Although it is commonly assumed that increases in mathematical knowledge and problem-solving skill alter one's understanding of mathematical problems, little research exists to support this assumption. The present study investigated the relationship between mathematical background and problem perception in two experiments. Experiment 1 employed hierarchical clustering analysis to compare the way that experts (nine mathematics professors) sorted 32 mathematics problems typical of college mathematics courses with the way that novices (19 undergraduates) sorted the same problems. The experimenters assigned an a priori mathematical "surface structure" and a mathematical "deep structure" characterizations to each problem. "Surface structure" refers to the items described in the problems themselves. "Deep structure" refers to the mathematical principles necessary for solution. Results indicated that the two groups use different criteria for considering problems to be related. Experiment 2 compared changes in mathematics problem perception of students who took a computer course during the same time period. Training in problem solving resulted in the experimental group's problem perception being more differentiated and more like that of experts. Appendices contain the 32 problems used in the experiments and the mathematics pretest. (Author/RL)