Journal Article

Analysis of Students’ Mathematical Proofs Viewed from Reasoning

Prasasti, Woro Dhiah, Hidayah, Indriati Nurul

2026

Overview

Indonesia’s students’ reasoning scores in PISA 2022 are low, and many students still struggle to complete proofs. This study aims to describe students’ proofs in terms of reasoning. The research was conducted with Grade VIII students from two public junior high schools in Malang City, Indonesia, using two validated proof questions and interview guidelines. A descriptive qualitative approach was employed. There are two problems in mathematical proofing: one about even numbers and one about the sum of consecutive integers. Students’ answers were categorised into high, medium, and low reasoning levels. Subjects were selected using purposive sampling. In problem number 1, three students served as research subjects, representing the high, medium, and low reasoning levels. In problem number 2, two students were selected as research subjects because their answers showed only high and low reasoning categories. Students’ answers were analysed using Miyazaki’s classification of four proof types. Results showed that all students used inductive reasoning, representing proofs with numbers. In problem number 1, high-category students could organise proofs and draw correct conclusions, while medium- and low-category students struggled, especially in drawing conclusions. In problem number 2, all students identified patterns, but low-category students were less precise in their conclusions. The use of examples supported the proof process. The findings suggest the need for instructional scaffolding to support students’ transition from inductive reasoning toward formal deductive proof.

• Publisher: IOP Publishing
• Subject: Instructional scaffolding / Reasoning / Scaffolding / Students