When faced with a mathematical problem, do children think about the problem conceptually, or do they instead work through a procedure to generate the “right answer”? This talk will focus on research I have done in my lab to answer this question, at least in regard to fractions. Although there has been some debate about whether conceptual knowledge precedes procedural knowledge (or vice-versa) in regard to fraction understanding, I will review research by myself and my colleagues that suggest conceptual and procedural knowledge are used differently by different groups of young people.  In other words, instead of arguing that one type of knowledge is somehow paramount to the other, I will argue that there are some children who rely more on conceptual knowledge, some who rely more on procedural knowledge, and some who rely equally on both. This trend will be demonstrated through data from several studies employing cluster analyses to detect if we can identify different learning profiles in regard to these two types of knowledge. Overall, these studies highlight how different students might take different approaches to solving fraction problems. Furthermore, I mean to present further data to support the contention that both conceptual and procedural knowledge are, practically, equally important to the learning of fractions. I will end with a description of future directions of this research, as well as possible implications for how math should be taught.