Artificial Intelligence versus Conventional Mathematics Teaching: An Empirical Assessment of Learning Outcomes, Cognitive Engagement, and Mathematical Reasoning

lessons are taught. This has led to important questions about how well these tools can improve math learning, cognitive engagement, and higher-order thinking skills. This paper describes a long-term experimental framework that we will use to compare how well (1) traditional math instruction, (2) unrestricted AI-assisted learning, and (3) pedagogically scaffolded AI tutoring work. The sample was made up of 720 high school students from nine schools, evenly split between the three teaching groups. A 10-week instructional intervention is what the study is based on. Assessments at the start, after the intervention, and later on are used to judge mathematical achievement, cognitive engagement, mathematical reasoning, knowledge retention, and learning transfer. The example sample shows that all three groups got better at math. The mean post-test scores for standard teaching, unrestricted AI help, and scaffolded AI coaching were 61.51, 73.16, and 77.94, respectively. When it comes to math reasoning (72.98), cognitive engagement (3.65/5), and learning transfer performance (75.93), scaffolded AI teaching also gets the highest scores. Also, delayed assessment patterns show that AI training with scaffolding improves retention even more. The suggested analysis plan includes multilevel regression, longitudinal mixed effects modeling, effect size estimates, and mediation analysis to look into differences in instruction while taking into account students' starting levels of skill and variation across the classroom. These trends show that organized educational scaffolding may be better than having free access to AI answers because it helps students understand concepts, use their brains actively, and do math on their own. The study gives us a scientific way to judge AI-assisted math education and stresses how important it is for educational design to combine technology with students' ability to learn on their own.