En los últimos 20 años ha aumentado la atención dispensada a las desigualdades sociales en los logros en matemáticas. Las perspectivas microsociológicas en las investigaciones sobre educación matemática apuntan a las particularidades de la cultura del aula y a los patrones, pero también a las contingencias, prevalentes en la construcción del significado en el aula de matemáticas. Con el objeto de generar una sociología de la instrucción matemática, el enfoque empírico de nuestra investigación se dirige hacia esos patrones microsociológicos de interacción en el aula relacionados con la construcción de una jerarquía de logros en las matemáticas escolares. La aplicación del marco teórico de Basil Bernstein resulta útil a la hora de explorar esos patrones de interacción. Dado nuestro interés en la elaboración de este marco, el propósito del presente artículo es doble: como resultado de nuestro estudio empírico presentaremos, en primer lugar, una lista de mecanismos de interacción que afectan a la estratificación de los logros del alumnado en matemáticas. Posteriormente reflexionaremos sobre los límites de la teoría de Bernstein que percibimos en nuestro trabajo y las expectativas de teorización e investigación adicionales. De este modo centraremos nuestro enfoque en la corporalidad, normatividad y derechos pedagógicos mostrando así su impacto que está aún, en gran medida, desatendido. Palabras clave: Basil Bernstein, desigualdades sociales, patrones de interacción, sociología de la instrucción matemática.

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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'.

Life in today’s world is characterized by complexity and rapid change. Twenty-first century skills and especially mathematical understanding are supposed to crucially contribute to meeting the demands of our world since mathematics offers strategies to structure or simplify complex problems. An open question is which teaching practices are appropriate to provide all students with such skills and to broaden the participation of underprivileged students. The present article explores these aspects by focusing on complex tasks, a practice that can be considered highly accepted in the context of mathematics education all over the world. We will concentrate on the perspective of the German mathematics education community as the foundation of our considerations. Based on an analytical investigation of mathematical literacy and twenty-first century skills (such as creativity, critical thinking, or problem-solving), we will address central ideas and characteristics of complex mathematical tasks. To complement the analytical approach, we will illustrate their characteristics as well as possible intersections with twenty-first century skills by presenting an elementary school teaching experiment. Finally, we will critically discuss the potentials and pitfalls of complex mathematical tasks from an abstract perspective and conclude by debating practical consequences for organizing mathematical learning-teaching-processes.

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