My typical structure for a lesson involves an introductory lecture regarding a new topic occasionally followed by a review of some relevant material covered in previous lessons. Throughout the lecture portion I periodically check to see if the students have questions and make sure that they are grasping the new concepts as we get deeper into them. I then will have some problems that I have made and I will do the first 1-2 problems with the class, walking them through and taking their input as to what should be done. After the first few problems, I will leave them with some additional problems to attempt by themselves and will be there to assist them with any questions, but encourage them to try to solve it by themselves first. Typically, I end a lesson with some "challenge" problems that take the material from that lesson and require slightly deeper thinking and abstraction in order to solve, usually incorporating some previous material.
I am a junior mathematics and computer science student at RPI. I have previous experience as a tutor and teacher for high school calculus for a small group of about 5 students. Those students all went on to perform very successfully on the AP calculus exam and have been consistently at the top of their respective math classes. I would host weekly lectures for the students as well as create my own problem sets for them to do after introducing the new material.
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