Rule Discovering and Justification in Magthematical Problem Solving Activities with Spreadsheet

Abstract

Mathematical modeling activities carry significance in that they offer students the experience of discovering and constructing their own mathematical knowledge, and in that they help students realize the applicability and necessity of mathematics. Generally modeling activities start from real-life situations, and therefore naturally accompany a great deal of complicated calculation and the discovery of patterns or rules implied within certain situations in order to understand and predict the problem situation. In such cases spreadsheet could be usefully used.

Not only is spreadsheet easy to use, but it can also provoke student-centered, discovery-centered learning. In the course of utilizing spreadsheet, the interaction between fellow students, teacher and student, and computer and student becomes active, and as students are enabled to design and manipulate more dynamic and visual spreadsheet models they are also able to explore diverse aspects of a phenomenon.

Such distinctive features of spreadsheet serve as significant factors when students are carrying out modeling activities in small groups. When spreadsheet is used such mathematical models as tables and graphs that are necessary in carrying out modeling activities can be easily constructed, and they are also conducive in enhancing the user's intuition in developing and using algorithms and models necessary for solving mathematical problems. In particular, the cell reference function of spreadsheet that when the value of referred cell is changed then the value in a cell in reference is changed and, consequently the related table and graph also are changed, makes students' exploration of a problem situation slightly more complicated and dynamic.

The present study attempts to look into how students discover rules inherent in problem situations and how they mathematically justify such discovery in modeling activities using spreadsheet.