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Hamdani, Deni; Purwanto; Sukoriyanto; Anwar, Lathiful – Journal on Mathematics Education, 2023

Failure to deduce false suppositions in proof by contradiction is still considered "more difficult" than proving the conditional ?? to ?? in proof by contraposition. This study aims to identify the types of proof construction failures based on the action steps of proof by contradiction, then offer a framework of construction failure…

Descriptors: Validity, Mathematical Logic, Mathematics Instruction, Guidelines

Setiawan, Yayan Eryk; Purwanto; Parta, I. Nengah; Sisworo – Journal on Mathematics Education, 2020

Linear pattern is the primary material in learning number patterns in junior high schools, but there are still many students who fail to generalize the linear pattern. The students' failure in generalizing the pattern occurred when the students ended to view the problems globally without breaking them into the constructors' components such as the…

Descriptors: Cognitive Style, Mathematical Concepts, Thinking Skills, Concept Formation

Suryaningrum, Christine Wulandari; Purwanto; Subanji; Susanto, Hery; Ningtyas, Yoga Dwi Windy Kusuma; Irfan, Muhammad – Journal on Mathematics Education, 2020

Semiotics is simply defined as the sign-using to represent a mathematical concept in a problem-solving. Semiotic reasoning of constructing concept is a process of drawing a conclusion based on object, representamen (sign), and interpretant. This paper aims to describe the phases of semiotic reasoning of elementary students in constructing the…

Descriptors: Semiotics, Abstract Reasoning, Geometric Concepts, Concept Formation

Santia, Ika; Purwanto; Sutawidjadja, Akbar; Sudirman; Subanji – Journal on Mathematics Education, 2019

Mathematical representation has an essential role in solving mathematical problems. However, there are still many mathematics education students who have difficulty in representing ill-structured problems. Even though the ill-structured-problem-solving tasks designed to help mathematics education students understand the relevance and…

Descriptors: Mathematics Instruction, Problem Solving, Mathematical Concepts, College Students

Sapti, Mujiyem; Purwanto; Irawan, Edy Bambang; As'ari, Abdur Rahman; Sa'dijahm, Cholis; Susiswo; Wijaya, Ariyadi – Journal on Mathematics Education, 2019

Mathematical thinking is an important aspect of mathematics education and, therefore, also needs to be understood by prospective teachers. Prospective teachers should have the ability to analyze and interpret students' mathematical thinking. Comparing model is one of the interpretation models from Wilson, Lee, and Hollebrands. This article will…

Descriptors: Comparative Analysis, Models, Preservice Teachers, Mathematical Logic

Kurniati, Dian; Purwanto; As'ari, Abdur Rahman; Dwiyana, – Journal on Mathematics Education, 2018

The Mathematics students who perform truth-seeking process upon solving mathematical problems were unique. Therefore, the study deems it necessary to know students' mental structure and mechanism so that they can make the right decision by performing truth-seeking. However, no research has delved into the mental structures and mechanisms of…

Descriptors: Mathematics Instruction, Problem Solving, Cognitive Structures, Cognitive Processes