The Interesting Activities For Learning The Concept Of Angle


The title of this research is Developing A Local Instruction Theory For Learning The Concept Of Angle Through Visual Field Activities And Spatial Representations. The research has been done by Bustang, graduate student of IMPOME, in 2013. Together with Zulkardi, Darmawijoyo, Maarten Dolk, and Dolly van Eerde, researcher published it in International Education Studies, volume 6, nomor 8, page 58-70.

The aim of this research is to contribute to the development of a local instructional theory for the concept of angle. It is very important because based on several researches, geometry, the topics that involve spatial visualization and reasoning such as the concept of angle, is one of the hardest topics for students. They often harbor many misconceptions, conceive an erroneous angle representation and get confused recognizing right angles in different orientation. It can be the problem for the students because these misconceptions will continue to exist until they learn geometry in the higher level. Furthermore, they will lack understanding about how the concept of angle is represented and used in everyday life situations.

Actually, the concept of angle is closely related to the real world situation such as using visual field activities. It can be the context to learn the concept of angle that is in line with the characteristic of the PMRI, in which use of context as an instructional sequence is aiming to foster the emergence of formal mathematical knowledge of students.

The subjects of this study were 43 third-grade students of a public elementary school in Palembang, Indonesia. Five students participated in a pilot experiment, while the other 38 students participated in the teaching experiment. The groups are from the same school but different classes.

The steps that was done by researcher were preliminary design, teaching experiment, and retrospective analysis. In preliminary design, researcher design the learning activities that is called HLT. In the teaching experiment, the sequence of activities was implemented in the classroom within two cycles (pilot experiment and the actual teaching process). In the retrospective analysis, HLT was used as a guideline and points of references in analyzing of the entire data set collacted during the teaching experiment.

This study was held during 4 meetings :

Meeting 1

Teacher gave the students a worksheet that consist of three problems about vision lines and blind spots with mice and a cat as the context.

Problem 1

(How many mice can the cat see? Explain and write down your reasoning! Students may make a drawing in the figure.)

 mc fgr 1

Figure 1. Panoramic drawing of the situation

Problem 2

(Is there any difference in the number of mice that the cat can see in Figure 1 and Figure 2? Explain and write down your reasoning! Students may make a drawing in the figure.)

 mc fgr 2

Figure 2. Top view of the situation


Problem 3

 mc fgr 3

Figure 3. The cat moves closer to the jar (top view)

Meeting 2

Teacher encouraged the students to conduct visual field activities of constructing vision lines and blind spots of the observer.

Meeting 3

Teacher presented the four different diagrams depicting the ground plan of the situation in the visual field activities. Then, the students were asked to colour or shade the blind spots (hidden area) for various positions of the observer, as in the visual field activities.

Meeting 4

Teacher encouraged the students to construct and draw the angle of vision for different position of the observer.

As the result, from the four-step instructional activities both visual field activities and spatial representations tasks, students could grasp the static sense of the concept of angle. Students can remember what they have experiented in the visual fields activities but that this does not mean that they are automatically able to transform their experience into abstract knowledge such as the concept of angle. In additian, the visual field activities also support social interaction among the students during the learning process. Considering the findings of this study, the suggestion for subsequent research is to use visual field activities and spatial representations to intertwine the topic of angle concept and coordinate system.


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