The Socratic method of teaching is based on the story about the famous philosopher Socrates. Rather than simply instructing his students on facts, ideas and texts that they should memorize, he engaged them in an interactive discussion. He taught by introducing new ideas, soliciting feedback and gradually exposing his students to new concepts. Today, many educators use this method to teach a wide range of subjects, including mathematics.
The Socratic technique of teaching is generally about expanding the student's mind through questions and discussion rather than "telling." It is one of the oldest and most powerful tools teachers can use to foster critical thinking in their students. Teachers continually prod and probe the minds of their students to allow the student to consider a concept from every different angle. After considering all of the different incorrect ideas, the student is left with the reasoning and base understanding of the idea being presented.
Math may be considered a particularly difficult subject to teach using the Socratic method because students must memorize formulas and learn concrete skills. However, most math can be framed in a very practical way that lends itself to the Socratic method. Teachers can approach the subject by questioning how a specific problem might be solved. For example, they can create a real-life algebra problem with an X value. Students would have to think critically before coming to the appropriate method for solving the problem.
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One educator taught his students binary arithmetic using the Socratic method. None of the students had any exposure to the subject in the past. Instead of telling the students the concept, he only asked questions. He began by asking them about the ways that ten can be written and questioned why we count from one to ten before starting over with eleven. Finally, he asked them to imagine the binary system of zeros and ones.
It may not be practical or appropriate to teach every concept using the Socratic method. In fact, book learning and memorization of some concepts is still important for learning math. Therefore, a teacher should be careful about what she wants to expose to students using the Socratic method and what she wants to teach using more traditional methods.