While students ought to learn BOTH the manual techniques AND the calculator techniques for algebraic concepts, this How-to-Guide will really step up the latter type of performance for your student(s). Fourteen (14) actual NYS Math Regents examples
Often Integration by Parts is demonstrated purely algebraically. Here's a resource that underscores how differentials work while simultaneously proving integration by parts within every localized (monotonic) subset of a function.
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2004 Glencoe Publications, Content Fluency Consultant, Grade 6-11 national series of textbooks
Contributing Author, New York State Mathematics League
Contributing Author, American Regions Mathematics League
Contributing Author, Mathematical Olympiads for Elementary and Middle Schools
Contributing Author, Australian Problem Solving Mathematical Olympiads
18+ years teaching (includes Math 7, Math 8, Algebra, Geometry, Algebra 2, Pre-Calculus, Calculus, Introduction to Contemporary Mathematics, Introduction to Finite Mathematics, Web Page Design, Computer Programming (multi-lingual), Introduction to Video Production, Cisco IT Essentials, ...)
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Learning endures best when ideas resonant with a mindset. As such, new topics should be presented as economically as possible within those mindsets.