Decomposing numbers in kindergarten

Common Core standard K.OA.3 states, ``Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).''

Although it falls under the general heading of addition and subtraction, the mathematical concept that this exercise is supposed to teach kindergartners is mystifying.  By ``pairs'', does it really mean ``groups''?  Is it an introduction to odd and even numbers?  The commutative property?  Transitivity?  Algebra?  Combinatorics?  Or to impress on the kindergartner that both 4 + 1 and 2 + 3 equal 5?

The concept of none

Common Core's first major blunder is its treatment of nothing.

From CCSSI K.CC.3: ``Write numbers from 0 to 20. Represent a number of objects with a
written numeral 0-20 (with 0 representing a count of no objects).''

Long before children read and write, they speak, and long before they write numbers, they count and conceptualize.  As young children, we don't count starting at zero, we start at one.

At what age can a child abstract that when you take away everything, you have nothing and that is represented by the number zero?  Obviously, it's a concept you introduce in stages: everyone knows ``none'' or ``nothing'' before you abstract to the number 0.  We don't claim to know what the appropriate age is, but we KNOW this doesn't belong in kindergarten, before counting is mastered.  We'd guess that by the end of first grade, after learning about ``taking away'' and subtraction, every child should understand both the concept and perhaps the number.  But the steps have to be clearly set out as part of the curriculum; otherwise, ``0'' will likely be glossed over by teachers in the classroom as something trivial and obvious, which it is not.

CCSSI's ``Mathematical practice No. 2'' is: ``Reason abstractly and quantitatively.''  The concept of none is the first major abstract idea in mathematics, and it needs careful treatment.

[CCSSI does in fact mention the sequence from concept of none to digit 0...in the Mathematical Standards for High School, p. 58.  Which elementary teachers are reading the high school standards?]

Does a kindergartner need to know what a hexagon is?

From CCSSI: Kindergartners ``identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons...''

Can every kindergartner visually distinguish between a square and a rectangle?  Likely.  Two dimensions and three dimensions?  Dubious.  And know what a hexagon is?  No, it's age inappropriate.  What's the point of pushing a kindergartner to know what a hexagon is?  Is this going to lay the foundation to be college ready?

From CCSSI, a question that a teacher should ask a kindergartner and they are expected to understand and complete the task: “Can you join these two triangles with full sides touching to make a rectangle?”

``with full sides touching''?  It sounds awkward because it is awkward.

Shouldn't a kindergartner be playing with blocks instead?  Any kindergartner playing with blocks knows there are rectangular blocks and triangular blocks.  If you put two triangular blocks one on top of the other, the top block will slide off.  Why make this a goal-oriented and evaluated task?

Leave it to CCSSI to take the fun out of blocks.