Many mathematics teachers struggle to support their students' developing understanding of proof as an essential element in investigations of mathematics. The area of mathematics where the development of an understanding of proof is most challenging is algebra. In the case of algebraic proof, analysis of student written work on tasks that demand generalization and explanation may yield insights into student use and understanding of justification and proof in algebra. These insights, in turn, may enable mathematics educators to develop instruction that supports and challenges student reasoning. In this article, the authors explore student work in an effort to analyze how students respond to a task that requests an explanation of why a numerical pattern is always true. To explore student approaches to algebraic proof and their use of explanations of various types, the authors analyzed twelfth-graders' written work on a 1996 National Assessment of Educational Progress (NAEP) mathematics assessment item (NCES 1996). The authors focus on student constructions of explanations, ranging from students' use of examples to their more formal algebraic proofs. In considering student reasoning, the authors share student work, discuss the nature of explanations provided, and draw inferences about the implications of student approaches to proof. From the analysis, the authors conclude that students need a better understanding of "what" mathematical proofs are and "how" they can construct them. (Contains 10 figures.)