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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.

As student diversity increases in many schools across the globe, teacher diversity may not be keeping pace with the ever changing student population. Along with this comes an increasing number of issues and queries around race and education. The ideas surrounding how race impacts the education of students have been shrouded in controversy given the sensitive nature of the topic and its troubled past in some countries. Countries across the world struggle to recruit a teacher workforce that matches that of the student population especially in pockets where there are a larger number of minorities students. Many education programs, policies, and interventions more recently have been reasserting the ways that addressing issues with race in schools can be a positive change, specifically seeking to diversify teacher recruitment and match teachers or mentors with groups of students based on race to serve as built- in role models. Indeed, our increased awareness of teacher recruitment practices and the need for a more diverse teaching force is based on some of those assumptions that student/teacher race matching is and can be a positive thing. This pilot study seeks to examine these assumptions by looking at how race may actually affect teacher student relationships. This study focuses on students and teachers in a low-income area of the United States to assess student perceptions of their teachers on several key attributes of quality teaching. The aim of the study is to see if classrooms of students with similar races to that of their teacher perceive their teachers differently. More directly, do students share more favorable perceptions of their teachers if they are of the same racial background? This study finds that students perceive that teachers of the same race are more effective and have more positive relationships with them. This finding is consistent for both white and black teachers. The paper concludes with a call for more research and a continued push to diversity the teacher workforce worldwide.

In the past five years our research team has studied and elaborated a teaching method called the schema-oriented education. Pupils do not receive mathematical knowledge from the teacher. Instead, they build own mathematical schemata through problem-solving and class discussion. Problems are nested in various semantic and structural teaching environments. This article describes in detail the building of a schema in relation to the solution of a system of two linear equations x + y = a, x – y = b in three of such environments.