A reflective or reflection essay asks the writer to look back on a certain event or situation--very often to look back on a class experience or on a semester experience--and compare or contrast then vs. now.
The essay content might involve reflecting upon what was learned, what was not learned, what the writer accomplished or what the writer would have done differently.
Student writers might also be asked to reflect on a piece of literature and relate it to their own experiences or emotions.
One way to consider this type of essay is that it starts by looking in the rearview mirror, and it is very much centered around personal growth and development.
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A narrative essay tells a story--it can be the writer's personal story OR it can be a story the writer tells about someone or something else.
One of the concerns of a narrative essay is time or the sequence of events.
Because the narrative is an essay (and not a short story or novel), it is important for the writer to drill down on just the right particular details that are important to the theme, and then organize the essay in a coherent pattern of progression.
The selected topic should also have an element of crisis, conflict, and potential resolution to bring the events to a close.
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A reflective essay is personal and concerned with growth and development of either the writer or ideas the writer has encountered.
A narrative essay does not always involve the writer directly but can be a story about someone or something else.
Be sure to understand the differences between a reflective and narrative essay and to follow guidelines for each respectively. Learn more about the differences between these writing modes here.