Tesis

Characteristics of mathematical mental models of junior high school students in understanding the concept of integers / Mutina

Abstrak
This study aims to describe the mathematical mental models of junior high school students in understanding the concept of integers. Mathematical mental models are defined as internal representations that students have in understanding certain mathematical concepts which are then constructed into external representations through drawings or writing. Meanwhile concept understanding in this study is emphasized on relational concept understanding where students can apply concepts accompanied by drawing conclusions and appropriate reasons. Based on the theoretical review and the results of the preliminary study the researcher wants to refine the characteristics of the mental model of the values and order of integers that have been initiated by several previous researchers as well as combining Bofferding s ideas regarding the mental model of the value and order of integers and the mental model of directed magnitudes (addition and subtraction of integers). This is supported by Peled s opinion that students first level of knowledge about integers is to know the order of all integers and then to be able to add and subtract integers. Thus the concept of integers referred to in this study is limited to integers comparison integers addition and integers subtraction. This research was conducted in class VII of junior high school consisting of 71 students. The research method used was qualitative with the type of case study research. Data collection techniques used tests and interviews while the selection of subjects used purposive sampling techniques namely there were 7 subjects to be explored. Data analysis techniques using the Miles and Huberman model include data condensation data display and drawing and verification conclusion. The results showed that the characteristics of students who are at the pre-initial mental model level can place positive integers on the number line. Students at the initial mental model level have the characteristics of being able to place zero and positive integers on the number line or students can place positive integers zero and negative integers on the number line but the order of negative integers is treated like positive numbers or place positive integers and negative integers but 0 and -1 are not written on the number line. Students at transition mental model level I have the characteristics of being able to place positive zero and negative integers on a number line and can compare the values of positive and negative integers. The characteristics of students at the synthetic mental model level can place positive integers zero and negative integers on the number line can compare the values of positive integers and negative integers and can compare the values of two negative integers. The characteristics of students at the transition II-inconsistent mental model level can place positive integers zero and negative integers on the number line can compare the values of positive integers and negative integers can compare the values of two negative integers can sort positive integers but are inconsistent in sorting negative integers. The characteristics of students at the transition II-consistent mental model level can place positive zero and negative integers on the number line can compare the values of positive and negative integers can compare the values of two negative integers and can sort positive and negative integers consistently. Finally the characteristics of students at the formal mental model level can place positive zero and negative integers on the number line can compare positive and negative integers can compare two negative integers can order integers can add and subtract integers as well as order them.

Informasi Detail

DDC

Rt 515.4307 MUT c

Prodi

Universitas Negeri Malang. Program Studi Pendidikan Matematika, 2025.

Deskripsi Fisik

xvii, 166 lembar. : ilus. ; 30 cm.

Bahasa

No Reg

00412/RT/25

Edisi

Tesis (Pascasarjana)--Universitas Negeri Malang. 2025

Subjek

1. INTEGRAL - PEMAHAMAN KONSEP
2. INTEGRAL - CONCEPT UNDERSTANDING

Pembimbing

1. Dr. Sudirman, M.si; 2. Vita Kusumasari, S.si, M.pd, Ph.d

Lampiran Berkas