The use of multiple representations to overcome student difficulties in multiplication with natural numbers: An action research study

The purpose of this research is to identify the difficulties that 5th-grade students encounter in multiplication of natural numbers and to examine classroom activity processes aimed at overcoming these difficulties through the use of multiple representations. Action research, a qualitative research design, was employed to observe the role of instruction using multiple representations in addressing the challenges students face in multiplication. The study group consisted of 21 fifth-grade female students selected through convenient sampling method. Teaching multiplication through multiple representations was implemented based on students' difficulties and misconceptions in multiplication, following the literature and mathematics teaching curriculum, structured in a six-activity action plan. Thus, in the data collection phase, semi-structured interview forms were first applied to determine students' understanding, misconceptions, and difficulties regarding multiplication. The data collection process spanned 6 weeks with a total of 22 lesson hours. Data collection tools included video recordings, visual materials prepared by students during activities, field notes kept by the teacher, teacher and student journals, and semi-structured interviews. The collected data was analyzed through constant comparative analysis. The findings revealed that teaching multiplication through multiple representations facilitated students in overcoming their difficulties and conceptual misconceptions, enabling them to grasp multiplication conceptually. Through the use of multiple representations, students came to realize that multiplication is repeated addition, discovered the quantity and magnitude meanings of factors such as groups and squares, and began to use mathematical language more effectively in multiplication contexts. Moreover, students were able to express a given number in terms of different numbers through repeated addition and grouping contexts, and conceptually structured the roles of 0 and 1 in multiplication. Students also created their own multiplication tables through multiple representations, thereby alleviating their concerns regarding multiplication tables.