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Some researchers stresses the importance of the historical development of a science not only  from a cultural and humanistic perspective but also from its role which facilitates individual to understand the concept of a topic. Hence, the integration of aspects of history in learning will be very helpful, either for students or teachers. Specifically, the historical perspective related to mathematics indicates that the concept of solving quadratic equations was built by geometric foundation. One of historical perspectives that was evidently found helpful for learning  quadratic equation is Old Babylonian Geometric approach. Therefore, such an approach is required to be included in the development of learning instruction to help students tackle any quadratic equation problems. Thus, the purposes of this research are to develop the learning instruction and know how the Old Babylonian Geometric Method can support students' understanding about the concept of solving quadratic equations.

 

This is a design research which aims at investigating on how students link the Babylonian Geometric approach with the solving of the quadratic equation especially on how student bring their geometric solution into algebraic form. The core of this type of research is formed by classroom teaching experiments that center on the development of instructional sequences and the local instructional theories that underpin them. This research was conducted at a Junior High school, Palembang, Indonesia involving 32 students. There were three main phases undertaken in this research, i.e. preliminary design, teaching experiment, and retrospective analysis. In the first phase, a Hypothetical Learning Trajectory (HLT) was formulated for learning the concept of quadratic equation which covers learning goals for students, planned instructional activities and and a conjectured learning process which anticipates how students' thinking and understanding could evolve when the instructional activities are used in the classroom. The instructional activities designed to achieve the learning objectives in this research consists of several activities, namely 1) manipulating geometric form to solve the problem, 2) Using the Babylonian geometric method to solve the problem, 3) Linking geometric problems to algebra, and finding common formulas to solve quadratic equations.

 

Based on the implementation of the HLT in teaching experiment, the use of Babylonian Approach method can be an alternative method for learning the concept of the quadratic equation because the conjecture in HLT that has been made of is quite in accordance with the result of teaching experiment. In common, the learning instruction developed in this study, which is based to on Old Babylonian Geometric Method, can support students' understanding of the concept of solving quadratic equations. The second cycle of teaching experiment lead the conclusion that through these activity the students can realize the idea of Babylonian Approach can be used to solve quadratic equations and finding a general form to solve quadratic equations. Through the geometric idea (reshaping into a square), the students are also encouraged to perform symbolic operations are meaningful because they are familiar with the context involved. However, from the implementation of learning activities, it is found that only students with 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.

 

In common, through activities that have been designed in HLT, the students learned to understand algebraic problems and how to solve them through geometric approaches with familiar context. Thus the students get a chance to learn how to find the solution of quadratic equations meaningfully. The implementation of HLT was pointed out to be in line with Freudenthal’s statement [14] that learning will happen when it is meaningful for students.

Babylonian Approach, Local Instruction Theory, Quadratic Equation