# Calculus via a constructivist approach

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.)

• (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. May 19, 2018 at 3:53
• @guest: This teacher has experience using a constructivist approach in geometry and algebra (grades 8-11). May 19, 2018 at 11:39
• 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. May 19, 2018 at 19:10
• Yikes! Why is constructivism getting so much hate here? You might disagree with the methods, but this is an established teaching philosophy. May 20, 2018 at 16:47
• I saw this pop up because someone did an edit, but looking at the comments, I wonder if people were getting confused between 1. constructivism in math which denies the law of the excluded middle and leads to non-standard analysis and specialized calculus texts with infintesimals and 2. constructivism in education which involves constructing meaning and understanding.