What's the Big Idea? Dimensional Thinking and Modeling

The chapter on dimensional thinking talked about many ways to think about dimension that I had not thought about before.  One example is the way that shadows behave under different conditions.  A single object can have an infinite number of differently shaped shadows depending on its position, the position and type of light, and the material from which it is made.  I was thinking back to the first zoom in from this course for which we zoomed in on an object and asked others to figure out what it was.  Perhaps students could capture several shadows of an object with the same goal in mind.  Similarly, what would different objects look like when sliced into layers.  Two different layers of the same food or toy may look like completely different objects. 

I sometimes forget in the routine of the day to stop and look at the concepts I am teaching from other angles.  Sometimes, especially in math, zooming in on a concept and really breaking it down into its simplest form can do a lot to help students see what is really going on.  Zooming out on the other hand, for instance in social studies, can help us to see how events in one part of the world relate to those in going on in others.  The events that were shaping Michigan history in the 1760’s and 1770’s were certainly affected by the events taking place in the colonies at that time.  To teach Michigan history without zooming out to capture the big picture would leave out large pieces of the puzzle.

            The chapter on modeling discussed the importance of model building over simply sketching or designing something using computers.  The act of physically creating a model allows a person to adapt and make changes when they are met with unforeseen challenges.  Models give us the feeling of being there and allow us to control a situation, or find out aspects of the situation we can’t control and give us clues as to why.  Even those who we consider to be original and innovative thinkers confess that they looked to people who came before them for a place to begin.  While their end product was something we hadn’t seen before, they used models created by previous artists and academics as inspiration.  Building models teaches us how to use imaging, analogizing, and dimensional thinking skills which will help us to create and explore in our occupations and our hobbies.

In the classroom models are imperative for teaching about things that we cannot show students in person due to size, distance, or practicality.  A functional model can help us show students how the heart pumps blood through the body.  A physical model can show us what the inside of our ear looks like.  Models also serve to help students to imitate a process such as poetry or multiplication.  They can observe us writing a haiku or working through a division problem and then use our model to try it for themselves.  As mentioned in the chapter, “Precise models represent precise thinking.”