How would you answer this test question? From a 1st grade Common Core test.

[Ms. Toad]

409. Not correct.

Number families have been taught for years - and are necessary to higher mathematics.

Teaching incorrect terminology is not. Unfortunately, elementary school teachers - and apparently test writers - don't know enough to understand the concepts they are teaching, and well intended parents (who also are generally not mathematically sophisticated) say, "we'll jut have to learn newer school thinking," without bothering to make sure that newer school thinking (1) is being accurately reflected in the material and (2) is well suited for use beyond high school level math.

It is a repeat of the elementary school teachers who teach squares, rectangles, and quadrilaterals as three distinct figures, which I had to repeatedly correct in my high school geometry students because it is critical that they understand that a square is always also a rectangle and a quadrilateral - and a quadrilateral is also sometimes a rectangle, and also sometimes a square.

Or perhaps a repeat of set theory (introduced as "new math" when I was in elementary school). A really powerful tool - but pretty much a useless waste of time through high school (below calculus) because the concepts repeated year after year are simple enough they can be learned by a college student in perhaps a single lesson - when they are needed and there is actually an instructor present who knows why it is important.

I'm all for teaching useful mathematical concepts to students earlier in their educational careers provided (1) those teaching them understand them and (2) those teaching them also understand how they might be useful 2-3 classes up. Teaching mathematically incorrect vocabulary (if the test reflects what is intended to be taught) is not helpful.

This kind of makes my point:

Generally, subtraction facts are harder for children to learn than addition facts. If a child knows that 6 + 9 = 15, and he or she sees the subtraction sentence 15 – 9 = __,

http://eduplace.com/math/mathsteps/1/b/index.html