Scheming and Re-scheming: Secondary Mathematics Teachers’ Use and Re-use of Resources

Abstract

In this article, we examine secondary mathematics teachers’ work with resources using the Documentational Approach to Didactics lens. Specifically, we look at the resources and a teacher’s scheme of use (aims, rules of actions, operational invariants, and inferences) of these resources across a set of lessons (macro-level analysis) that aim towards students’ preparation for the examinations and how this use emerges in a set of three lessons on the same topic (micro-level analysis) as a response to contingent moments. We propose the terms scheming—a teacher’s emerging scheme of use related to the same set of resources used for the same aim—and re-scheming, namely, shifts in such scheming. Our analysis of lesson observations and the teacher’s reflections on his actions from a post-observation interview demonstrate the interplay between the stable characteristics of the scheme of use and the scheming and re-scheming in individual lessons. We conclude this article with a discussion on the methodological potential of using both macro- and micro-level analyses in the investigation of teachers’ use of resources.

Deepening a conceptual framework in travelling between languages and cultures: the case of the documentational approach to didactics

“…A scheme can evolve in different ways, when new resources are used and appropriated, or new situations appear. Kayali and Biza (2021) coined the term re-scheming for such evolutions.…”

“…Lina investigated a secondary mathematics teacher's (George's) documentation work (Kayali & Biza 2021). The data collected were video-recorded lesson observations, followed by one audio-recorded interview providing information about the resources that the teacher used in general.…”

Afinando o Foco em Matemática: Desenho, Implementação e Avaliação de Atividades MathTASK para a Formação de Professores de Matemática

“…Os dados que inspiraram este exemplo de mathtask vêm da pesquisa de doutorado da segunda autora, que aborda o trabalho de professores com recursos (KAYALI, 2019;KAYALI;BIZA, 2017BIZA, , 2021. Recursos aqui são definidos como "qualquer coisa que pode intervir na atividade [de um professor]"; pode ser um artefato (por exemplo, uma caneta), um material de ensino (por exemplo, uma folha de exercícios), ou mesmo uma interação social (por exemplo, uma conversa com um colega) (GUEUDET; BUTEAU; MESA; MISFELDT, 2014, p. 142).…”

“…(MOUSTAPHA-CORRÊA, 2020; MOUSTAPHA-CORRÊA; BERNARDES;GIRALDO, 2019; MOUSTAPHA-CORRÊA et al, 2021). No segundo e no terceiro exemplos, o desenho das mathtasks foi influenciado pela observação de pesquisa de uma sala de aula de matemática escolar(KAYALI, 2019;KAYALI;BIZA, 2017BIZA, , 2021, no primeiro caso; e de práticas de avaliação no primeiro ano de graduação em matemática(THOMA, 2018;THOMA;, no segundo. O primeiro e o segundo exemplos abordam o ensino de matemática na escola básica do Brasil e do Reino Unido, respectivamente, e foram usados no desenvolvimento profissional de professores em exercício.…”

Elements for the Design of a Teaching Experiment for Mathematics Teachers in Engineering Careers

“…They are no longer limited to those found in the classic library. However, it opens the universal library that includes specific software for the different mathematical contents and examples and topics linked to the different disciplines of the training line in engineering, architecture, and economics, among others (Kayali & Biza, 2021).…”