How is the learning trajectory of polynomial division topic?

Abstract

The objective of this research was to describe the learning trajectory for topic of polynomial division. The research was carried out through design research. This research used the approach of Gravemeijer & Cobb that consists of : 1) Preparing for the experiment covering the preparation of Hypothetical Learning Trajectory (HLT) comparing three components, i.e. learning objectives, learning activities, and students' hypothetical learning trajectory; 2)Experimental design was conducted in class of 53 students of XI MIPA 3 and XI MIPA 4; 3) Retrospective analysis, comparing HLT to actual learning practice. The result of this research indicated that the learning trajectory for topic of polynomial division was began with polynomial division by divisor (x - h) first, then (ax + b), and was divided by (ax2 + bx + c). Next, the methods in solving for polynomial division were long division, Horner, algebraic operation, and Horner-Kino, respectively. The next topic was the remainder theorem, consisting 3 subtopics, i.e. the remainder theorem with divisor (x - h), (ax - b) and (x - a)(x - b). The last topic was factor theorem.