From time to time, when I am in a reminiscing mood, I read some of my old articles, editorials, and blog entries. I reflect on what has changed in the ensuing years.

]]>As an example, think about the math knowledge and skills in decimal arithmetic, percentages, angles, and the use of a protractor and compass needed to create pie charts. A couple of years before students acquire such knowledge and skills in the traditional grade school curriculum, they can create and use pie charts with the help of computers. The key idea is that they can make use of their vision abilities (their “mind’s eye”) in understanding pie charts, and creating them on a computer, before they have developed the math knowledge and skills to create them using “by hand” methods. Jim Fey referred to this specific visual math approach to curriculum change as an inverted curriculum.

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