Developing Flexibility in Mental Arithmetic in Interactive-Cooperative Learning Situations: Interaction as an Occasion for Productive Learning Processes

The article presents a design research study focusing on the encouragement and investigation of flexibility in mental calculation of elementary students. It is argued that the development of flexible mental calculation can occur in student-to-student interactive-cooperative learning situations. To investigate this idea, 14 pairs of German second and third graders (paired with and without learning difficulties) were observed solving and exploring addition tasks within a designed interactive teaching-learning arrangement. Transcripts of paired interactions were analyzed. Results show specific learning processes and fruitful 'productive moments' in the interactions, which occurred in every student-to-student pair. The results of this study about the existence of these 'productive moments' and the types of impulses that can lead to them can be recommended as a basis for didactical planning interactive activities to improve students' cognitive flexibility in mental arithmetic.