Three-Dimensional Thinking

Behind, beside, in front, to the left, to the right are all important in the development our understanding of objects in three dimensions.

 

However, we live in a three-dimensional universe, but act as if the physical world is as flat as a worksheet or the page of a book.

 

Typically, we call our attention to numbers and letters, but we neglect to remark upon the spatial properties of the objects around us: how tall or short they are, how round or pointy, how close or far.

 

 Teaching how to think in 3D space is a great way to engage and see what and how math acts in the real world.  Though, a natural extension of drawing in two dimensions is drawing in three dimensions. In this direction, we have been using 3D printing as an aid to visualizing mathematical objects.

 

We design sculptures that help to understand the mathematics better. Also, these sculptures are attractive in their own right. Similarly, spatial thinking skills, and those skills, in turn, support achievement in subjects like science and math, such as playing with blocks and puzzles.

 

 We would do well to begin describing the world in 3D, helping to develop the habit of seeing the world in all its dimensions.

 

When thinking of 3-D, our initial thoughts ranged around planes and intersecting lines, three dimensional coordinate geometry and all sorts of 'hard and scary' maths.

 

We realized that the starting point is the language that we use to describe positional relationships of objects in space.

 

Behind, beside, in front, to the left, to the right are all important in the development of understanding of objects in three dimensions, and make the leap from 'seen' to 'imagined'.