Development and Validation of an APOS-Based Mathematics Mental Structure Scale

Author Information

Ella Tricia Aquino, Kalinga State University, Philippines
Dominga Valtoribio, Saint Mary's University, Philippines

Abstract

Action-Process-Object-Schema (APOS) theory emerges as an extension of constructivism, but it takes a more robust and targeted learner-centered approach to mathematics instruction. As a basic mathematics requirement, problem-solving skills and the development of mathematical mental structures are important. By aligning the scale’s statements with the APOS theory, this study aims to bridge the gap between students' prior mathematics learning and their current educational needs. Therefore, given the critical need for a proper tool to measure the mathematical mental structure of students in the study's locale and mathematics education at large, this study provided a valuable scale. The scale development followed the process: (1) item generation, (2) item evaluation, (3) pilot-testing, (4) Exploratory Analysis, (5) final evaluation. Several studies and literature have been reviewed to generate the 62 items or statements for the scale. The items are evaluated, and only 54 of them are used for the draft scale for the pilot test. The scale was administered to 330 students for the pilot-test, and responses were screened and then subjected to Exploratory Factor Analysis (EFA). One factor was extracted. To establish internal consistency, the factor was correlated with other established constructs – motivation levels, with the scale being substantially correlated, and mathematics self-efficacy and anxiety, with the scale having predictive validity. Further tests were done, and the final scale consists of 40 items, which confirmed validity and reliability.

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