knowing “the role that mathematics plays in the world”) could at the same time not see mathematics as useful or relevant. If mathematical literacy “assists” in recognizing mathematics’ relevance, then this very recognition appears to be a consequence of literacy itself, since the mathematics framework as a whole “is designed to make the relevance of mathematics to 15yearold students clearer and more explicit” (OECD, 2023, p. 20).
The overlap between these dimensions seems to have accompanied the OECD’s discourse from its inception. For instance, in the first 2000 framework we read that
Mathematical literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make wellfounded judgements and to engage in mathematics in ways that meet the needs of that individual’s current and future life as a constructive, concerned, and reflective citizen. (OECD, 1999, p. 41)
In the same document, it is further explained that attitudes, curiosity, interest, and other dispositional features should not in principle be linked to literacy.
Attitudes and emotions, such as selfconfidence, curiosity, a feeling of interest and relevance, and a desire to do or understand things, to name but a few, are not components of the OECD/PISA definition of mathematical literacy but nevertheless are important prerequisites for it. In principle it is possible to possess mathematical literacy without harbouring such attitudes and emotions at the same time. In practice, however, it is not likely that mathematical literacy, as defined above, will be put into practice by someone who does not have selfconfidence, curiosity, a feeling of interest, or the desire to do or understand things that contain mathematical components. (OECD, 1999, p. 42)
Nonetheless, in a later version of the same 2000 mathematical framework it is said that an inclination to employ mathematics is “implied” by mathematical literacy.
Mathematical literacy also implies the ability to pose and solve mathematical problems in a variety of contexts, as well as the inclination to do so, which often relies on personal traits such as selfconfidence and curiosity. (OECD, 2000, p. 50)
Possibly this inclination is distinct from the aforementioned affective or dispositional features. Nevertheless, the problem of the distinction and of the mutual interdependence between the construct of mathematical literacy and these other constructs seems to be difficult to unravel, in particular with respect to the recognition of mathematics’ relevance or utility. This is because all definitions of mathematical literacy seen above involve the recognition of mathematics’ relevance and utility and thus imply a nonneutral view of mathematics and mathematical instruction. Another example is the 2003 framework, where mathematical literacy is
an individual’s capacity to identify and understand the role that mathematics plays in the world, to make wellfounded judgments and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen. (OECD, 2004, p. 24)
The latter expression “to use and engage with” is explained in the document as follows.
The term “to use and engage with” is meant to cover using mathematics and solving mathematical problems, and also implies a broader personal involvement through communicating, relating to, assessing and even appreciating and enjoying mathematics. Thus, the definition of mathematical literacy encompasses the functional use of mathematics in a narrow sense as well as preparedness for further study, and the aesthetic and recreational elements of mathematics. (OECD, 2004, p. 25, emphasis erased)
Hence, here we also see that mathematical literacy “implies a broader personal involvement” and “encompasses” also aesthetic enjoyment. In consistence with this, the current PISA 2022 states that
Students who enjoy mathematical activity and feel confident to undertake it are more likely to use mathematics to think about the situations that they encounter in the various facets of their lives, inside and outside school. (OECD, 2023, p. 50)
Finally, it must be noticed that changing the views that people hold about mathematics should be an explicit objective of education, according to the OECD. Indeed, in PISA 2012 it is explicitly stated that changing people’s views of mathematics is a goal that should be pursued.
one goal of mathematics education is for students to develop attitudes, beliefs and emotions that make them more likely to successfully use the mathematics they know, and to learn more mathematics, for personal and social benefit. (OECD, 2013, p. 42)
Similarly, in PISA 2022 it is stated that the aforementioned affective or motivational components should be taken into account when trying to achieve the “broader goal of evaluating educational systems” (OECD, 2023, p. 49), which thus seemingly should strive to promote them. Finally notice that, relying on the aforementioned distinction between dispositions and literacy, the PISA 2022 framework also states that
attitudes, emotions and selfrelated beliefs […] dispose students to benefit, or prevent them from benefitting, from the mathematical literacy that they have achieved. (OECD, 2023, p. 50)
Fostering these dispositions as an explicit educational goal is connected not only to the problem of students’ mathematical proficiency but also to the general problem of people losing interest in mathematics at some point in their life. With specific reference to low achievers, educational systems should teach them to recognize the value of mathematics and to see its relevance in connection to tasks or problems related to their everyday life (OECD, 2023, p. 50).
In summary, both implicitly and explicitly, according to the OECD, it is not only the case that students should learn mathematics, but they should learn to enjoy it and to see its relevance as well as its benefits to their lives. Not only learning mathematics but also internalizing a cluster of discourses concerning the meaning of mathematics has thus been set consistently through the years as an objective of mathematical instruction as understood by the OECD.
5 Conclusions
Overall, the meaning of mathematics articulated in the PISA mathematics frameworks contributes to what Skovsmose (2020) discussed as a narrative of the sublime concerning the teaching and learning of mathematics: the fact that mathematical instruction is a sublime object in view of the aesthetic or utilitarian advantages or virtues that it would bring to individuals or to society at large. In particular, the discourses articulated by the OECD fundamentally stress the utilitarian component of mathematical instruction as conveying skills or advantages narrated primarily as utilities benefitting individuals which would also reflect on society as a whole (cf. Lundin, 2013; Pais, 2013). Furthermore, we have seen how discourses articulating meaning, despite acknowledgement of problems and difficulties, are repeated almost unaltered across the years. Rather than doubting the organization’s mission of delivering mathematics to all students, the meaningfulness of such enterprise for individuals and society is reiterated as a dogma, despite the recognition of mathematics’ increasing irrelevance in most fields. Moreover, we have seen how the OECD’s program of subjectformation extends towards the affective and ideological dimension: not only the aforementioned meaning provides reasons for enforcing mathematical instruction to all students, but also this very same instruction explicitly or implicitly has to include agreement with such a meaning.
This finding epitomizes a phenomenon which, according to Lundin (2013), is characteristic of the working of institutional mathematics: that of “a simultaneous formation of competence to understand and master the world and the formation of a perspective which makes the world appear in such a way as to make this competence relevant” (p. 23). This renders the type of mathematical instruction proposed by the OECD aptly describable as a potentially most effective Foucauldian technology of the self. Indeed, the OECD does not only aim to test and deliver knowledge of mathematics and ability to apply it to various contexts, but also aims to test and deliver the very same discourses through which people can make sense of their involvement with mathematics (and retrospectively of the overall OECD’s enterprise and mission with respect to mathematics).
This extends our knowledge of part of the mechanism of reproduction of the institutional system of mathematical instruction over which the OECD exerts an important influence. The OECD does not only attempt to reproduce the offer of its own educational services with respect to mathematics, but also concomitantly provides a potentially most effective educational way through which the demand of these very services is reproduced. In more mundane terms, by attempting to educationally reproduce also the discursive reasons which justify its own existence, the PISA mathematics frameworks thus constitute a potentially perfect case study of selfreferential marketing practices (cf. Kanes et al., 2014).
Taking consciousness of this phenomenon can possibly serve to widen discursive spaces of critique and resistance towards the OECD’s project concerning mathematical instruction. Indeed, in conclusion, a final general point concerning social reproduction must be stressed. On the one hand, as said in Sect. 2, it is true that explicit institutional programs are crucial to the formation of the subjectivities of those who participate in them. On the other hand, following Foucault (1993, 1997), this is not (only) a onesided process by which people internalize institutionallymandated identity projects. People participate actively in their own government by processes of constitution of the self which (may) happen by means of the reinterpretation of the meanings which are offered to them as available. Thus, the resulting form of social institutions is really a tension, an equilibrium, between what is explicitly programmed and the way people interpret such programs (Foucault, 1993, p. 204). A full sociological understanding of mathematical instruction in terms of meaning and subjectivity will thus have to complement the analysis offered in the present article with further accounts of discourses articulated within nationallysituated policy documents or uttered by groups directly involved in education (e.g., students, parents, teachers, researchers, policy makers). Indeed, it remains to see how and to what extent people and communities operating in various nations and cultures support, accept, endure, or perhaps even resist individually or collectively the influence of the OECD’s powerful discourses.
Data availability
The data analyzed in the current study are published (OECD, 1999, 2000, 2004, 2013, 2023) and hence publicly available.
Notes
I employ the expression “mathematical instruction” to mean the ample and diverse phenomenon of the teaching and learning of mathematics, typically happening in educational institutions (cf., e.g., the name of the influential International Commission on Mathematical Instruction).
That of reproduction is a category employed by philosophers and social scientists to make sense of the persistence over time of social institutions (cf. Weiss, 2023; Althusser, 2014; Bourdieu & Passeron, 1990). It crucially implies continuity and repetition, but also entails variation and discontinuity (cf. the term “reproduction” in biology).
The passages were selected in particular in view of their significance to the notion of mathematical literacy (chosen as a focal point of the analysis, as said). Specific attention was also paid to their relevance to the problematization of its dispositional components (cf. Section 2).
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Acknowledgements
The reflections on whose basis this article matured were partially developed within my doctoral thesis, which was written under the auspices of the Department of Mathematics of the University of Turin. My living stipend at that time was entirely sustained by the Department of Mathematics of the University of Pavia. I thank in particular Ornella Robutti and Paola Valero for openminded and helpful discussion on these and related topics. I also wish to thank the participants of the SOCAME seminar in Stockholm for collectively discussing a previous version of this article.
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Beccuti, F. Meaning and subjectivity in the PISA mathematics frameworks: a sociological approach. Educ Stud Math 116, 49–65 (2024). https://doi.org/10.1007/s1064902310296z
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DOI: https://doi.org/10.1007/s1064902310296z