Towards a research base for textbooks as teacher support: the case of engaging students in active knowledge organization in the KOSIMA project

Abstract

Engaging students in processes of mathematizing and active knowledge organization (instead of telling and rehearsing ready-made mathematics) is a key demand for high quality mathematics instruction. Although many mathematically rich context problems have been designed and published in textbooks, their impact on regular mathematics classrooms remains limited, as teachers face challenges in shaping and enacting the important phase of knowledge organization. The 15-year project KOSIMA presented in this paper was aimed at supporting teachers in really enhancing these processes by means of a textbook for Grades 5–10. The paper provides an overview of different studies conducted during the project in order to show how the project developed a research base for the support of teachers. The paper also shows that different research approaches need to be combined to establish an appropriate research base: In iterative design research cycles of topic-specific didactical design research, learning environments were designed and investigated with the aim of understanding the obstacles encountered in implementing the desired processes. In this paper, we focus on an example of one particular obstacle, namely, teachers’ need of support in engaging students in processes of active knowledge organization. This obstacle was overcome by developing new types of tasks for active knowledge organization. The theoretical outcome of the design research resulted in two hypotheses for improving relevant features of the design of these tasks, which were tested in two controlled trials. Finally, a longitudinal field study of 312 students gave first indications that the classes that worked with the textbook had significantly higher learning gains than classes using other textbooks. In sum, we can show that textbooks can support changes in classroom practices when the obstacles that occur for both teachers and students are carefully investigated and treated.

Mathematics textbooks and curriculum resources as instruments for change

“…In these projects, mathematics textbooks were developed on a research base and refined in ongoing cycles of formative evaluation (Burkhardt & Schoenfeld, 2020). An overview of the KOSIMA-project is provided by Prediger et al (2021) in this special issue. This is a rare example that shows how design principles for a reform-textbook are constantly evaluated and improved in design research cycles.…”

“…This is a rare example that shows how design principles for a reform-textbook are constantly evaluated and improved in design research cycles. On a meta-level, Prediger et al (2021) provide an example of how an interventionist rather than a descriptive research base for textbook design can be established by combining different research approaches. This paper outlines an approach that could be paradigmatic for designing reform curriculum resources in the future.…”

Are textbooks facilitators or barriers for teachers’ teaching and instructional change? An investigation of secondary mathematics teachers in Shanghai, China

“…In terms of ‘instruction’, it was reported that teachers’ use of examples of textbooks might help their students overcome difficulties (Davis, 2009 ; González-Martín et al, 2018 ) and engage in active knowledge organization (Prediger et al, 2021 ). Furthermore, regarding assessment or ‘evaluation’ in Shulman’s terms, some researchers found that textbooks provided problems and applications that were helpful (O’Keeffe & White, 2017 ) or not so helpful (Divrik et al, 2020 ) for teachers’ assessment and evaluation, and textbooks could also serve as a reference in teachers’ ‘reflection’ on their teaching, which was the case in a Shanghai teaching research group’s attempt to support a junior teacher’s professional learning (Ding et al, 2017 ).…”

Digitaler Mathematikunterricht in Forschung und Praxis. Tagungsband zur Vernetzungstagung 2022 in Siegen

“…Um der Flüchtigkeit des aufgebauten Wissens entgegenzuwirken, ist das Sichern von Wissen (DG2) entscheidend. Dies erfolgt in digitalen Wissensspeichern, an deren Entstehung die Lernenden aktiv beteiligt werden (Prediger et al, 2021) und auf die sie in der weiteren Arbeit zurückgreifen können.…”