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  • Three students working on a project together.

    Visualize Calculus. It’s a Revolution.

    By Eric Schulz

    Many virtual resources exist in MyLab and elsewhere to help students see concepts of calculus. For example, we have embedded almost 800 interactive figures in our Calculus eTextbook (Briggs, Cochran, Gillett, and Schulz) in MyLab. The figures available in our interactive eTextbook have been used successfully by tens of thousands of teachers and students to master calculus concepts, such as finding the volume for a solid of revolution. However, an interactive figure on a device screen is not helpful for every calculus student and is likely useless for a visually impaired calculus student.

    The challenge of helping every student learn mathematics has weighed on me throughout my teaching career; that is one reason I have been passionate, obsessed perhaps, about creating interactive visualizations. However, I have had students for whom the interaction of a figure on screen has not been sufficient for them to understand the concept being visualized in the figure. For these students, a physical 3D object to feel and manipulate would have been helpful. Furthermore, 3D objects have great potential to help us teach calculus to students with significant visual impairments.

    I have embarked on a new project this year to create a large number, say 100 or so, of 3D printable objects for calculus, beginning with solids of revolution and continuing through multivariable and vector calculus. For example, the following image is a 3D solid used for approximating the volume of the solid of revolution created by revolving the area in Quadrant I beneath the curve around the -axis using cylindrical shells, with .

    For each 3D object, an image of the solid, an STL file, and the Mathematica source code used to create the STL file will be accessible from within any course in MyLab using our current calculus materials. The 3D objects can be sliced and printed on your own 3D printer or easily sent to an online 3D printing service.

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