Investigation of learning processes of the sixth grade students about algebra learning: A teaching experiment based on hypothetical learning trajectory

The aim of this study is to observe mathematical thinking while solving the arithmetic and algebra tasks of three learners chosen among the sixth grade students in a teaching process based on the hypothetical learning trajectory [HLT] and to determine the tools to support the students' transition from arithmetic to algebra. In this study, which was designed as a teaching experiment, five-week period with classroom practices were carried out in two stages in the form of class discussions with a sixth grade student group consisting of 24 learners. Three learners with low, medium and high achievement levels were identified among the students in the classroom and this process was aimed to monitor and reveal the cognitive development of these learners. In this research, classroom video recordings of pre, intermediate and final clinical interviews and teaching courses with focus students, worksheets used in activities in group discussions, student diaries and researcher diary were used as data sources. At the end of the teaching process based on HLT, findings of this study reveal that three focus learners, especially the learner with a low level success, can perform introduction to algebra in terms of pattern generalization, verbal and algebraic expressions, interpreting algebraic expressions and operations with algebraic expressions. It was observed that the sign of equality and relational thinking played an important role in the meaning of the focus students' entry into algebra via this process. Keywords: Hypothetical learning trajectory, Introduction to algebra, Relational thinking, patterns, Operations with algebraic expressions.