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Knowledge Representation of Mathematics Education Program among Students in Euclidean Parallelism

This research aims to reveal students' perception-based knowledge representation from mathematics programs in Euclidean Parallelism. Students were asked to do parallelism exercises presented in a verbal and picture form. The data were analyzed by knowledge representation theory based on meaning and perception. There were students who have amodal-multimodal-transition hypothesis. Students' assumptions about the verbal and picture information of not-perfectly-drawn parallel lines varied: assuming that angles appear to be the same measure are congruent, the two lines would intersect, considering the two lines parallel but redrawing picture to determine the pair of congruent angles and using other perspectives to interpret the picture. This study recommends action research for geometry learning that provides not-perfectly-drawn parallel lines for students who have amodal and amodalmultimodal- transition hypothesis and observe its effect on their non-Euclidean geometry learning. It may also familiarize students with getting to know parallelism in R3.