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Using technology and IBL to return the ‘Fundamental’ to the Fundamental Theorem of Calculus Gregory L. Macklem History of Science Society

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The FTC Fundamental, but typical teaching approaches undercut its importance Introduction and ordering of topics telegraphs the FTC Use of inquiry in combination with technology can drive home the significance of the FTC without sacrificing deeper understanding Course populations

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Reordering Topics

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Laying Groundwork Begin integral calculus with area under curve; do not make any links to derivative calculus or antiderivatives Use curves and rulers to come up with method of estimating area and discuss Develop Riemann sums Introduce summation formulas Develop definition of definite integral, explore properties

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Technology and the FTC Used graphing calculator, but software like Excel could also be used Explore definite integrals to try to find patterns; looking for an easier way than “grind and find” Can vary the amount of guidance based on the course Easy to know when students have found it Still need to prove it, still possible to look at other ways of thinking about how the FTC “makes sense”

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4.3 Finding Area Under A Curve Using Area Formulas Objective: Understand Riemann sums, evaluate a definite integral using limits and evaluate using properties.

4.3 Finding Area Under A Curve Using Area Formulas Objective: Understand Riemann sums, evaluate a definite integral using limits and evaluate using properties.

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