An atomistic approach refers to a method concerned with the separated, individual parts of a subject, rather than approaching the subject as a whole. The word atomistic is an adjective defined as having to do with separate parts that can also be disparate from each other.
This approach is essentially the opposite from a holistic approach, where the subject is taken as a whole instead of through the individual parts that make it up. This approach is less concerned with the separated aspects of something and more inclined to look at a subject, goal, topic and so on as something to be conceived in its most all-encompassing view.
An example of atomistic and holistic approaches can be shown by how an English teacher explains a sentence of language to his students. In a holistic approach, the teacher would be concerned with making sure the students understand the meaning of the sentence taken as a whole. He would want to communicate the message that the language is getting across, paying less attention to the particulars of the thought, with more emphasis on the complete meaning. By contrast, in an atomistic approach the teacher could analyze the sentence through its various syntactical methods, its grammatical features, its irony and other individualized dimensions. The teacher would be more inclined to break the sentence into pieces, showing the class the meaning of each individual word in the sentence, rather than how the words work together to form a complete thought.