A STUDY OF MATTHAYOMSUKSA 3 STUDENTS' GEOMETRIC REASONING BASED ON THE CONCEPTS OF GUTIERREZ & JAIME

Abstract

This research aims to investigate the geometric reasoning of Grade 9 students with high, medium, and low academic achievement in mathematics, specifically focusing on the reasoning of triangles and quadrilaterals, based on Gutierrez and Jaime’s framework. A qualitative research methodology was employed, with data collected through transcribed audio recordings of interviews. The data were analyzed using protocol analysis according to Gutierrez and Jaime’s framework, which categorizes reasoning into 4 aspects: 1) recognition, 2) definitions, 3) classification, and 4) proof. The target group consisted of 9 Grade 9 students from the Demonstration School of Phranakhon Si Ayutthaya Rajabhat University (Secondary Section), divided into 3 groups: 3 high-achieving, 3 medium-achieving, and 3 low-achieving students. The research instruments included practical tasks, interview forms, and interview transcripts.

The findings revealed the following: 1) Recognition: All 9 students (3 high, 3 medium, 3 low) demonstrated reasoning at Levels 1 and 2. At Level 1, students classified geometric shapes based on external characteristics. At Level 2, students classified shapes by considering definitions or geometric principles they had learned, such as the number of sides, angles, or whether the shape is closed. 2) Definitions: This aspect was divided into 2 sub-aspects: use of definitions and establishment of definitions. For the use of definitions, 2 students (low-achieving) exhibited Level 3 reasoning, proving with a single step by referring to theorems, definitions, or given conditions but lacking logical conclusions. 8 students (3 high, 3 medium, 2 low) demonstrated Level 4 reasoning, proving with multiple steps by referring to theorems, definitions, or given conditions and reaching logical conclusions. 1 student (high-achieving) did not meet any level due to misinterpreting the problem. For the establishment of definitions, 8 students (3 high, 3 medium, 2 low) showed Level 2 reasoning, defining shapes based on definitions, theorems, line construction, and measurement. 3 students (2 high, 1 medium) exhibited Level 3 reasoning, defining shapes based on definitions, theorems, line construction, and measurement with single-step proofs. 7 students (3 high, 2 medium, 2 low) demonstrated Level 4 reasoning, proving with multiple steps by referring to theorems, definitions, or given conditions and reaching logical conclusions. 3) Classification: 1 student (low-achieving) showed Level 1 reasoning, classifying shapes based on external characteristics. 6 students (3 medium, 3 low) exhibited Level 2 reasoning, explaining similarities and differences of shapes by considering self-constructed diagonals and right angles using relevant theorems. 4 students
(3 high, 1 medium) demonstrated Level 3 reasoning, explaining similarities and differences of shapes by considering self-constructed diagonals and right angles using relevant theorems, along with single-step proofs of geometric properties. 4) Proof: 4 students (2 medium, 2 low) showed Level 3 reasoning, proving with a single step by referring to theorems, definitions, or given conditions. Eight students (3 high, 3 medium, 2 low) demonstrated Level 4 reasoning, proving with multiple steps by referring to theorems, definitions, or given conditions and achieving the desired conclusions. 2 students (low-achieving) did not meet any level due to illogical proofs.