Hypothetical learning trajectory in student’s spatial abilities to learn geometric transformation

Ricki Yuliardi(1*), Rizky Rosjanuardi(2)

(1) Department of Mathematics Education, Universitas Pendidikan Indonesia, Indonesia & Department of Mathematics Education, STKIP Muhammadiyah Kuningan, Indonesia
(2) Department of Mathematics Education, Universitas Pendidikan Indonesia, Indonesia
(*) Corresponding Author


The relationship between spatial conceptions and students' spatial abilities is still rarely studied specifically, even though this is the basis for students to think in learning geometry. This paper aims to explore spatial abilities and the development of spatial ability theory, discusses the relationship between spatial conceptions in students' understanding, and how to develop HLT (Hypothetical Learning Trajectory)in transformation geometry learning. HLT design consists of three stages: initial design, experimental, and retrospective analysis. The results of HLT are then refined into LIT (Local Instructional Trajectory). Then this paper present the empirical results of the perceptions of twenty  9th grade students in one of Islamic private school in Kabupaten Kuningan, West Java, Indonesia, towards the corresponding geometric and math questions. Literature review analysis was used to analyze the retrieved articles. At the end of the paper, we explain and discuss how to apply mathematical conceptions in learning geometry. This research is expected to be a guidance for teachers to develop learning in accordance with the students' spatial thinking process in studying geometry.


Spatial abilities, spatial conception, geometric transformations, hypothetical learning trajectory

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