Investigating students' learning trajectory: a case on triangle

Learning trajectory becomes the main issues in mathematics education research. However, there have been limited studies of students' learning trajectory for triangle construction. Therefore, this design research was conducted to investigate students' learning trajectory for the topic of the triangle. The study involved 22 students from 7^th grade in Malang, Indonesia. Data were collected through a videotaped, a student's worksheet, and a classroom observation. The results showed that students discovered the requirement of forming a triangle given three side lengths. In this condition, the starting point of students' learning trajectory was the drawing of a line segment from the given three side lengths. Students examined two side lengths whether these side lengths can be joined to the line segment as a triangle or not. Students used rulers for determining those three side lengths that could form a triangle. They made a statement that the sum of any two sides of a triangle must be greater than the third side. Furthermore, teachers should consider students' learning trajectory for achieving successfully the learning goal.