Addition and subtraction ad nauseam

The pre-CCSSI 2008 Final Report of the National Mathematics Advisory Panel, commissioned by the U.S. Department of Education, in a section entitled ``A Need for Coherence'', was bluntly critical of

``...U.S. curricula [that] generally review and extend at successive grade levels many (if not most) topics already presented at earlier grade levels, while the top-performing countries are more likely to expect closure after exposure, development, and refinement of a particular topic. These critical differences distinguish a spiral curriculum (common in many subjects in U.S. curricula) from one built on developing proficiency—a curriculum that expects proficiency in the topics that are presented before more complex or difficult topics are introduced.''

Every math teacher knows the concept of spiraling, the revisiting of old problems to ``reinforce'' concepts lest students should forget.  The NMAP in no uncertain terms clearly rejected this approach, but what does Common Core do?  It introduces addition and subtraction in kindergarten, ``students should see addition and subtraction equations,'' yet CCSSI is still covering addition and subtraction of whole numbers into the fourth grade:

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