Mathematical abstraction process of sixth grade learners in a teaching experiment designed within the frame of hypothetical learning trajectory

The aim of this study is to observe mathematical abstraction process of sixth grade students in a classroom-based teaching experiment within the frame of hypothetical learning trajectory [HLT], concerning volume measurement of rectangular prisms in geometry and measurement teaching, considering the social and socio-mathematical norms and to reveal their abstraction mechanisms at the end of this process. In this teaching experiment, classroom practices in a nine-week period were fulfilled with 12 learners of a secondary level sixth grade in two phases in the form small groups and class discussions. Small groups were composed of three learners with one low level, one medium level and one high level and one of these groups was determined as the focus of this study to observe the mathematical abstraction of group learners and to reveal their abstraction mechanisms. Piaget's abstraction mechanism was used as a theoretical frame to reveal the abstraction mechanisms of the learners in the focused group. In this study, video recordings of pre, during and final clinical interviews with focus learners, as well as the teaching sessions, worksheets used in small group discussion activities and semi-structured learner diaries were used as data sources. At the end of the teaching experiment designed within the frame of HLT, the finding of this study revealed that three focus learners, especially the learner with a low-level success, performed reflective abstraction related to volume measurement of rectangular prisms. Besides, it was observed that the social and socio-mathematical norms, along with their own actions, play a supportive role in reflective abstraction of focus learners.