The use of visual thinking based problem solving method in early algebra learning

This study aims to examine the use of the Donguri method, developed as a problem solving method based on visual thinking, in the early algebra learning process. For this purpose, the types of representations that students used in the process of applying the Donguri method and their development of abstraction through these representations were examined. A radical constructivist teaching experiment was used to individually examine students' representation development. The research was conducted with the participation of four students attending the 3rd grade of a public primary school in the central district of Eskişehir province in the fall semester of the 2022-2023 academic year. Determining the problem-solving conditions of the students, the condition determination phase was carried out in the first three sessions, and then a 12-session teaching phase was implemented, in which six arithmetic and six early algebra problems were solved with the Donguri method. Understanding how learning the Donguri method changed students' problem-solving approaches, a condition determination phase was carried out in two sessions, six weeks apart. As a result of the study, it was observed that while the students mainly used abstract symbolic representations in the condition determination phase, they started by using concrete pictorial and linguistic representations in the application of the Donguri method and used figurative representations to generalize the relationships, and then switched to symbolic representations. Thus, in this process, students realized their abstractions, starting from concrete representations and moving to abstract representations step by step. Various thinking skills such as relational thinking, quantitative reasoning, and functional thinking, which were included in early algebra problems, emerged clearly in the process of applying the Donguri method.