Case of Actualizing Geometry Knowledge in Abstraction Thinking Level for Constructing a Figure

Abstract

The purpose of studying geometry is for the development of student thinking, able to abstract and reason, against concepts in the object. Note on some study results that the combination of the student's conceptualization process and knowledge of geometry are a source of barriers to their learning. This study aims to investigate how students actualize their geometry knowledge for the development of thinking to the level of abstraction. Investigations on input, internal processing, and output. This study was conducted on high school students use questions regarding object and product of thought in geometry thinking at analysis and abstraction level. Based on study findings, students actualize their knowledge through figural aspects then developed into the conceptual aspect, and the two aspects are integrated with the relationship between properties. There is a mathematical connection to the integration process. However, because most students' understanding of geometry knowledge is still prototypical figural concepts, so there is an interaction issue between figural and conceptual aspects, namely the validity of relationship between properties. Therefore, students learn geometry in order to investigate the connections between objects and properties as a whole.

Students’ Inconsistency when Solving a Geometry Problem in Three-Dimensional Context

“…This indicates the relevance and inconsistency of students in completing geometry task. Because of the problem of consistency, there is a certain part of relevance between students' concept knowledge, abilities, and learning processes that should be considered for their cognitive activities in class geometry (Fiki Alghadari et al, 2020;Isnawan et al, 2022;Noor & Alghadari, 2021a), including representation of 3D shapes, spatial structuring, conceptualization of mathematical properties, and measurement (Pittalis & Christou, 2010). Therefore, some researchers have recommended the need for an analysis of how students conceptualize problem solving to explain the phenomena of cognitive restructuring and conceptual reorganization when they engage in complex domains that describe problem solving behavior and affect their performance (Biccard, 2018;Suwa, Gero, & Purcell, 1998;Yee, 2017).…”

“…Thus, solving problems is a way to conducted new knowledge which is constructed through the conceptualization process (Dossey, 2017;Fauskanger & Bjuland, 2018;Simon, 2017;Ward, 2012). When students have problems with the conceptualization process, problem solving abilities become inconsistent due to the complexity of cognitive ability to process conceptual knowledge (Noor & Alghadari, 2021b;Yee, 2017). That can happen because there is a basic knowledge whose construction is not complete, or the conceptual knowledge is complete but there is a misconception (Rahayu & Alghadari, 2019;Rosilawati & Alghadari, 2018).…”

A Bibliometric Analysis of Geometry Education Research Based on Web of Science Core Collection Database

“…This encourages researchers to study geometry intensively. With each passing day, the value of scientific studies is increasing, especially studies that reveal the problems faced by students, teacher candidates and teachers in the field of geometry teaching and focus on how it should be by offering solutions with the teaching understandings required by the age (Birni, 2016;Noor & Alghadari, 2021).…”

Assessment of primary schoolchildren’s fluid intelligence using Raven's Colored progressive matrices: A pilot cross-sectional study in Lebanon

“…Abstract Reasoning is the main drive of thinking outside the box, troubleshooting, decision-making, innovation, research, and a valid link between ideas and events. Developing it can help foster the individuals' innovative and creative ability and intellectual capacity (Colom et al, 2022;Nur & ALGHADARI, 2021). Abstract reasoning or fluid intelligence can be applied to school children or employees to help them develop and achieve better goals throughout their education or work tasks (Johann et al, 2020;Syawaludin et al, 2019).…”