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For a Calculus I class, I usually: Don't teach limits first. Limits, as they are currently taught, lead to confusion. You don't do anything with them except prove the derivative. After that they are largely forgotten, basically leaving students feeling they wasted their time, and they are quickly forgotten. Instead, teach limits at the end to justify ...


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I'm not in education, so take my answer with a grain of salt. I am merely approaching this from a perspective of someone who is really frustrated with how mathematics is taught. Mathematics is a tool we use to understand the universe. If you want to make math more engaging, it would be useful to actually show how one could use math to solve problems. For ...


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It's about the learning experience. An issue with project based learning is the need for objective grading isn't going away. Since the first semester of mathematics is what serves to filter out under performing students there is a desire to have an unmovable bar. Without it you get grade inflation. This isn't to say there can't be projects. You just have ...


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I'm an engineer who really likes and uses mathematics on work and daily life. Myself, I would try to make the course as much self-contained in classes, but still stick to some written material the students have access to. This allows the subject to be more complex and extensive while keeping down the difficulty settings. I'd prove theorems as much as ...


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Select and use an open textbook. Students who wish to use a physical textbook will be able to get a copy run off and hole-punched at a local print shop, then put in a binder, for far less than the cost of a conventional textbook. You will save your students a pile of money and there are enough available options that you should be able to find something ...


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Without directly answering your question, you don't seem to have the background you need to be "improving" the undergraduate experience yet, and have some work to do. I think you're right in sensing that your question is too general Don't talk about the "difficulties in forming such a course", and spend your initial time finding out what aspects of the ...


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Given 100% control, I would have one-to-one instruction. One instructor meeting individually with each student. That instructor can change the approach, the speed, the order of topics, the method of instruction, based on that individual student. But of course hiring (and training) enough instructors for that is probably way beyond any reasonable budget. (...


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