We report a comparative study using "knowledge space theory" (KAT) to assess the impact of a hands-on laboratory exercise that used molecular model kits to emphasize the connections between a plane of symmetry, Charity, and isomerism in an introductory organic chemistry course. The experimental design compared three groups of students--two that carried out the laboratory exercise (treatment groups) and one that did not (control group). Our assessments revealed that all three groups made significant improvements in their understanding of Charity and isomerism, but that the two treatment groups showed more improvements than the control group. The KAT analysis showed that the acquisition of the skills for finding a plane of symmetry in a molecule came late in the students' critical learning pathways, which indicated that this was difficult for many students. Students were unfamiliar with this type of reasoning, and our studies revealed that the laboratory exercise was useful in teaching the method to introductory organic chemistry students. (Contains 3 notes, 1 table, and 3 figures.)