Module6 What's the big idea?

Dimensional thinking involves moving from 2D to 3D or vice versa. (p204) Every time we make a paper airplane from a flat piece of paper and send it flying or draw a map of the neighborhood with directions to our house, we are using dimensional thinking. Dimensional thinking pervades our lives. We usually overlook this fact, but in most all fields (professions), the dimensional thinking process plays a very important role. For example, Archeologists reconstruct the size and weight and height of creatures from their 2D foot prints. Physicians analyzing x-ray photographs and MRI, which only shows static sliced images through their patient’s bodies, have to interpret what they see in terms of dynamic living beings. Dimensional thinking involves mapping, perspective, anamorphosis and fractional dimension processes which is just starting to be understood. In all of these processes, size and time certainly matter. Scaling down and up can both be equally problematic. Also we need to think differently about time itself, depending on the scale and the perspective we take. Depending on our own time and perspective, every object has very different looks. It is true that moving real and imaginary things between dimensions in time and space plays an important role in a wide range of endeavors, form mundane manufacturing to modern arts, and in science from astronomy to biology. (p218) However, most people are unable to integrate information given in one set of dimensions into a model or image in another set of dimensions.

Modeling always provides deep insights of the objects so that we can capture the essential operations of the real objects and its mechanism. . Models can be made only after real situations and objects have been intensively observed. Thus, by embodying both abstraction and analogies and usually, dimensional alterations, modeling can become a very practical thinking tool for us. Once the model has been made, experimenting or playing with it determines whether the properties modeled are accurate abstractions of real situations or systems. To make this right, near all models utilize dimensional-thinking skills as well.  The huge size of the model allows us to play- act the part of something. Also, scale-downed models enable us to manipulate and control the objects and ideas with limited budgets and space. Models can allow us to reify ideas and concepts that are otherwise difficult to understand. To avoid confusing models with pure concepts themselves, making a 3D physical model is important. As computer graphic model is the 2D experience, it cannot provide us the same multisensory experience as the physical model does for us.

Both dimensional thinking and modeling require intensive observing of the objects (or the situation) to capture the essence in them. Also the modeling requires dimensional thinking process as well, because to make a correct model, scaling properly and putting in right dimensions are indispensible.  To increase these two thinking abilities, students can be encouraged to make 3D objects with flat materials, model familiar objects (house, school) after intensive observation of the objects. Trying to have a visual thinking process will also help the student to model objects, as our kinesthetic sense is directly connected to our visionary sense.