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This week we feature a guest post by Dr. David Thornburg, Director of Education, Polar 3d, LLC on the benefits of three dimensional thinking in the K12 space.

The benefits of three dimensional thinking

While we live in a multidimensional world, many of the tools of education are restricted to showing objects in two-dimensional representations, either as pictures on paper, or as displays on a screen.  This can lead to inadvertent but serious misperceptions.  For example, while the orbits of planets in our solar system are nearly circular, they are often shown from an angle that makes them appear elliptical.

solar system

This leads many students to conclude that the seasons are caused by the proximity of the Earth to the Sun — a conclusion they would not have drawn if they knew from the start that the Earth’s orbit is nearly circular.

While having a good collection of accurate physical models in the classroom is a step in the right direction, I think it is more powerful for students to design and make their own 3D objects to not only replicate real

world items, but to develop their capacity to think in three dimensions.   Traditionally, for example, students are taught courses in Euclidian Plane Geometry, and then advance to multidimensional geometry in which they can explore Platonic solids, etc.   Rather than wait until high school, I think 3d thinking should be explored from the very start.


Let me give a trivial example: Ask a student to make a triangle with three toothpicks.   This is simple.  Next give the child three more toothpicks and have her make an object with four equilateral triangular faces.   As long as the child stays on the plane, frustration sets in.  But as soon as you move to the third dimension, you get a tetrahedron, and the problem is solved!

Fortunately, there are great solutions to the challenge of developing three-dimensional thinking — and the most powerful one is the 3D printer.   These inexpensive machines allow students to design and build plastic objects with a volume of about 10 cm on a side or more.  These objects may be simple or complex, and they (unlike Lego blocks) are so cheap students can keep their finished projects forever.

Student designs can be made with a variety of free or inexpensive design tools, ranging from Transform Doodle 3D ( that lets a kid scan a pencil drawing and turn it into a 3D  model, to Tinkercad, BlocksCAD, and the Maker’s Empire application.   These last three are on the Online Design tab on the Polar Cloud site ( Each has unique appeal and application across the grade levels.

Of course, content without context is meaningless.  This is where the curriculum comes in.  Three-dimensional thinking is important not only in the STEAM fields (science, technology, engineering, arts, and mathematics) but in history, and numerous other subjects.   The Makers Empire and STEAMtrax curriculum (available through the Polar Cloud) is not only aligned to the NGSS and Common Core standards, but incorporates three-dimensional thinking throughout.

The Power of the Polar Cloud

I’ve already mentioned the free Polar Cloud in this document.   It has tremendous power for teachers and students alike and I want to spend a few minutes explaining why its unique features are so valuable.


The Polar Cloud is your one-stop shop for making things – including 3D printed artifacts.  Because it is browser based, it  runs on just about anything, including Chromebooks, iPhones, tablets of all flavors and, of

course, traditional computers.  It builds seamless connections between tools.  For example, a 3D design can be sent directly from a design tool to the printer build plate with a single click, as long as your printers are on the Polar Cloud.  For example, this simple name tag was built using BlocksCAD and the file can be sent directly to the build plate of any printer in my account with a single mouse click.

When I click on the Polar Cloud button, this model instantly gets sent to the build plate of my default printer!

And, as they say on the TV ads, “But Wait, There’s More!”

As a teacher you can set up groups for your classes, where students have access to printers, design tools, curriculum subscriptions, a message board, and collections of objects to be printed.  If you use Google Classroom, your students can be added to your group with great ease.


Three-dimensional thinking that was hard to develop in the traditional textbook-driven classroom is now made far easier with the rapid rise of 3D printing.  The 3D printing ecosystem ranging from curriculum to object design, and the printers themselves, is all supported by the free Polar Cloud which not only integrates these disparate elements, but allows access from virtually any browser-based device.

About the Author

David Thornburg is the Director of Education for Polar3D, a leader in cloud-based environments for educational “making” technologies, including 3D printing. He has been active in educational technology for decades and presents at conferences worldwide. David is an award-winning futurist, author and consultant whose clients range across the public and private sector across the planet. His razor-sharp focus on the fast-paced world of modern computing and communication media, project-based learning, 21st century skills, and open source software has placed him in constant demand as a keynote speaker and workshop leader for schools, foundations, and governments.

Dr. Thornburg has shared his expertise with Standard For Success schools on a regular basis at annual conferences and it an advocate for teacher and student engagement in the learning process.


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