This book focuses on the analysis and application of cognitive simulation in problem solving. It constructs a cognitive model of mathematical problem solving, and based on this model, analyses typical mathematical problems, programs using Lisp language, and subsequently simulates the problem-solving process in Adaptive Control of Thought Rational (ACT-R). This book introduces the method and process of one-on-one cognitive diagnosis, and designs and implements experiments following the method and process. It serves as a stepping stone for both researchers and practitioners who are interested in using cognitive simulation for students learning.