Preparing Future Faculty Worksho p Object Teaching and Model Building Dr. Eugene F. Provenzo, Jr. Department of Teaching and Learning School of Education

Piaget—To Understand is to Invent

Model Building in Teaching Making models is an effective way of testing out and representing ideas in the real world. Sometimes these models can deal with complex ideas in philosophy or mathematics. For example, the German founder of the Kindergarten movement, Friedrich Froebel (1782–1852) created many educational devices and activities for children, including a device made up of a wooden sphere approximately three inches in diameter; a wooden cube; and wooden cylinder.

Model Building in Teaching How could a toy like this be used to demonstrate a philosophical principle?

Model Building in Teaching The toy physically demonstrated the dialectical principle of the German philosopher Georg Wilhelm Friedrich Hegel (1770– 1831). According to Hegel’s theory, “Thesis and antithesis yields synthesis.” Thus, seemingly opposite things can be “synthesized” or combined together through the dialectic process to create a new unity. In the case the sphere, all sides of the object are round. In the case of the cube, all sides are flat. By combining these two seemingly opposite objects, a synthesis is achieved in the form of the cylinder, which includes both flat and rounded sides—thus providing a tangible demonstration of the dialectical process.

Model Building in Teaching—Create A Volcano Brainstorm in groups to see if they can invent a model to represent an idea, concept,or event within the individual’s field. For example, create a model for lava bubbling in a volcano (pea soup bubbling in a pot on top of a stove). Extension: Discuss how a metaphor (“her eyes were blue as the ocean”) serves as a model to describe an object or thing.

Columbus Egg Problem According to legend, Christopher Columbus (1451– 1506) was having dinner with a group of Spanish gentlemen. A rather proud and conceited lot, they said to him that his discovery of new lands across the Atlantic Ocean wasn’t that much of an accomplishment. In fact, discovering them was the simplest thing in the world.

Columbus Egg Problem Columbus at first did not make any reply. After a bit though, he took an egg from a dish on the table and asked, “Who can make his egg stand on end?” Each of the men tried. None of them was successful. All of them said it was impossible for the egg to stand upright on its own.

Columbus Egg Problem = Demonstration of Thomas Kuhn’s notion of paradigm breaking in the sciences. Finally, Columbus took the egg and gently crushed its bottom, allowing it to stand upright. He then said, “What you said is impossible is the simplest thing to accomplish when you have the answer.”

Paradigm Breaking in the Sciences What Columbus did was break the existing paradigm. A paradigm is a way of looking at or interpreting the world. This is sometimes referred to as “thinking outside the box.”

“Thinking Outside of the Box” A good follow-up to the Columbus egg problem is the puzzle that has you connect nine dots using only four lines while not lifting our pencil from the paper. Most people try to figure out the problem staying within the boundaries of the dots.

“Thinking Outside of the Box” This does not work. What is needed is to “think outside the box.” In other words, to extend the line beyond the boundaries of the dots. Then the solution to the puzzle becomes very simple.

“Thinking Outside of the Box” Louis Padgett and his classic story ??? Which became the basis for the movie The Mimsy.

Gerhardus Mercator (1512–1594) Gerhardus Mercator (1512–1594) is the Latin name for the Flemish geographer, mathematician, and cartographer Gerhard Kremer. Mercator is most well known for creating the type of map known as a Mercator projection.

Mercator Projection In a Mercator projection, the parallels of latitude, which on the globe are equal distances apart, are drawn with increasing separation as the areas being mapped move closer to either the North or South Pole.

Mercator Projection Mercator’s approach makes it possible to take a round planet (the Earth) and map it on a flat surface paper). However, using this process creates some problems, since areas mapped are exaggerated as they get more and more distant from the equator.

Mercator Projection Thus, the size of Greenland and Antarctica are exaggerated in a Mercator projection, while preserving their actual shape. As a result, Mercator projections give an incorrect idea of the relative size of different land masses in which those closer to the North or South Pole seem larger than those closest to the Equator.

Mercator Projection How could a Mercator Projection be used to teach about cultural relativism?