Mathematical Discovery Process through Modeling Activity in Spreadsheet Environments

Abstract

Mathematical modeling is the process to represent real-world situations through mathematics. Modeling a wide variety of phenomena makes students realize the power of mathematics and understand the real world better. For this reason modeling activity gets becoming more important in mathematics education. Students in modeling activity need to make and use representational forms which describe mathematical ideas and situations. With technology, students can create a diverse set of representations and explore various situations more easily. As one of the technologies, spreadsheet creates symbolic, numerical, and graphical representations and makes connections among them. These functions help students understand real-world situations deeply. The aim of this study is to explore the mathematical discovery of six 10th grade Korean students through modeling activities in spreadsheet environments. They investigated modeling problems with the spreadsheet, which seem to be very difficult to solve in the inactive paper and pencil environments. In spreadsheet environments, it is easy for students to list various variables on the sheets and form a data table by inputting and copying spreadsheet formulas. And the graphs can be easily drawn from the tables. In this study these functions of spreadsheet played an important role in modeling activity. This study shows the results of classroom activities in which students focused on patterns and regularities rather than on isolated pieces of information, and finally discovered the mathematical invariance underlying the problems by operating data tables and using 'what if' strategy.