The distinction between a narrative review and a problem identification review is defined in Machi & McEvoy's The Literature Review: Six Steps to Success (p. 3-5). Be aware that this distinction has been referred to as "basic vs. advanced" and "simple vs. complex" literature reviews in previous editions of this book.
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Narrative literature reviews fall into the category of papers that document, analyze, and draw conclusions about what is known on a topic. In the introduction, the author(s) will introduce an argument in the form of a thesis statement before analyzing the literature to draw a conclusion. To check to see if you're looking at a narrative literature review, read the introduction and conclusion of the article. If the author(s) discuss the literature only as it relates to their thesis statement, you're looking at a narrative literature review.
Problem Identification literature reviews include many of the features of narrative literature reviews, but they go beyond simply analyzing articles and tying them to a thesis statement. They often end by posing new questions that might be looked into through a new research study. To check to see whether you're looking at a problem identification literature review, skip to the conclusion. If the author(s) end the paper by asking questions and proposing a new study that might be conducted to answer these questions, you're looking at a problem identification literature review.
Literature reviews are examples of scholarly sources, so library databases are great places to start your search.
Literature reviews often state in the title or abstract if the article is a literature review, and databases also often use the term "Literature Reviews" as a Subject to help classify and organize articles with similar topics. Since databases look for exact word matches in articles, you can use that to your advantage to find what you need.
The main difference between a Narrative and Problem Identification lit review is whether the authors simply summarize how a topic has been covered in relation to their thesis or if they take an additional step and propose questions for future study. Once you find a lit review, skip to the article's conclusion section (generally directly above the reference list). For Problem Identification lit reviews, look for additional questions or future research opportunities, such as the example in the screenshot below: