Designing an APOS-Grounded Contextual AI-Based Deep Learning Model to Improve Mathematical Communication and Creativity of Prospective Mathematics Teachers

Ilham Jaya; Isna Muhammad Fathoni; Widiastuti Widiastuti; Izzar Turrahman; Susila Afriyani; Marisa Marisa

doi:10.37630/bijee.v4i2.5066

Authors

Ilham Jaya Universitas Bani Saleh
Isna Muhammad Fathoni Universitas Bani Saleh
Widiastuti Widiastuti Universitas Bani Saleh
Izzar Turrahman Universitas Bani Saleh
Susila Afriyani Universitas Bani Saleh
Marisa Marisa Universiti Tun Hussein Onn Malaysia

DOI:

https://doi.org/10.37630/bijee.v4i2.5066

Keywords:

APOS theory, artificial intelligence, contextual learning, deep learning, mathematical communication, mathematical creativity

Abstract

Mathematical communication and creativity remain weak among Indonesian undergraduate Mathematics Education students, the future mathematics teachers of the country. A baseline observation of 84 fifth-semester students enrolled in Multivariable Calculus at Universitas Bani Saleh showed that 79.8 percent could not generate more than one solution approach, 76.2 percent struggled to express mathematical reasoning in coherent written form, and 83.3 percent reproduced textbook solutions without alternative reasoning. This study therefore designed and tested a Contextual AI-Based Deep Learning (CAIDL) model grounded in APOS theory that integrates contextual problem framing, AI-mediated Socratic scaffolding, deep learning pedagogy through reflective abstraction, and APOS-staged concept formation. Following the five-stage Plomp research and development model, the study involved seven expert validators, 12 students in a small-group trial, three lecturers, and 60 fifth-semester students assigned to experimental (n = 30) and control (n = 30) groups. Data were collected through expert validation sheets (Aiken’s V), feasibility and practicality questionnaires, and a 24-item essay test on mathematical communication and creativity (Cronbach’s α = .91). The CAIDL model was rated very valid (88.80 percent), very feasible (87.08 percent), and very practical (89.37 percent). On the posttest, the experimental group (M = 80.10, SD = 7.20) significantly outperformed the control group (M = 64.50, SD = 7.41), t(58) = 8.31, p < .001, Cohen’s d = 2.14, with a mean N-Gain of 0.582 (medium category). The largest indicator-level effects were found for solution fluency (d = 1.71) and coherent mathematical argumentation (d = 1.68). These findings indicate that the CAIDL model strengthens mathematical communication and creativity simultaneously and offers a replicable instructional design for mathematics teacher education programs.

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