Psychometric Evaluation of a Metaphorical Thinking Instrument in Mathematics Learning: Graded Response Model

Oryza vini Faradila; Ilham Falani; Mujahidawati Mujahidawati

doi:10.58421/misro.v4i4.873

DOI:

https://doi.org/10.58421/misro.v4i4.873

Authors

Oryza vini Faradila Universitas Jambi
Ilham Falani Universitas Jambi
Mujahidawati Mujahidawati Universitas Jambi

Keywords:

Graded Response Model, Item Response Theory, Metaphorical thinking, Validity and reliability

Abstract

This study aims to develop and psychometrically validate an assessment instrument designed to measure students’ metaphorical thinking ability in mathematics learning, with a specific focus on the Pythagorean Theorem. The instrument was developed using a Research and Development (R&D) framework based on the Oriondo and Antonio model, encompassing test design, empirical tryout, and measurement stages. Six polytomous essay items were constructed according to six indicators of metaphorical thinking: connect, relate, explore, analyze, transform, and experience. Content validity was established through expert judgment using Aiken’s V coefficient, with all items exceeding the minimum validity threshold, indicating strong agreement among experts. Empirical validation was conducted using Item Response Theory (IRT) with the Graded Response Model (GRM), selected for its suitability in analyzing ordered polytomous response data. The results demonstrate that the instrument satisfies the unidimensionality assumption, exhibits strong item discrimination parameters, and shows good model fit across all items. Analysis of the Test Information Function indicates high measurement precision within the ability range of θ −1 to +1, confirming strong local reliability. These findings indicate that the developed instrument is valid, reliable, and capable of providing accurate diagnostic information regarding students’ ability to construct mathematical meaning through metaphors. The study contributes methodologically by demonstrating the applicability of GRM-based IRT analysis for essay-type instruments and substantively by supporting the assessment of higher-order cognitive processes in mathematics learning.

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