Introducing Concept of Angles with RME Based Learning

Summary of:
Bustang, Zulkardi, Darmowijoyo, Dolk, M., van Eerde, D. (2013). Developing a local instruction theory for learning the concept of angle through visual field activities and spatial representations. International Education Studies, 6(8), 58-70. doi: 10.5539/ies.v6n8p58

The notoriety of geometry among Indonesian students as one of the hardest topics is not without proof. Studies found many misconceptions experienced by the students, especially in angle representation which might impact on their difficulties in learning geometry in the higher level.

In order to deal with the problem, Bustang has designed a four-step learning activitiy for teaching and learning the concept of angle. The design has been tried out to the third grade students of a public school in Palembang, Indonesia.

At first, the students were familiarized with the real situations involving vision lines and blind spots through an activity called ‘Now you see it, now you don’t’. Here, the students were provided with three problems related to a cat’s vision over a group of mice by representing the ‘top view’, ‘side view’, and additional case if cat do a ‘movement’.


It was found, from the first activity, that most of the students could realize the existence of the vision lines and blind spots. This also leads that constructing vision lines would be a good choice to introduce the angle since they could notice how observer’s position affects the vision line.

The second activity was to encourage students to construct vision lines and blind spots through field activities. The situation (cat and mice) in the previous meeting was reconstructed by involving the students (role playing), one as the cat (observer) and others be the mice. A screen is placed in the center as the jar behind which the mice hide. The students-mice move out of the screen and stop by the time the student-observer see them. Their last positions, later on, will form the vision line of the observer.

Following the activity, the teacher asked the students to predict the position of the next bag. This is to ensure their understanding of the vision line by identifying the pattern of the bags.

predicting visual line
A student tried to predict the position of the next bag forming the visual line

This stage helped the students to grasp the idea of angle. Unfortunately, it still failed to prevent the students from misconception that the measure of an angle is based on the length of its arm. Additional activity is, therefore, conducted.

The third activity involved four diagrams (representing the observer’s views). The students were asked to shade the invisible region for the observer. The goal of the activity is to encourage them imagine and visualize the vision lines as well as to build their reasonings on angle.
student work visual linesThe last activity aims at helping students to construct angle of vision. In the beginning, the teacher asked one of students to stand in front of the door and looking into the classroom. Using rope, two other students tried to make visual line of the standing student. Afterwards, the teacher gave them worksheet asking them to draw visual line of similar cases from various positions.

Finally, through this activity, the students could construct their angles and understand that the how their position determine the measure of the angle.

This post is written based on my own understanding toward the article

The complete article could be accessed in


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