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

Eunice Kolitsoe Moru(1*), Maqoni Malebanye(2), Nomusic Morobe(3), Mosotho Joseph George(4)

(1) Department of Mathematics and Computer Science, National University of Lesotho
(2) John Maund High School, Maseru
(3) Department of Science Education, National University of Lesotho
(4) Department of Chemistry and Chemical Technology, National University of Lesotho
(*) Corresponding Author


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.


Geometry, 2-dimensional shapes, 3-dimensional shapes, Van Hiele Theory

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