When switching disciplines, one of the hardest tasks is gaining the background knowledge necessary to be successful. This is especially the case if you're no longer a student or have no access to the classes that you need. Fortunately, there are many ways to counter that and learn what you need. One method that is often overlooked is teaching, both formally in a classroom or informally through outreach or just talking with family and friends.
In order to successfully teach, you must have a solid understanding of the topic yourself. Having a thorough understanding of a topic means that you have multiple ways to think about or explain it. When faced with a question from your student, an inability to answer the question, or to answer it satisfactorily, can be a good indication that you need to improve your understanding. This is perhaps the most obvious way to learn from teaching, but there are more subtle ways as well.
A great method for anyone, teacher or student, to learn is metacognition - essentially, thinking about thinking. Metacognition is commonly used by teachers to help determine why a student is struggling or having difficulty with a concept or assignment. We ask questions such as "how did you come to this conclusion?" or "why did you choose that method?" to gather information about how the student is thinking. This method, however, is often overlooked when it's the teacher who wants to learn from the students. Asking these questions to the best, most successful students can provide the teacher with new ideas and new ways of thinking about the topic, thereby increasing the teacher's own understanding.
To get started with metacognition, you first need to learn the correct types of questions to ask. While some questions are useful for drawing out thinking patterns, other questions only probe knowledge of facts. So-called Socratic questions are very good at pulling out the types of information desired by metacognition. Before using them for teaching, you might try using them on yourself. How do you think?
References:
Promoting Student Metacognition by Kimberly D. Tanner
Socratic Questioning by David Straker
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