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.

使学生参与数学过程和积极的知识组织（而不是讲和练习现成的数学）是对高质量数学教学的关键要求。尽管已经设计并在教科书中设计了许多数学上丰富的情境问题，但由于教师在塑造和实施知识组织的重要阶段时面临挑战，因此它们对常规数学课堂的影响仍然有限。本文提出的为期15年的KOSIMA项目旨在通过5-10年级的教科书来支持教师真正地改善这些过程。本文概述了该项目期间进行的各种研究，以显示该项目如何为教师的支持建立了研究基础。本文还表明，需要组合不同的研究方法来建立合适的研究基础：在主题特定的教学设计研究的迭代设计研究周期中，设计和研究学习环境的目的是理解实现预期目标时遇到的障碍。流程。在本文中，我们重点关注一个特殊障碍的例子，即教师在让学生参与积极的知识组织过程中需要支持。通过为主动知识组织开发新型任务克服了这一障碍。设计研究的理论成果得出了两个假设，以改善这些任务的设计相关特征，并在两个对照试验中进行了检验。最后，一项针对312名学生的纵向田野研究首次表明，使用该教科书的课程比使用其他教科书的课程具有明显更高的学习收益。总而言之，我们可以证明，如果认真研究和处理老师和学生双方遇到的障碍，教科书可以支持课堂实践的改变。