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A University Math teacher in Russia wrote a dissertation on this. The result of her research is a series of text books for Linear Algebra and Calculus. One of techniques that she used is to make reader choose to either underline or cross strike`?not?`s in proofs...
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Another one is that when proofs refer to other theorems and lemmas, they list multiple options and you are supposed to choose which one is actually used here. There were many others.
She was one of the best teachers I've met: Petrova Vera Timofeevna
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Her books are only available in Russian: books.google.com/books/about/%D
She wrote a dissertation on pedagogy about her approach of "intensification of learning mathematical subjects": dissercat.com/content/nauchn
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Another example of an interactive course is "Aufgaben und Lehrsätze aus der Analysis"("Problems and theorems in analysis“) by George Pólya and Gábor Szegő from 1925. This book that almost replaces lectures with sequence of exercises where reader gradually is given harder tasks.
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Thank you so much for these references! I’ve spent some time with Polya’s work, but Timofeevna’s is new to me. I’m going to ask a Russian friend to help me dig in.


