First, the terms are largely meaningless. People just say “new math” to mean whatever they want from a teaching a political standpoint. There is no widespread understanding of what new math is.
That said, new math is largely incorrectly thought to be Common Core and is usually Singapore Math.
Common Core is not a new math or new way of teaching math. It is a set of standards for testing if kids understand math. It does not specify how math is to be taught. However, for political reasons a lot of people attack Common Core as a whole and therefore claim that the confusing new math is Common Core.
However, “new math” is usually Singapore Math. Singapore Math is a way of teaching math that became popular in Singapore in the 80s and then was adopted in other countries. It became widely adopted in the U.S. in the 2000’s.
Old math was generally rote memorization. Kids were taught 2+3=5 and to memorize that. But Singapore Math teaches kids why 2+3=5 so that they understand how math works.
Singapore math teaches students mathematical concepts in a three-step learning process: concrete, pictorial, and abstract
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