Students' Spatial Ability During Geometry Learning through a Realistic Approach In Terms of Their Genetic Decomposition

K. U. Z. Nugroho, Y. Sukestiyarno, I. Hidayah
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Abstract

Geometry is a part of mathematics that students must learn. Spatial ability as a basic ability that students must have to learn more geometry. The realistic mathematical approach provides horizontal processing towards formal understanding. The purpose of this study is to interpret the characteristics of students' spatial abilities during learninggeometry through a realistic mathematical approach in terms of APOS Theory. This research uses quantitative qualitative and descriptive methods. The focus of this research is to explore students' spatial abilities after learning geometry through a realistic approach in understanding geometry concepts reviewed from APOS (Action-Process-Object-Schema) Theory. To comply with the COVID-19 health protocol, the implementation of learning was carried out online with as many as 30 students in the Mathematics Education Program in Rejang Lebong Regency, Bengkulu Province, Indonesia. This study also has exploratory characteristics. The researcher acts as a teacher as well as the main instrument in this study. Researchers use spatial ability test instruments to explore qualitative data. The test result data is used as the basis for determining the research subjects to be interviewed in depth to explore students' spatial abilities during geometry learning through a realistic mathematical approach. The subjects of this study were three students selected from three categories of test results, namely the high, medium and low groups of one person each. Interviews of subjects were conducted using whatsapp media via video call. These interviews are recorded to obtain complete and accurate data. Research data are analyzed through genetic decomposition analysis (description of their actions, objects, processes, schemes, and relationships that individuals have for concepts and principles in spatial geometry). The result of this study was that it was found that students had a mature scheme about the properties of building space. He was able to perform the tematization of objects about the diagonal of the plane and the diagonal of space can be represented in good mental activity, he was a student of the trance level. Inter students are able to carry out action-process-object-and schematic activities, but the embedding is incomplete. Intra students are able to do perceptions of space, but are unable to do interiorization and encapsulation so they fail to solve the given problem. The conclusion of this study is that there is an increase in the spatial understanding of students who are taught through a realistic mathematical approach. There are three levels of students' spatial ability after learning geometry through a realistic mathematical approach. Those are the trance level, the inter level and the lowest intra level.
从遗传分解的角度看学生几何学习中的空间能力
几何是学生必须学习的数学的一部分。空间能力作为学生学习几何必须具备的基本能力。现实的数学方法为形式理解提供了横向处理。摘要本研究旨在以APOS理论为基础,运用现实数学的方法来解释学生几何学习过程中空间能力的特征。本研究采用定量、定性和描述性的方法。本研究的重点是探讨学生在学习几何后,对动作-过程-对象-图式(APOS)理论中几何概念的现实理解。为遵守2019冠状病毒病卫生方案,在印度尼西亚明古鲁省Rejang Lebong县的数学教育项目中,对多达30名学生进行了在线学习。本研究也具有探索性的特点。在本研究中,研究者既是教师又是主要工具。研究人员使用空间能力测试工具来探索定性数据。测试结果数据作为确定研究对象的基础,深入访谈,通过现实的数学方法探讨学生在几何学习中的空间能力。本研究的研究对象是三名学生,从三种测试结果中选出,即高、中、低组各一人。使用whatsapp媒体进行视频通话访谈。这些访谈被记录下来,以获得完整和准确的数据。研究数据通过遗传分解分析(描述个体对空间几何概念和原理的行为、对象、过程、方案和关系)进行分析。本研究的结果是发现学生对建筑空间的属性有一个成熟的方案。他能够将平面对角线上的物体和空间对角线表现在良好的心理活动中,他是一个处于恍惚状态的学生。学生能够进行动作-过程-对象-图式活动,但嵌入不完整。校内学生能够感知空间,但无法做到内化和封装,因此他们无法解决给定的问题。本研究的结论是,通过现实数学方法教学的学生的空间理解能力有所提高。通过现实的数学方法学习几何后,学生的空间能力有三个层次。这三个层次分别是出神层次,中间层次和最低的内部层次。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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