The notions of meaning and sense, which are closely related to understanding, play an essential role in educational processes in general and, therefore, in the teaching and learning of mathematics. However, the terms ‘meaning’ and ‘sense’ are unevenly used in the theory of language, semiotics, philosophy and psychology. After describing the main characteristics of the referential and pragmatic theories of meaning, in this article, we detail various approaches to the notion of meaning, and present the perspective suggested by the onto-semiotic approach (OSA) of mathematical knowledge and instruction. This proposal partially incorporates the semiotic, ontological and epistemological assumptions of three general semiotic theories (by Hjelmslev, Peirce and Wittgenstein), with a holistic approach to the notion of object, sign and meaning, and takes into account some referential and operational theories, as well as other cognitive and sociocultural theories, about meaning. We also analyse how the meaning of mathematical objects is addressed in three models that have an impact on mathematics education: Frege's logical-realist position, Vergnaud's conceptual triplet and Steinbring's epistemological triangle. We finally suggest some implications for instructional design and teacher education of the OSA holistic approach to the meaning.

Una crítica tradicional a la investigación científica en el campo educativo ha sido la desconexión con la práctica docente, motivada por el fraccionamiento de los problemas de investigación. Para resolver esta disociación, las investigaciones de diseño instruccional plantean problemáticas de tipo predictivo más próximas a dicha práctica, pero deben ser complementadas con una interfaz que aporte los componentes valorativos y normativos que se deducen de la aplicación eficiente de los resultados de la literatura previa. En este trabajo usaremos algunas herramientas del Enfoque Ontosemiótico (EOS) para esbozar una agenda de investigación que tiene en cuenta los componentes científico (descriptivo, explicativo y predictivo) y tecnológico (valorativo y normativo) de la investigación didáctica. Asimismo, describimos las herramientas metodológicas que aporta el EOS para abordar los mencionados problemas, en particular la noción de idoneidad didáctica que sirve de nexo entre el componente científico-tecnológico y la práctica de la enseñanza.

We prove that every bounded local triple derivation on a unital C*-algebra is a triple derivation. A similar statement is established in the category of unital JB*-algebras.