Designing hypothetical learning trajectory based on van hiele theory: a case of geometry

Abstract

This study is aimed to develop a hypothesis of learning trajectory based on the van Hieletheory which can assist students in comprehending the volume of cuboid. This study used design research to create a hypothetical learning trajectory for students to learn the volume of cuboid. Out of the three stages of design research, this study focused on the first stage, i.e. preliminary design because the main focus was to develop a sequence of learning activities to learn the volume of cuboid on the basis of van Hieletheory. The results of this study is a HLT on discovering the concept of volume of cuboid. This HLT consists of four stages of van Hiele, i.e. 1) visualization stage at which students discover the volume of cuboid by counting a number of unit cubes construct the solid; 2) analysis phase at which students identified the volume of cuboid by looking for the length of edges without counting unit cubes; 3) informal deduction stage at which students find out the volume of cuboid by looking at the length of the sides, 4) deduction phase at which the students discovered the general formula of volume for all types of cube, and cuboid.