Chapter 6 • Modeling • Think Differently

“All models are wrong; some models are useful.” –George E.P. Box
We need to make our models more useful and make nonsense into sense. To create a model is to represent something in real or theoretical terms in order to study its nature, composition or purpose. Artists create and draw on models often by preparing smaller views of a piece of art in advance of creating it. Scientists also employ basic models of things and processes. Modeling requires that we employ abstractions or analogies, and more importantly that we use the facility of dimensional thinking, that is our thinking with respect to space and time. Creative people think dimensionally when they change the scale of things, when they take two-dimensional information (blueprints, etc) and construct them in three dimensions; or vice-versa, when they plot things that occur in three dimensions into two dimensions. This can be either (or both) a scientific or an artistic aspect of thinking. In the arts, this is the very crux of drawing in perspective; similarly, engineers must constantly think dimensionally in order to toggle between blueprints/plans and actual structures. Dimensional thinking, paired with abstractions and analogies, help create models of things or processes that explain the real world.

Dimensionally Speaking ...

When someone asks you to think dimensionally, what comes to mind is usually 3-D, unless you are a fan of Back to the Future where Marty McFly is constantly reminded to stop thinking 3-D and think 4th dimensionally (Back to the Future III). This is a case of conceptualizing dimensions beyond space and time as we know them. [204]

So what does it mean to think in dimensions? Have you ever made a batch of Rice Krispies treats? They are delicious and a good treat for your
kids. Now the Scout troop is coming over, so you have to make a triple batch. All you need to do is multiply the quantity for each ingredient by three. For example, if the recipe calls for 3 tablespoons of butter to make triple the recipe, you will need 9 tablespoons of butter. With something so simple you used dimensional thinking. You were "altering the proportions of an object or process within one set of dimensions" [204].

Super Models!
Dimensional thinking involves moving from 2-D to 3-D or vice versa; mapping, or transforming information provided in one set of dimensions to another set; scaling, or altering the proportions of an object or process within one set of dimensions; and conceptualizing dimensions beyond space and time as we know them. [204]
So how does an everyday occurrence turn in to something dimensional? Create a paper airplane and give it a toss. You took a flat sheet of paper that was 2 dimensional and have created a new 3 dimensional object from it. Once again, you used dimensional thinking. Origami, it turns out, is actually an art of complex multi-dimensional thinking. As Brian Hayes has noted, “A sculptor who carves stone or models clay begins with a medium that is already three-dimensional, but the paper folder must envision the solid object in the flat and formless sheet. [212] This type of paper play, leads to dimensional thinking and modeling.

Creating a paper airplane

How does one take a globe and squish it into a map? Anyone who has experimented with peeling the rind of an orange and flattening it out knows how many possibilities there are. The fact is, there is no single right way to do this, either for an orange or for the globe. [207]

Take the MRI for instance. It takes slices of pictures that are 2 dimensional. For a brain scan this will happen from one ear to the other. Again this is a 2 dimensional picture. Now take and stack all of there pictures on top of each other and you have a 3 dimensional representation of
the brain. Here once again we have used dimensional thinking This time though it is a full circle process as we started with a three dimensional head, took 2 dimensional pictures every few millimeters, and recreated the three dimensional object in a way that we can see inside the head. So along with our dimensional thinking we have also performed transforming. Another aspect of moving from plans to reality involves the dimensional skill of scaling. Like mapping or making things in 3-D, changing the size and proportions of an object within a single set of dimensions is a skill required in many disciplines. It is, in fact, possible to identify with some accuracy a person’s academic discipline by the scale he or she works with. [213]

Morph of Globe to a Map

Surveyors and landscapers have come to use the 2D to 3D aspects in their every day work. A surveyor must look at the land as it is (3D) and then recreate it as a 2D drawing so that the viewers of the drawing can understand it's meaning. Viewers of the drawing, on the other side must be able to look at the 2D drawing and translate its meaning into 3D reality of what it means.

Someday science will be able to devise a holographic device small enough for each person to carry (like a GPS) that gives a real 3D rendering o
f the road ahead, but for now that is just in the movies. One example of this concept is the movie Avatar by James Cameron. In the video clip, notice how the group is looking at the landscape of the planet using a virtual 3D hologram.

When Root-Bernstein first offered that scaling…up or down involves risks [215], they were referring to orchestration of music. Continuing on the reader will note that this applies to other disciplines and fascets of life as well. Sizing things up or dawn takes thought. There is much to ponder. Some considerations may include strength and flexibility of materials, the change in chemical reactions, weight, mass, surface area of the object being resized and life support systems, to name a few.

As scaling up or down in music, science or architecture involves risk, so does scaling ideas or lessons in ther classroom. In the push for Universal Design for Learning, learning for all, teachers must constantly evaluate their lessons, methods and models. Ideally, these should be scaled to meet the needs of the individual learner. Reading and comprehension levels as well as writing and other communication skills must be considered. The risk comes in lacking the ability to properly analyze and calculate the correct degrees to which lessons and activities should be scaled up or down. Miscalculations can have catastrophic consequences for the learner at the high and low ends of the spectrum.

“As soon as we cease to rely exclusively on our temporary position and view things from all possible positions, in short, as soon as we being to see universally, then we no longer view things from a unique viewpoint.” [219] The reverse is also true. A reliance on still or moving 2-D visual images in preference to 3-D object can stunt our ability to think from multiple points of view, both literally and figuratively. This brings to mind teaching students to write descriptively. A teacher might show students a photo of a tree and ask them to write about what they see. In most cases the writing would be lack-luster because they would only write about their view of the two-dimensional representation as well as any previous opinions they might hold in regard to trees. How different might their writing be if they were taken out to meet the tree, look under it over it through it and touch it? One would guess the expanded view and knowledge would produce a broader description and more creative writing.

Consider, too, Cloud Gate, the famous sculpture in Millenium Park in Chicago. It is commonly referred to as "The Bean." It's easy to see why when looking at the center photo in the collage. But, to an observer who takes some time to investigate from many view points the "bean" becomes so much more. Take some time to examine the six photos. How does the image change from one angle to the next? How do the
representations of people, places and things change with each view? As one hurries
about Chicago little thought, if any, might be given to the relationships between the buildings, people, earth and sky. Those changing relationships can be viewed when gazing at the sculpture from many angles. A final question might be, "How does our perception of Chicago and "the Bean" compare to the changes in our thinking as our points of view expand?"

Granted the need for dimensional thinking skills…how might they be taught?...One method is to play with geometric shapes and connect them to objects in the real world. [220] One vision that readily comes to mind is play time in an early elementary classroom, preschool and kindergarten in particular. On any given day students can be seen "building" in the block center. In the beginning they rely on the models they
Photo credit:

have seen in real life and use the cube or rectangular blocks as the bases for houses. The triangles are always the roof. As they play and explore they begin to put different combinations together to build more complex structures. Eventually they incorporate other shapes and begin to expand to building communities.

Legos hold particular fascination for adults and children alike. One has only to take a trip, virtual or in person, to Legolandto realize the impact playing with the small shapes has had on creativity and thinking.

When working with students in schools master pumpkin sculptor Ray Villafane says' "If you wanna create a good pumpkin you have to push the limits." It's a different way of thinking." In the fall of 2010 Ray was featured on CBS: Assignment America.

In conjunction with the Halloween season, the 3D art class at Carrollton High School in Saginaw, Michigan created monsters. Each project
Carrollton High School: Monsters in the Making
began as a line drawing. Students then worked in groups to build a 3D representation of the line drawings. As they worked various shapes were taped to the structures to achieve the desired look. Plans were revised along the way to reflect the changes in the artists thinking. The final result will be Carrollton's gallery of monsters.

It is possible to learn to think beyond three dimensions [223]. It is a skill that we can teach to our students by utilizing the fourth spatial dimension that can only be experienced indirectly [224] as Richard Feynman and his sister Joan have demonstrated.

In almost all cases, the point of a model is to make accessible something that is difficult to experience easily. [229] Think about all of the
simulation opportunities available to us today. Many of the games on X-Box, Wii, PlayStation 3, DS and PSP are really simulations of hard to experience or unsafe environments brought into our homes for our pleasure and experience. Whether it is a battle field mission, an ace combat battle, the nurturing of a simulated society, an Alaskan fishingexpedition, a challenging workout or an NFL football game, these are all available as simulations. The GameZone web site lists hundreds if not thousands of simulation games. While these are simulations produced for their entertainment value, there are many other simulations that carry a much greater gravity.

Models can be smaller than life, life-sized or bigger; the Chicago Art Institute's Mrs. James Ward Thorne collection of model room interiors, which allow visitors to look inside 1/12-scale recreations. [229] Below is a recreation "South Carolina Drawing Room from 1775-1800.

Models can be formulated only after a real system or situation has been intensively observed, simplified by abstracting critical features, rescaled for human manipulation, and embodied physically or expressed in some verbal, mathematical, or artistic form. [230] In these cases
Mrs. James Ward Thorne, American, 1882-1966, A28: South Carolina Drawing Room, 1775-1800, c. 1940, Miniature room, mixed media, Interior: 12 1/4 x 22 1/4 x 21 1/2 in. Scale: 1 inch = 1 foot, Gift of Mrs. James Ward Thorne, 1942.508, The Art Institute of Chicago. Photography © The Art Institute of Chicago. Copyrighted image not provided under the Creative Commons license. All rights reserved by the Art Institute of Chicago.
rescaling is not used. The level of detail in these simulators is unmatched.
The Federal Aviation Administration oversees simulation training activities of cockpit pilots, flight crews, unmanned aerial vehicle (UAV) operators and air traffic controllers. Airlines provide the required semi-annual recurrency training for their pilots and flight crews, although third
party vendors contract some simulation services. Chesley Sullenberger credited his simulation training for his calm and controlled responses during U.S. Airways flight 1549 emergency landing on the Hudson River in January 2009. Sullenberger is a former Air Force fighter pilot and a 29-year veteran of US Airways. Quantas airlines is training pilots for their
new Airbus 380 in an advanced flight simulator. Models that render imperceptible phenomena accessible to direct cognition require strong imaging skills. Models that “stand in” for the “real thing” depend upon analogizing and abstracting…[230]
Transformative learning focuses on changing what we know" (Kegan, 2000), and this process often includes three key concepts, including life experiences, critical reflection, and the connection between transformative learning and development (Merriam et al., 2007, p.144). Mezirow's (2000) transformative learning theory is focused on "the process of using a prior interpretation to construe a new or revised interpretation of one's experience in order to guide future action" (p. 5) Clearly modeling is a higher-order thinking tool dependent upon the skilled use of many of the tools discussed in this book. [230]Lexus has developed a new generation driving simulator to enhance their safety systems by testing and understanding driver responses, reactions, and perceptions. If we are bringing learners to the simulation center to develop new skills or to change frames of reference that the adult learner brings into the environment, experiential, active learning will likely be an important element in
the transformative learning process described by Mezirow (1991).

The Military Channel's At Sea:Training Simulation shows us a Navy simulator used to train its submarine crews. While the model is life sized, the entire submarine is not. The huge size of the model allows them to play-act the part of something much smaller [230] and gives our military the opportunity to simulate different situations that may occur during their missions.

"At sea"

The field of medicine may have the widest range of representational and functional human models. [235] Laerdal Medical and Medical Education Technologies Inc. (METI) are leading makers of high fidelity human patient simulators. Some incorporate computer based, full
physiologic and pharmacological models with a human-like mannequin to re-create human patients and their reactions to care provided. Their use in training medical care providers means that actual patients are not being used as a learning platform.

The role of scientific models can be compared to that of the scaffolds and cranes erected around large buildings as they are being built. There is no way to construct the building without these scaffolds and cranes, but once the building is completed, they need to be removed. [240]

Different types of models:
Models range in all different types from graphic models to physical models. One reason that graphic models are not as good as physical ones is that abstract “maps” do not always correspond to real “terrain.” [241] Physical models use tactile and kinesthetic modes to help portray a certain image. Though graphic
models allow us to do things physical models can’t do and allow us to view the images in different dimensions, it lacks the hands-on

experience we need to
understand the model. In
order to learn and experience a model the way it is intended, we need
to be able to look at them and feel them. Hands on modeling allows us to explore all aspects of a model, to understand it in ways that just seeing it doesn’t allow us to do, and create new ideas from the look and feel of the old models. Without being able to have these different experiences, it is hard to imagine what these models would do if they became a reality. Just as students (whether in kindergarten or 80 years old), we all learn better if we have real experiences and can explore the way things work by touching and experimenting with them, rather than just reading or listening to the way it works. Would the models be successful in its purpose or would they become a disaster if no one can touch them?
A lot of models begin as a drawing, or in this case, a blueprint. We get the general idea of what the house is supposed to look like, but much is lacking. Though we can see what the house will look like, much of the pattern is missing. What size wood and at what angel do things need to be cut? Though this is a good representation and starting point for building a house, I wouldn’t want my house to be based solely on a drawing. How would I know if it would fall down?

We can then use graphic models to help us see the dimension of the house. We can see the different angels and how the structure of the house is intended to be. By looking at this model, we can see what materials would be used and what the final product would look like.
However, if we left it as this model, how do we know the weight, touch, and exact look of the material? We might assume that a piece of metal
is smooth based on the graphic model, when in reality, it may have a rough edge which would mess up the design and structure of the house. Or maybe we need the rough edge, but the graphic image doesn’t show us the benefits of having that material.

A model built from intended materials allows us to see what the house would do if it were built at a larger scale. We can actually touch and manipulate the materials, in order to make sure they would work during the larger process of constructing. If on the computer an angel is wrong, we would be able to tell in the physical model how exactly it needs to get cut, in order to support the entire house. Though all three representations of a model are useful, the best is a physical model. However, in this case, we need all three models to ensure the best success with building a house. For something else, we may only need a physical model.

Why model?
There are many reasons for modeling. It helps put into perspective how an image should be and how the image can become a reality. Out of modeling comes understanding and control. [243] If we can physically see a model of something, we are able to view it through different perspectives and angels. With physical models, we can manipulate and experiment with the model to have better control or understanding over it. Modeling provides people with real experiences, which can help aid in the development and understanding of a project or idea. Visual modeling can also be improved because there is a direct connection between the kinesthetic sense and vision. [ 245] As mentioned before, modeling provides us with useful representations of objects. Without this usefulness, it becomes difficult to understand the intentions of an image. If we are to understand the world around us, we need to create useful, often multiple, models. [242] It’s important to remember that models aren’t just in one form. As discussed earlier, models take different formats, and we need to make sure we are representing models in the best, most useful way. As with the example of the house, we need to use the three different models to help make an image a reality and use those models to create the house that was intended.

Let’s imagine, in our heads, an object that is 9 inches long and 3-4 inches tall. It has a rounded front and holes on the top with string coming out. This object comes in different colors and is made of a cloth material and rubber on the bottom. Can you guess what it is?
Though it may be possible, it is hard to imagine this in our heads and make sense of the object. However, if we can draw it out, we have a better model representation of what our object is. It’s a shoe!

Through this perception, we can create a physical model of the shoe, to then construct one ourselves!

Anyone who has played by assembled self-designed objects, whether as architect, carpenter, modeler, or builder, undoubtedly has imagined something on paper that he or she has not been able to construct. Working in time and space is not the same as working in equations, in graphics, or on paper. Dimensional issues become important. [242] When children are allowed hands on experiences in learning, they are more likely to understand those difficult concepts. Just as doctors would never know what to do if it weren't for models, children don't know what it's like, unless they have something concrete to work with.

Do you need more examples?
Powers of 10

Discovery Channel: Time Warp

Imagining the Tenth Dimension

Classroom examples:
Example #1: Verbs
When teaching children about the language and structure of a sentence, it’s important to start with one element of it, such as verbs. In each sentence, the verb changes, thus making the sentence change in time and space. If we look at the sentence as a whole, young students have a hard time making sense of what it really means. But if we, “zoom in and out” of the three sentences, we can see how the verb changes in time and space. When teaching students about the verb in each sentence, the model begins to change. First we identify the verb-to run. Then we break each sentence up by identifying the meaning of it. To create a physical representation of this, it could be done in a number of ways. The model representation could vary from acting it out, to drawing, or creating something else using any type of medium to help make sense and represent models.

Example #2: Advertisements
In working with ads and campaign ideas, students must narrow the focus and brainstorm the idea of the writing before it becomes published as an advertisement. A few questions to consider before writing are, what is the purpose of the ads and what are the desired results? After identifying the purpose behind the intended advertisement, the writing may start. As students think and navigate through the production process they will be making decisions as to which elements will combine best to achieve their goal. They will be selecting visual representations of humans, in most cases aural representations of humans and background items that will add emphasis to their writing. By the time the projects are complete, students will have taken a broad idea and zoomed it all in to something very specific. By publishing their assignment, in a medium other than word processing or Power Point students have an opportunity to report in ways that allow them to think outside the box and create in ways writing a report just doesn't allow for. This example of student work is used with permission of the creator.

Example #3: Web design
In web design, one needs to begin with an idea of "what is my web page/site all about". We start this process with a model from 30,000 feet zoomed out. We think about the entire page as a whole, here within this model. Starting from the 30,000 foot view we need to use imagining along with modeling to "see" how the page will come together. The header area, the navigation, the main content, the sidebar, the footer. Our model now begins to take structure. We then zoom in to each area in turn. Jump into the header and build the model further. Is the image to be on the left or the right or both? Zoom out to the whole again and then back in to the navigation. Is it vertical or horizontal? Is it fly out or drop down? Zoom out again and back in to the next area. So as we keep zooming in and out looking at the "look and feel" of the page, we are constantly changing the model of what we initially thought to make it better and better. So what we have done is to get and overall idea to start with and using dimensional thinking, we have look at the details and back to the overall again. Once the model for one page is done, then we can use that model for the rest of the pages on the site.

Example #4: Syllables
When teaching syllables, students begin by identifying the syllables by clapping out the number of sounds. Though this is modeling the number of syllables, in order to take it one step further, students could roll a long roll of play-doh and cut it into parts, once we figure out how many syllables in has. If the word flower has two syllables has two parts, they would cut it in half. Once students are starting to read, in order for them to practice the chunking of parts, students would be given a cut-out of an object, but this time it would have the word spelled on it. They would have to cut the flower between the letters to separate the parts. This could also be done by “giving a haircut” where students have a paper doll and strips of paper as the hair with words written on them. We could cut the hair, to break apart the word into syllables. These ideas would be visual for a student and would help to concentrate on the word and how the break-up of the letters and words help to create syllables and chunking patterns in reading and writing.

So how do we build our skills in dimensional thinking and modeling?
How to start creating models
Now that we know that creating models in important, how do we start?

*In any library or bookstore one can find books on how to build models using anything from corrugated cardboard to balsa wood, from wire and plastics to cloth and paper. These simple materials are not to be scoffed at. [244] Modeling varies in so many different ways, from the ways that we model to the materials we use to construct our model. Books are an excellent place to start.

*It is so important to start children young in modeling. We can offer them ideas on how to draw images, such as animals, so that they can visually see an object and understand that a drawing model can be formed based on shapes and lines. We also need to give children open ended toys and blocks to play with. This helps children use their imagination and create an endless array of things from one object. Creativity is key here, in the sense that they have the freedom to think of objects in new ways.

*More structured models can be presented to students, such as dioramas, which help make an idea a reality. With young students, dramatic play is a way for students to model an idea. In school modeling can also be directed toward master of various subject. Making models in math class, for instance, reinforces the concepts. The earlier a student learns that every equation has its physical manifestation and every physical phenomenon its mathematical model, the better equipped he or she is to be inventive.

*Visual thinking can also be improved by modeling, because there is a direct connection between the kinesthetic sense and vision. [245] The hands on approach here is an important component to understanding concepts. Without this model paired with visual and kinesthetic learning, mastering these concepts become much more difficult.

VizThink All you need to know about visual thinking

Kid Pix offers a wide range of tools (2-D and 3-D) for students to create stories, maps, and organizers, using virtual media.



The people who help us think dimensionally and model!
Dimensional thinkers:
Agnes de Mille

Hugo Steinhaus

John Conway

Edwin A. Abbott

Leon Battista Alberti

Gene Davis

Albrecht Durer

Gaspard Monge

D’Arcy Thompson

Charles and Ray Eames

Tom van Sant

Iannis Xenakis

Henry Moore

Margaret Geller

Johannes Itten

Frank Lloyd Wright

Friedrich Froebel

Richard Feynman

Joan Feynman

Constance Reid

Roger Penrose

People who model:
H.G. Wells

Winston Churchill


Auguste Rodin

Igor Strvinsky

Christopher Isherwood

Roger Sessions

Iannis Xenakis

Philip Glass

Isamu Noguchi

George Segal

Greogor Mendel

Alexander Fleming

Jean Gimpel

Linus Pauling

Watson and Crick

Ernst Kummer

August Ferdinand Mobius

Felix Klein

Georgia O’Keeffe

Claes Oldenburg

Let's pull it all together!

Dimensional thinking and modeling go together when it comes to learning. When we create models, we want to make sure that we can look at an object from different perspectives, views, and understanding, in order to fully represent the intended model. Without the hands-on experience from these models, we can't get a full grasp on the intended learning. By allowing for this creativity and play, whether in the workplace, or the classroom, we can have a sound understanding and portrayal of the object. We all learn better by doing, so why wouldn't we allow for others to do, more often? Though it's good for teachers to model examples for students, we also have to allow them to model on their own, too. By allowing students and adults to model, we are, in a sense, allowing them to play and empathize with one another. The goal is for them to become one (embodiment), in order to more fully understand a concept through their model. Once we are able to zoom in and out of something (dimensional thinking) and create models based on those understandings, through play, we are then able to feel at one with it. There are many views to this world, and by using dimensional thinking and modeling, we can allow for students, and others, to look more deeply into the world, and see things through different perspectives.

Zemeckis R. (Director/Writer), & Gale B. (Writer). (1990). Back To The Future III [Motion Picture]. United States: Universal Pictures.
Cameron J. (Director/Writer). (2009). Avatar [Motion Picture]. United States: 20th Century Fox.