images-4Different media represent different aspects of a concept. David Olson demonstrated this many years ago in his book on how children develop the concept of what a diagonal is. He showed that after a child can recognize a diagonal, they next learn to draw it. Drawing a diagonal is easier than making one on a chessboard, which in turn is easier than creating a diagonal on a grid of lights, when the lights only stay turned on for a second after they are switched on. Each of these uses a different medium. Each medium reveals new information about the diagonal and enriches the concept. Unknown

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Concepts are an important way that we learn. Through experiences, including reading, we gradually develop a concept that is more and more elaborated. The more media in which we experience the concept, the deeper is our understanding. In addition, when a child does not understand a concept in one medium, it may become crystal clear in another.

Objective for Children: To practice translating concepts and problems into concrete, metaphorical, and other forms and media.



  • Present a math problem, number or other concept in words.
  • Have children illustrate the problem or math concept using different kinds of media. These may include numbers, sets of things, drawings, models, graphs, photos, dramatizations and other media.
  • If a problem, show how it looks in numbers and signs.
  • (Optional: Have the children add the numbers and signs to their products.)

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  • Make a conceptual web around a word that represents a concept or at least write it on the board.
  • Ask children to add ideas to the web to show what the concept means.
  • Read about the concept or have an experience related to the concept that will deepen understanding.
  • Ask children to show their own definition of the concept in words, drawing, by making a model and/or by creating a metaphor.
  • Take notes on how each child responds.


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