Profile of Cognitive Structure of Students in Understanding the Concept of Real Analysis

Abstract

The purpose of this research is to describe proil cognitive structure of students in understanding the concept of real analysis. This research is part of the research development of the theory of cognitive structure of students Mathematics Education Program at the University of Bengkulu. The results of this research are: 1)there are seven models decompositions of genetic students mathematics education reviewed based on the SRP Model about the concepts of Real Analysis namely Pra-Intra Level, Level intra, Level semi-inter, Level inter, Level semi-trans, Trans Level, level and Extended-Trans (only theoretic level while empirically not found); 2) There are six models decompositions of genetic students mathematics education reviewed based on KA about the concepts of Real Analysis namely Level 0: Objects of concrete steps; Level 1: Models Semi-concrete steps; Level 2: Models Theoretic; Level 3: Language in Domain Example; Level 4: Mathematical Language; Level 5: Inferensi Model. Profile of cognitive structure of mathematics education student at the University of Bengkulu is 6.25% Students located on the Basic Level (Pra-Intra Level with concrete objects), there is 8.75% Students located at Level 0 (intra Level with concrete objects), there are 15,00% Students located at Level 1 (semi-Level inter with Semi-Concrete Model), there are 33.75 percent students located on Level 2 (Level inter with theoretical model), there are 22.50 percent students located at Level 3 (Semi-trans Level with the Bible in Domain example), there are located on the student percent during the Level 4 (Trans Level with the language of Mathematics), and there are 0 percent students located at Level 5 (Level Extended-Trans with Inferensi Model). Students Education Mathematics at the University of Bengkulu pembangunnya element is functional can achieve Trans Level, students will be able to set up activities and make the algorithm that formed the concept/principles with the right. Functional students can also perform the process of abstraction using the rules in a system of mathematics.

Pengembangan Multimedia Interaktif dalam Pembelajaran Matematika dengan Pendekatan Kontekstual Ditinjau dari Pemahaman Konsep Siswa

“…Melalui pengembangan pola pikir ini, siswa dapat menentukan dengan baik konsep-konsep matematika. Pemahaman konsep matematika yang dilakukan siswa melalui pengolahan informasi sistem tentang ide-ide abstrak menggunakan media atau benda dari langkah-langkah konkret untuk diklasifikasikan (Widada, 2016).…”

The Scheme Characteristics for Students at the Level of Trans in Understanding Mathematics During Etno-Mathematics Learning

“…The description states that learning ethnomathematics has a positive effect on the ability to understand mathematics. To find out, students' cognitive processes can be determined through the APOS framework (action-process-object-schema) [13][14][15][16][17]. To determine the cognitive structure of students an analysis of genetic decomposition is carried out [18].…”

“…Other research found that, the student cognition framework in understanding mathematics is categorized in seven levels [16,17,19]. The seven levels in a row were pre-intra, intra, semi-inter, inter, semi-trans, trans, and extended trans levels [17].…”

“…The intra students having genetic decomposition are only taking actions or processes separately, and cannot determine the relationship of actions, processes or objects [17]. As for the extended trans students, aside from being in the trans level, they can build new structures based on the mature schemes their already have [16,17,24].…”

“…The majority of trans level students have unique characteristics [14,16,17]. Therefore, these characteristics need to be studied.…”