Mathematicians’ perspectives on their pedagogical practice with respect to proof

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Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey. (2016, methodology): “A in his interview and in our other interviews with mathematicians (Weber, 2004, 2012).”
How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition (2014, background): “Also, calculus teachers require students to use the Fundamental Theorem of Calculus—an indispensible tool for computing integrals—even though they acknowledge that students are unable to understand why this theorem is true11 (Weber, 2012).”