A Van Hiele Theory analysis for teaching volume of three-dimensional geometric shapes

Geometry is among the cornerstones of mathematics because of its applicability in real life and its connection to other areas of mathematics. The reported study explored how the volume of 3D geometric shapes was taught in one high school in Lesotho. One male teacher and an intact class of sixty high school students were the participants of the study. The study was exploratory in nature. This was in order to understand the phenomenon under study so as to suggest ways on how to make some improvements for the future. Data were collected through classroom observations, photo shootings, note-taking, and interviews. Classroom observations enabled the researchers to start the analysis while also observing. The photos taken captured the nature of the tasks given to students, some explanations, and class interactions. The Van Hiele theory of geometric thought was used as the framework of analysis. The findings of the study show that at level 1, the teacher focused mainly on the vocabulary of the concept at hand, the information phase. Another phase which was dominant in the teaching at the same level is the direct orientation. The free-orientation phase was not fully realized. The analysis level was achieved through the information phase and the direct orientation phase. Thus the progression from one level to another by students occurred having some phases of learning being skipped due to the way the instruction was organized. It is postulated that lack of proper understanding of some concepts in geometry by students may result from this kind of instruction.

Pengembangan Perangkat Pembelajaran Kesebangunan Bangun Datar Berbasis Teori Van Hiele Untuk Meningkatkan Kemampuan Berpikir Tingkat Tinggi Siswa

In implementing the 2013 curriculum, Higher Order Thinking Skills (HOTS) must be integrated into learning activities. Similarity are sub material of similarity and congruence that students must learn. In fact, the higher order thinking skills of junior high school students in similarity material is low. To overcome this problem, it is necessary to develop a learning materials for learning in the form of plane similarity according to the level of student thinking in geometry, which is based on Van Hiele's theory to improve students' higher-order thinking skills. Van Hiele's theory was chosen because it suggests the development of students' thinking in learning of geometry occurs through five levels sequentially so that learning devices can be developed according to the level of van Hiele students. The purpose of this research is to obtain a description of the learning materials of plane similarity based on van Hiele theory based on van Hiele theory to improve students' high-level thinking skills that are valid, practical, and effective. This type of research is a research development using the 4-D model proposed by Thiagarajan then simplified to a 3-D model. Validation of learning devices, participant observation, questionnaires, and tests are the data collection techniques used. The results showed that the RPP, LKS, and THB were said to be valid then, the learning materials was declared valid; the management of learning is said to be good, the overall evaluation on the validation sheet of the learning materials is stated to be used, and the percentage of active student activities at the second meeting and the third meeting respectively is 91.25% and 91.25% then, the learning kit is declared practical; and the percentage of positive responses of students by 71% and an increase in higher order thinking skills seen from the results of the N-Gain pretest and posttest of 0,728 categorized as high then, the learning device is declared effective. Keywords: learning materials, plane similarity, van hiele’s theory, higher order thinking skills.