Developing a Local Instruction Theory for Learning the Concept of Solving Quadratic Equation Using Babylonian Approach

The purpose of this research is to develop a set of learning instructions and investigate how the Old Babylonian Geometric Method: Naïve Geometry can support students' understanding about the concept of solving quadratic equations. This study aims to investigate on how students relate the Babylonian Geometric approach with the solving of the quadratic equation especially on how student bring their geometric solution into algebraic form. This research was conducted at a state junior high school in Indonesia. Design research was chosen as the method to reach the purpose. The instructional activities designed to achieve the learning objectives in this research consists of several activities, namely manipulating geometric form to solve the problem, using the Babylonian geometric method to solve the problem, linking geometric problems to algebra, and finding common formulas to solve quadratic equations. Through these activities, students acquire the idea of solving quadratic equations using algebraic completing perfect square method by manipulating and reshaping a rectangle into a square. However, our important finding is that only students who have high mathematics ability who reach the learning objective until the last stage of activity, which is to reinvent the common algebraic formula in solving the quadratic equation.