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Vortistic Traditionally, the teacher taught the mathematics, the students practiced it for a while, and then they were expected to use the new skills or ideas in solving problems. This approach, strongly engrained in our culture, has rarely worked well. First, it assumes that all children at that time possess the ideas required (the blue dots) to make sense of the explanation in the manner the teacher thinks is best. This means that there is only one way for each student to "get it." It's the teacher's way or no way. However, it is unrealistic to expect the existence of a singular set of ideas across any typical class. Although a show-and-tell approach sometimes succeeds with some children, showing and telling depends on passive absorption of ideas and leaves most students believing that mathematics is mysterious and beyond understanding.
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