A high-school teacher in the US whom I know, is teaching AP AB Calculus for the first time. He would like to use a constructivist approach:

students explore mathematical problems and ideas and then, through whole-class discussions, students present their thinking and we as a class generalize the ideas and codify their findings.

He is seeking materials in line with this approach, to address the following topics:

  • Limits and their properties
  • Differentiation
  • Applications of Differentiation
  • Integration
  • Logarithmic, Exponential, and other Transcendental Functions
  • Applications of Integration

I can make a suggestion for the functions item,* but not so much the other topics.

* "From Pop-Up Cards to Coffee-Cup Caustics: The Knight's Visor." (arXiv abs.)

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    $\begingroup$ (1) I suggest he teach it the normal way first. Why do something in a non-standard fashion when you don't have knowledge of the standard? This is hubris. (2) Whole class discussion is inefficient with large groups (normal class size) because few people are actively in the discussion. (3) You are going to lose the benefits of drill. $\endgroup$ – guest May 19 '18 at 3:53
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    $\begingroup$ IMHO it would be a disservice to students to spend more than a single class on such an eccentric approach. It is not even widely taught in universities. $\endgroup$ – Dan Christensen May 19 '18 at 18:18
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    $\begingroup$ As one example, the prolific cognitive scientist Daniel Willingham argues against this approach. I would recommend his book for K-12 teachers, "Why Don't Students Like School?". Ch. 6 has the following evidence-based thesis: "Cognition early in training is fundamentally different from cognition late in training." Implications for the classroom: "Students Are Ready to Comprehend but Not to Create Knowledge", "Don't Expect Novices to Learn by Doing What Experts Do", etc. $\endgroup$ – Daniel R. Collins May 19 '18 at 19:10
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    $\begingroup$ Yikes! Why is constructivism getting so much hate here? You might disagree with the methods, but this is an established teaching philosophy. $\endgroup$ – Steven Gubkin May 20 '18 at 16:47
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    $\begingroup$ The University of Michigan has been using a constructivist IBL ("inquiry-based learning") approach for its introductory calculus courses for nearly 20 years now with great success. I think the skepticism expressed in the comments above is not well-founded. Having said that, teaching in a constructivist manner requires exceptionally deep and flexible knowledge of the subject matter, and if this is the teacher's first time teaching Calculus then I am skeptical of how successful this will be. $\endgroup$ – mweiss May 23 '18 at 21:28

I'd suggest that he check out the POGIL approach to teaching. They have a Calculus book that he might find useful.

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    $\begingroup$ POGIL = Process Oriented Guided Inquiry Learning. $\endgroup$ – Joseph O'Rourke May 19 '18 at 1:07

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