Hauke Straehler-Pohl

Learning to fail and learning from failure – ideology at work in a mathematics classroom

When actualised in a concrete school, the official discourse of inclusion and equity often encounters a series of obstacles that research strives to identify and address under the imperative to eliminate them. Through the exploration of classroom episodes, teacher interviews and field notes from a German secondary school, we take failure not as a correctable obstacle but as a symptom of the ideology at work in current educational practices. Symptoms, as Žižek (after Lacan) suggested, cannot be eliminated but always (re)emerge since they concern the impossibility of official discourses actualising themselves. We thus argue for a research agenda that learns from failure instead of research concerned with the possible successes that might prospectively be brought into existence, if just the ‘right’ theory was applied ‘correctly’.

Towards a Bernsteinian language of description for mathematics classroom discourse

This article aims at developing an external language of description to investigate the problem of why particular groups of students are systematically not provided access to school mathematical knowledge. Based on Basil Bernstein’s conceptualisation of power in classification, we develop a three-dimensional model that operationalises the contextual boundaries, the linguistic features and the structure of knowledge, and their respective relations to power on a not too high level of abstraction. The contribution of this article consists of a systematic connection of classification with the latter two dimensions that abides the generative principles of Bernstein’s internal language of description. Finally, we illustrate the analytical potential of the three-dimensional model through a brief discussion of one classroom episode.

Welcome to the Jungle. An Orientation Guide to the Disorder of Mathematics Education

This introductory chapter builds on the assumption that the sociopolitical dimensions of mathematics education have been gradually recognised as an important part of mathematics education research. We problematise the process of institutionalising these dimensions as a firm strand of mathematics education research just as “philosophy of mathematics (education)”, “history of mathematics (education)”, “modelling and applications” or “geometry”. This leads us to identify and conceptualise “disorder” as the foundation of the sociopolitical dimensions and accordingly to propose a shift from focussing diversity towards focussing disorder. Finally, we illustrate how the chapters of this book contribute to such an alternative self-conception of sociopolitical research in mathematics education.

De|mathematisation and Ideology in Times of Capitalism: Recovering Critical Distance

This essay takes an ethical dilemma posed by current technological developments as a point of departure for discussing the dialectic of mathematisation and simultaneous demathematisation as a social phenomenon and a challenge for society. This dialectic of de|mathematisation is discussed in relation to a conception of ideology that has been developed within the field of mathematics education as well as in relation to an alternative conception recently imported to mathematics education from the field of political psychoanalysis. By analysing media reports, advertisement campaigns and a sociological study on dating portals, the analysis reveals shifts that have recently occurred in de|mathematisation and its ideological framing. This embedding in popular culture allows for a better understanding of the interplay between de|mathematisation and the sphere of political economy within late capitalism. Finally, the author provides an outlook on how the conclusions drawn could contribute to a further development of a mathematics education that critically reflects its role in society.

Interrupting Passivity: Attempts to Interrogate Political Agency in Palestinian School Mathematics

This chapter attempts to question the sociopolitical structure and conditions that Palestinian students live in and under which they are expected to learn mathematics and other subjects in schools. We describe these sociopolitical conditions and then focus on education and mathematics education in an attempt to illuminate the relationship between learning mathematics and the sociopolitical context that it “lives” in. This is achieved by using textbooks as an example of how ideology shapes education in Palestine generally, and mathematics education particularly. The analysis illustrates how learners of mathematics are constructed as passive subjects, separated from the sociopolitical conditions they live in. Based on this analysis, the chapter provides drafts for two hypothetical classroom activities that are designed as provocations for teacher education and seek to tease out the potentials for interrupting this passivity.

Bildung und Teilhabe im Kontext „pädagogischer Rechte“

Dieser Beitrag exploriert den normativen Rahmen Bernsteins Bildungssoziologie. Hierbei werden die Begriffe Teilhabe und Bildung in den Kontext von padagogischen Rechten gestellt, welche die Bedingungen fur eine effektive Demokratie sichern, bzw. schaffen sollen. So rucken Teilhabe und Vertrauen als notwendige Bedingung fur Demokratie in den Fokus. Die Institutionalisierung eines Rechts auf Bildung wird als eine zentrale Form der Realisierung dieser Bedigungen herausgestellt. Anhand von Vignetten aus dem Mathematikunterricht in sog. sozialen Brennpunkten illustriert der Beitrag empirisch-rekonstruktiv, wie die padagogischen Rechte gewahrleistet oder auch vorenthalten werden und Unterricht so zur Schaffung der Bedingungen fur eine effektive Demokratie beitragt − oder auch nicht.

Establishing Mathematics Classroom Culture: Concealing and Revealing the Rules of the Game

In this chapter we will propose several mechanisms in classroom interactions that give rise to disparity in learning opportunities. We will use terminology derived from the work of Basil Bernstein to describe these mechanisms in four episodes of classroom discourse. We conclude that efforts to enable “less able” students by incorporating elements of everyday “horizontal” discourse into school mathematics, which is oriented towards “vertical” academic discourse, can instead deny these students learning opportunities that are available to more privileged peers.

The Recognition of Pedagogic Rights in Mathematics Classrooms: A Framework for Reflecting Implicit Normative Assumptions in the Sociology of Mathematics Education

In this chapter, we set out to propose a framework for reflecting the normative assumptions that often remain implicit in sociological analyses of school mathematics practices. We begin by problematizing the implicit normativity in our own prior research on mathematics classroom registers in contexts of low expectation. This leads us to assume that normativity is an intrinsic feature of critical sociological research in mathematics education. With the model of pedagogic rights, we propose a heuristics for analysing classroom discourse in a way that a) allows explicit and substantiated normative judgments, and b) problematizes its very own political foundation, from where normative judgement is carried out. Firstly, we re-analyse two classroom episodes in order to reveal how students’ pedagogic rights are recognized or denied in mathematics classrooms. Secondly, we explore a third classroom episode to suggest that teachers should be considered holders of pedagogic rights in a similar manner as students. In the concluding remarks, we summarize the main potentials of the normative framework of pedagogic rights and problematize the implications of an explicit injection of normativity.

Towards an Ethics of Mathematical Application

In the light of growing public attention to the influence of algorithms on our lives, this chapter addresses the question of how an ethical perspective on mathematical application could be conceptualised in contemporary late-modern societies. Firstly, we recapitulate some of the recent theoretical developments on the ethics of mathematical application in the field of mathematics education (Skovsmose in Mathematics education in a knowledge market: developing functional and critical competencies. Opening the research text: insights and in(ter)ventions into mathematics education. Springer, New York, pp. 159–188, 2008; de Freitas in Int Electr J Math Educ 3(2):79–95, 2008). Secondly, based on the work of the sociologist Luhmann (Thesis Eleven 29(1):82–94, 1991), we develop theoretical outlines of an ethics of mathematical application as a reflexive theory of moral communication on mathematical application. We then move into the sphere of the social and confront these theoretical considerations with a critique of the ideology of “solutionism”. Solutionism refers to a semantics that links the mathematisation of the social to ‘the morally good’. This critique leads us to suggest firstly, developing an ideology critique of the underlying semantics as a desideratum; and secondly, a systematic further development of an ethics of mathematical application that could inform moral communication on mathematical application in (critical) mathematics education.

Zum Verhältnis von Theorie und Praxis

In Theorien materialisieren sich Weltbilder, Forschungsinteressen und Forschungsziele. Sie umreisen, was in ihrem Rahmen als bedeutsam, problematisch und interessant erscheint und erforscht werden kann und soll. Auch geben sie meist Auskunft daruber, welche Methoden fur eine Annaherung an die Forschungsziele und Forschungsfragen als sinnvoll erachtet oder privilegiert werden. Vor allem aber grenzen sie ein, was als ein Forschungsresultat zahlen kann und was nicht. Theorien konnen als mehr oder weniger scharf abgegrenzte Sprachen verstanden werden, die auf prazise Beschreibung und kreative Diskussion ausgerichtet sind.