There is a great piece in The Atlantic on the positive effects of focusing students on the basics of analytic writing. Things like basic sentence construction, using coordinating conjunctions, organizing paragraphs and connecting thoughts in a logically constructed narrative. The article reports how New Dorp, a high school in Staten Island, New York, greatly improved its students overall performance by focusing on the improvement of their writing skills. In every subject except Math teachers focused on writing skills and saw improvements in overall performance across the spectrum.
This is not surprising. Learning to write well naturally improves thinking. Writing is about organizing thoughts and meanings and then arraigning them in the flow of written words. Language and logic have a natural connection. Building a coherent narrative forces you to clarify your thinking and pay close attention to words and their meaning.