Totéž a odlišné: O praktikách sémantizace a instrumentalizace v učebně (matematické)

Vzdělání není možné bez obsahu. Vyučování a učení ve školách se věnuje „něčemu“, ne „ničemu“ nebo „čemukoliv“. Čím více heterogenní, multikulturní a jazykově různorodá je výuka, tím více je během vyučování a učení nutná sémantizace vzdělávacího obsahu. V tomto článku rozvíjíme teorii transformace obsahu a představujeme koncept operačního isomorfismu a jeho potenciálu v oblasti didaktiky, výzkumu výuky a vzdělávání a vzdělávání učitelů. Pomocí případové studie výuky matematiky ilustrujeme, jak mohou studenti těžit ze sémantizačních a instrumentalizačních postupů ve třídě a jak tyto procesy nabývají podoby extenzionální dekonstrukce a intenzionálního rozšiřování nebo zhušťování.There is no education without content. Teaching and learning in schools is devoted to “something,” not to “nothing” or “anything.” The more heterogeneous, multicultural, and multilingual the classroom, the more semantization of educational content within teaching and learning is needed. Therefore, the role of various languages in the classroom is revisited. In this article, we elaborate on the theory of language-sensitive content transformation and introduce the concept of operational isomorphism and its potential in the field of didactics, research on teaching, and learning and teacher education. Using a case study of mathematics teaching, we illustrate, how students can benefit from semantization and instrumentalization practices in the classroom and how these processes take the form of extensional deconstruction and intensional expansion or intensional condensation

Professional development models for whole number arithmetic in primary mathematics teacher education: a cross-cultural overview

The goal of the chapter is to explore and discuss teacher education in different parts of the world and to emphasise the commonalities and differences not only in the panellists\u2019 countries, but in a broad perspective. By looking at differences in the parts and processes of different educational systems, we can learn from each other and develop a more integrated perspective on teacher education. Most research studies in the field of primary mathematics teacher education at the international level focus on curricula within teacher education and on the knowledge a primary teacher needs for teaching well. WNA provides a context for developing understandings and constructing arguments that adhere to the practices and norms of more advanced mathematics. Two key issues frame the chapter: ways to increasing and deepening teachers\u2019 mathematical understandings and developing tools that support their mathematics teaching. Examples from seven countries are accompanied by brief information about the organisation of primary teacher education in each of them