Some Difficulties in Understanding Negative Numbers Faced by Students: A Qualitative Study Applied at Secondary Schools in Indonesia

Abstract

This study revealed how students' understanding of negative numbers and identified their difficulties related with the concept of integer and its counting operation as part of identifying epistemological obstacles about negative numbers. Even though teachers have explained counting operation procedure of integer, but there was concept misunderstanding among students. The concept difference between what was comprehended by respondents in their learning process and knowledge science has resulted in wrong perceptions about the negative numbers. In this article, the authors explained how these misunderstanding in concepts occurred among students and how these ideas were expressed by the students in solving the problem which was related with counting operation of negative integer. This study was part of Didactical Design Research using qualitative approach in negative number learning by involving 96 students of 7th grade as participants in three different schools. This study showed some difficulties by the student to understanding negative numbers in terms of prerequisite knowledge, understanding concepts, procedures, principles and problem solving.

Analisis Data Miskonsepsi Siswa Sekolah Menengah Pertama dalam Menyelesaikan Operasi Aritmatika Dasar

“…Penelitian tentang miskonsepsi aritmatika telah dilakukan di berbagai negara (Aliustaoğlu, dkk., 2018;Bolognese, Fellows, & Schuhl, 2019;Bush & Karp, 2013;Dhlamini & Kibirige, 2014;Ojose, 2015;Vermeulen & Meyer, 2017), begitu juga di Indonesia (Fuadiah, Suryadi, & Turmudi, 2016;Herutomo & Saputro, 2014;Malihatuddarojah & Prahmana, 2019). Akan tetapi, penelitian yang dilakukan di Indonesia umumnya membahas miskonsepsi yang terjadi pada topik aljabar yang merupakan lanjutan dari aritmatika (Herutomo & Saputro, 2014;Malihatuddarojah & Prahmana, 2019).…”

Emphasizing Concrete Representation to Enhance Students’ Conceptual Understanding of Operations on Integers

“…One of the causes mentioned by Khalid and Embong (2020, p. 2) is due to "students being taught to follow rules and procedures in a very abstract manner without going through the models for better conceptual understanding". Many researches have been conducted to document students" errors and misconception, but only a few of the researches involved intervention study to lessen the errors and enhance students" understanding of integers (Fuadiah, Suryadi & Turmudi, 2017;Makonye & Fakude, 2016;Okpube, 2016). Consequently, this paper will relate the findings of a quasi-experimental research study that highlights multiple representations to enhance students" understanding of operations on integers.…”

Identifikasi Kesalahan Siswa Berdasarkan Newman Dalam Menyelesaikan Soal Pada Materi Persamaan Kuadrat Tingkat Sekolah Menengah Pertama

“…Sering kali terjadi konsep matematis yang dimiliki siswa didasari pada definisi yang mereka ketahui dari sudut pandang mereka sendiri sehingga terjadi perbedaan konsep antara apa yang dipahami siswa dalam proses pembelajarannya dengan ilmu pengetahuan yang sebenarnya (Fuadiah, Suryadi & Turmudi, 2017). Ramadhani, Yuwono, Muksar (2016) menyatakan bahwa kesalahan yang dilakukan setiap siswa dapat dijadikan referensi oleh guru untuk merancang pembelajaran maupun tolak ukur untuk membantu siswa menyadari kesalahannya.…”