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Using 3D printed manipulatives to promote active learning

3D printed objects

Ryan Hansen, an instructor in the Department of Mathematics, is combining 3D printed manipulatives with custom crafted active learning activities to excite, explain and interest students in the mathematics that they are learning (and also in 3D printing).  

The manipulatives, designed by Hansen and others, are used in introductory through upper-level courses. 

“Computer software definitely allows for the demonstration of such objects; however, they are still represented in a 2-dimensional manner to the user.  With a properly crafted 3D printed object, it is as accurate as possible and the user interface is as intuitive as it gets,” Hansen said. 

Previously, such objects had to be created with painstaking effort or were extremely expensive. However, in the last several years, both 3D printing technology and software that can generate mathematically accurate 3D models has rapidly become more accessible. This truly lets you “get a handle” on mathematics.

Such methods even help in clearly visualizing advanced mathematical objects in higher dimensions. The famous German mathematician Felix Klein (1849–1925) even used such concrete haptic examples of mathematical objects in his teaching.  

“The purpose of the model was not to compensate for the weakness of the view, but to develop a vivid and clear perception,” Klein once said.