Author Archives: epgoldenberg

Pre-Service Mathematics for Elementary (and Secondary) Teachers: a third essential element

by Paul Goldenberg and Al Cuoco Content is essential; so are strategies and craft for teaching; but there’s more. It’s often said that “many elementary teachers don’t really know the content; the content they ‘know’ they don’t really understand; often … Continue reading

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Interactive Images—Pictures for the Mind’s Eye

By Judah L. Schwartz, Harvard University a step in the direction of enhancing mathematical insight for teachers and the students they teach What is the real value of interactive manipulable mathematics software? Many educators see value in hands-on learning. To … Continue reading

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A Physicist’s Lament

By Judah L. Schwartz, Harvard University From whence this blog Nearly twenty years ago Paul Lockhart wrote a brilliant essay, A Mathematician’s Lament[1], on the parlous state of mathematics education. In it, Lockhart laments that mathematics education does not celebrate … Continue reading

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Ideas under construction: children saying what they know

Alli entered kindergarten quite skilled at mental addition and proud of her skill. Subtraction followed quickly. Near the end of her kindergarten year, Alli bounced into class and said that her father had taught her about negative numbers. To assure … Continue reading

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