Within the historical context of the development of chemistry, Avogadro's hypothesis represents a fundamental concept: It allowed Avogadro to explain Gay-Lussac's law of combining volumes and it allowed Cannizzaro to establish a more accurate set of atomic mass values. If students are going to understand the concept of relative atomic masses and how they are determined, then the road to that understanding should pass through Avogadro's hypothesis. Unfortunately, this concept is counter-intuitive, which is perhaps part of the reason it was almost a half century before it gained some level of acceptance among chemists. For students, this concept is as difficult to understand today as it was for the chemists of the 19th century. This article uses a model from educational psychology--Chi's theory of ontological misclassification--to explain the source of that difficulty. More importantly than offering this explanation, though, the article discusses how Chi's theory can be used to teach this concept in a manner that has proven quite successful in the author's classroom. (Contains 12 notes.)