\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016a.00823}
\itemau{Gethner, Robert}
\itemti{Definite integration and the ``need to know" principle.}
\itemso{Math. Teach. (Reston) 108, No. 4, 313-318 (2014).}
\itemab
From the text: Ever since I learned, in my first calculus course, how to evaluate definite integrals using trigonometric substitution, I have been puzzled by the standard method of computing the limits of the transformed integral. Recently, I have come to terms with the problem and have begun to clarify a pedagogical dilemma that has presented itself several times in my calculus classroom. An important issue that teachers face with some regularity throughout the curriculum is this dilemma: How do we introduce to students new ideas that they need but are not yet ready to fully comprehend? I have formulated what I call the ``need to know" principle, which I use to think about the challenge of presenting difficult ideas.
\itemrv{~}
\itemcc{I50 E40}
\itemut{concept formation; introduction of mathematical concepts; understanding; approach; real numbers; addition; circular reasoning; missing explanation; definite integrals; trigonometric substitution; reverse substitution; tangent substitution; secant substitution; graph of a function; area; derivatives}
\itemli{http://www.nctm.org/Publications/mathematics-teacher/2014/Vol108/Issue4/Definite-Integration-and-the-%E2%80%9CNeed-to-Know%E2%80%9D-Principle/}
\end