Fostering students' analytical thinking and applied mathematical skills through 3D design and printing

The new standards for school mathematics and science education refer to analytical thinking (AT) as the target skill necessary to logically and systematically solve complex problems by their decomposition. The standards also point to the applied mathematical skills (AMS) needed to understand ill-defined problems, collect and quantify relevant data, and construct and inquire mathematical models. This study explores the integration of learning activities in digital design and 3D printing as a strategy to foster analytical thinking and applied mathematical skills among middle school students and prospective teachers. The study involved 32 seventh grade students and five prospective teachers of technology. Both groups learned a 10-hour workshop, "Make a spinning-top." The participants designed spinning-tops that can fit into a Kinder Surprise egg and analyzed their geometric and mechanical properties. We evaluated students' worksheets, designed artifacts, and discussions. The results indicated that the assignment prompted the participants to apply AT and AMS. School students designed complex 3D models and analyzed their properties, using geometry concepts and theorems, and verified their designs through 3D printing. The worksheet was an effective tool to frame and guide the school students to think about specific problems in the design task and create and test mathematical models. For the prospective teachers, the workshop accompanied by lectures on the methodology of experiential learning was the way to acquire pedagogical content knowledge in the subject.