摘要：Proportional reasoning is essential for the learning of numerous mathematical concepts. Proportional reasoning is based on linking composite units and iterating linked composites, rather than repeated addition. Those skills are referred to as early proportional reasoning skills in this study. In a three-year-long design research project, a hypothetical learning trajectory for proportional reasoning was developed, tested, and revised. To this purpose, a classroom design research study aimed at developing a hypothetical learning trajectory and related instructional sequence was conducted. This trajectory includes the big ideas of proportional reasoning, the tools and imageries to support those ideas, and possible mathematical discourse and gesture use. In this particular study we present the first phase of this trajectory, which is related to the development of early proportional reasoning. The data of this study consist of video recordings of classroom sessions conducted in a public school in Ankara and audio recordings of student/teacher and design team meetings. The classroom sessions were analyzed by constructing related argumentation schemes to evaluate meaningful learning of students. The findings of the study showed that the learning trajectory developed to support the big ideas of early proportional reasoning has substantial potential for the development of early proportional reasoning.
