## 3D-Print: Touching Physics and Math

This project is motivated by the need to take away the perception that mathematics and physics are totally unrelated to reality. The intention is to bring science concepts closer to the students through the visualization of objects printed in 3D.

3D printing can contribute to the visualization of concepts for which there is no direct physical counterpart. For example, it is possible to print physical models of graphs (or more generally, information sets) with color codes for better understanding. Three-dimensional models of a mathematical phenomenon has an advantage over computational or pictorial models: it eliminates the possible confusions involved in representing something essentially three-dimensional with a smaller dimension. Touching Physics and Math picks up several of the concerns about the teaching-learning process of physics and mathematics, using mathematical visualization, problem-based learning, and challenges to put mathematics and physics in context. In this way meaningful learning is finally achieved!

3D printers are used to print models that allow students to see and to touch what is on their mind. Moreover, 3D printers bring to life what it is hidden in an equation or in an inequality ! 3D objects, for which flat representations are used, are now printed and used for pointing out complex concepts for further understanding. 3D printers are also useful to print scale models of real surfaces in order to find out the area or the volume. Solar stoves, perfume containers, hovercrafts have been some of the assigned projects that the students have worked out with 3D printers.

A significant increase in math visualization skills has been achieved:

• After seeing and touching printed objects, students are able to better imagine, to fully describe and to properly draw these objects.

• Students are able to move from a verbal language to a mathematical language in a faster and more appropriate way.

• Students are able to correctly perform mental mathematical operations with objects. For example, now the projections on different planes, the interception and the union are finally understood thanks to 3D printing.

Before

After

With the use of 3D prints students are more motivated, have fun in the class and work collaboratively in a more efficient way.

When I use 3D printers in math, I feel...

The tool was very useful to understand...

I recommend this tool to be used in Math III courses...

Strongly disagree

Strongly agree

## Créditos/Credits

This is a NOVUS 2016 funded project.

Participantes/ Project Participants:

Dra. Linda Medina: Multivariate Calculus

Dra. María Alicia Aviñó: Math for Design

Mtra. Marlén Aguilar: Multivariate Calculus

Mtra. Araceli Reyes: Integral Calculus

Dr. Jaime Castro: Multivariate Calculus

Dr. Gerardo Aguilar: Integral Calculus

Dr. Saúl Juárez: Multivariate Calculus

Dr. Martín Pérez: Multivariate Calculus:

Dr. Luis Neri: Physics I

Dr. José Luis Escamilla: Physics II

Dr. Andrés González Nucamendi: Integral Calculus

Mat. Alejandro Flores Benitez