Stuffs Arrangement for Learning Volume Measurement

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The title of this research is Spatial Visualization Tasks To Support Students’ Spatial Structuring In Learning Volume Measurement. The research has been done by Shintia Revina in 2011. Together with Zulkardi, Darmawijoyo, and Frans van Galen, she wrote it in Journal on Mathematics Education, volume 2, nomor 2, page 127-146.

The aim of this research is to develop classroom activities with the use of spatial visualization tasks to support students’ spatial structuring in learning volume measurement. It is very important because most of students in grade five tented to have difficulty in fully grasping the concept of volume measurement. In volume measurement, students have to build their competence in spatial structuring. The unit of volume “packing” measurement  must be integrated and coordinated in three-dimension. Unfortunately, students often made error on the volume measurement tasks with three-dimention cube arrays that are related to some aspects of spatial visualization. They need to practice with concrete tasks in which they can well perceive the constructed views of the organization of a three dimensional rectangular array made of unit cubes before engaging with its pictorial representation.

Based on that condition, researcher used RME (Realictic Mathematics Education) in that research. It was chosen because one of the principals in RME is bridging from a concrete level to a more formal level by using models and symbols. Beside that, RME allows and encourages the students to invent their own idea and use their own strategies. Therefore, in this study, students could develop their own model or symbol to represent the arrangement of the packages in three dimension array.

The subject of this research was 32 students and a teacher of grade 5 of SD Pusri Palembang. They worked in groups of 4 or 5. The teacher classified the students based on academic ability and gender. Therefore, in each group there were high achievers, average students, and also low achievers.

In this research, students did a series activities :

  1. Students visualized the three-dimensional object into the two-dimensional drawing (Teacher arranged some stuffs such as tea boxes, tissue packages, and wafer bars in a three-dimensional array arrangement on students’ tables and then asked the students to draw the arrangement on the paper so that the people who see their drawing can understand the situation)
  2. Second, the students were asked to build a construction made of cube blocks (The teacher gave them pictures of the construction from side, top, and front views)
  3. The last, students were asked to count the number of blocks in their friend’s construction. And also they were asked to estimate the number of blocks needed to cover up such an empty rectangular box

From pre-test, researcher found that the students seemed have little difficulties in determining the number of concrete objects in the pictures such as tea boxes or soap bars arrangement because they were familiar with the soap and the tea. However, they have difficulties in determining the number of blocks in the drawing which is more abstract. They tended to count the number of square rather than count the number of blocks. After a series activities in this study, students could count the number of the blocks.

In conclution, the building blocks activity has helped the students to coordinate the separates views of the arrays. It influenced the students in counting the block arrangement and predicting the number of blocks needed to cover up a box. The students gradually become capable of coordinating the separate views of the arrays and they integrated them to construct one coherent model of the array.

From this research, we can learn many things, such as :

  1. Concrete situation help the students to understand the material
  2. Building blocks activity can help students’ spatial structuring in learning volume measurement
  3. RME can help the teacher to reach the goals of the learning.
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