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Teaching Arithmetic Classically

In this session we will challenge popularized notions of the “grammar of mathematics” as well as critique the prominence of “rote memorization’ in our grammar school instruction. Then we will explore an alternative approach to teaching arithmetic, moving from the concrete to the pictorial to the abstract in a way that honors the structure of the classical Trivium and restores the ancient art of memory. This approach will be modeled through the teaching of simple addition and the development of more sophisticated addition algorithms. Particular emphasis will be placed on the notions of composing and decomposing units of higher value – unfortunately two concepts that are better known as “carrying over” and “borrowing from.” Finally, correspondence will be demonstrated between classical pedagogy and best practices proven by the recent success of Singapore mathematics.