Developing Conceptual Perceptions of Measuring Volume in Everyday Life Using Modeling Activity Systems

The present research has aimed to develop conceptual perceptions of measuring volume in students’ everyday life. The statistical population involved all junior high school students in Kahnouj, in the province of Kerman. The sample studied consisted of 60 female students of grades seven, eight and nine selected by means of purposive sampling. Observations, interviews and classroom discussions were the data collection tools. The methodology of the research was based on qualitative methodology, in which qualitative data analysis was done using the activity theory analysis method. Since the activity theory studies human activities in the framework of a system, and mathematical modeling is done through a cycle, the activity system of the activity theory was integrated with the modeling cycle, thus defining a modeled activity system which has been used as the tool for data analysis. The data for the study were collected over a 9-month period, the sources of which were 2 modeling activities regarding the consumption of water. In the activity systems, two elements were used -- tension (pressure, anxiety, challenge or a dispute students encounter) and modifying it -- in order to develop conceptual perceptions. Analyzing the data obtained by the research pointed out two tensions -- perceiving the formula for measuring the volume of a cylinder and reporting water consumption. The students were able to, using the modeling process and with the guidance provided by their teachers, modify the tensions that had arisen and develop the measurement of volume in their everyday lives. This research showed that mathematical modeling can prove to be an appropriate tool in the integrated curriculum and has a high capacity for the development of mathematical concepts.