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

Ricki Yuliardi,Rizky Rosjanuardi

doi:10.23917/jramathedu.v6i3.13338

Abstract

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.

Highlights

The use of the term Hypotetichal Learning Trajectory (HLT) was initiated and implemented in the process of mathematics learning by a mathematician, named Simon. Simon (2017) focused his attention on the ways teachers teach and present information to students how the flow of thinking about the concept of mathematics, as well as the creation of new experiences or problems that are designed to assist the processof better student understanding
This paper aims to explore spatial abilities and the development of spatial ability theory, discusses the relationship between spatial conceptions in students' understanding, andhow to develop HLT (Hypothetical Learning Trajectory) in transformation geometry learning
From the results of this study, it can be concluded that HLT is very important for teachers to arrange learning trajectories as a reference in designing learning that can optimize spatial skills.Especially spatial abilities that are needed for students to learn geometric concepts, in this study it cannot be separated from constraintsexperienced by students from the initial initiation stage to the retrospective stage

Summary

Introduction

The use of the term Hypotetichal Learning Trajectory (HLT) was initiated and implemented in the process of mathematics learning by a mathematician, named Simon. Simon (2017) focused his attention on the ways teachers teach and present information to students how the flow of thinking about the concept of mathematics, as well as the creation of new experiences or problems that are designed to assist the processof better student understanding. The use of the term Hypotetichal Learning Trajectory (HLT) was initiated and implemented in the process of mathematics learning by a mathematician, named Simon. The learning process and the level of thinking called HLT are something that must be considered in order to achieve the expected goals (Clements & Sarama, 2011). From the objectives stated by NCTM, it is implied that in the learning process, students build knowledge from the experiences they find in their lives (Kartianom & Retnawari, 2018). Teachers need to see how students think about mathematics itself and relate that knowledge to experience (Retnawati, Djidu, Kartianom, Apino, & Anazifa, 2018). Following what Ausuble stated, meaningful learning is a learning process that actively

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