Search systems are often used to support learning-oriented goals. This trend has given rise to the "search-as-learning" movement, which proposes that search systems should be designed to support learning. To this end, an important research question is: How does a searcher's \emph{type} of learning objective influence their trajectory (or \emph{pathway}) towards that objective? We report on a lab study ($N=36$) in which participants gathered information to meet a specific type of learning objective. To characterize learning objectives \emph{and pathways}, we leveraged Anderson and Krathwohl's (A\&K's) taxonomy \cite{anderson2001taxonomy}. Participants completed learning-oriented search tasks that varied along three cognitive processes (apply, evaluate, create) and three knowledge types (factual, conceptual, procedural knowledge). A \emph{pathway} is defined as a sequence of \emph{learning instances} (e.g., subgoals) that were also each classified into cells from A\&K's taxonomy. Our study used a think-aloud protocol, and pathways were generated through a qualitative analysis of participants' think-aloud comments and recorded screen activities. We investigate three research questions. First, in RQ1, we study the impact of the learning objective on pathway characteristics (e.g., pathway length). Second, in RQ2, we study the impact of the learning objective on the types of A\&K cells traversed along the pathway. Third, in RQ3, we study common and uncommon \emph{transitions} between A\&K cells along pathways conditioned on the knowledge type of the objective. We discuss implications of our results for designing search systems to support learning.