Book

This book presents a comprehensive exploration of critical thinking in mathematics education through three interrelated studies that examine the phenomenon from distinct methodological perspectives. The first part investigates the critical thinking levels of pre-service mathematics teachers using a quantitative approach with 60 seventh-semester students, revealing that 58.3% of participants demonstrate low critical thinking abilities, with the evaluation indicator emerging as the most challenging aspect. The second part adopts a qualitative lens to explore the beliefs and critical thinking practices of 74 eighth and ninth-grade learners about their own mathematics learning process, uncovering significant inconsistencies in their beliefs and the hidden potential that often goes unnoticed in traditional classroom settings. The third part shifts toward instructional innovation by presenting the development of the PjBL-GeoGAI learning model, which integrates Artificial Intelligence, GeoGebra, and Project-Based Learning to enhance calculus education at the tertiary level. The quantitative study in Part I offers empirical evidence from 60 pre-service mathematics teachers at UIN Syekh Ali Hasan Ahmad Addary Padangsidimpuan, revealing that the majority of students (58.3%) exhibit low critical thinking abilities, with evaluation being the most challenging indicator (mean score 38.5 out of 100). Only 16.7% of students demonstrated high critical thinking skills, and analysis of variance revealed significant differences in performance across critical thinking indicators (F = 12.34, p < 0> Part II builds upon this foundation by delving into the voices of 74 eighth and ninth-grade learners across two schools in Indonesia, demonstrating that although students possess hidden potential for critical reflection, they are unaccustomed to examining and correcting their beliefs about mathematics—a practice that is essential.