re: 9 reasons why public educ fails

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Right off the bat, #2 is wrong. It's dumb to have an opposition to concepts and theories taught under the label "new math". Sure, a lot of students only have the brain power for rote memorization of arithmetic, and a lot of them will need nothing more in their future limited lives, but science and technological progress depend on the ability to THINK AND CONCEPTUALIZE rather than just to memorize, and the future competitiveness of this country depends on having people who can do so.

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most of these new math theories discard rote memorization almost completely, if not completely ... the rush to incorporate "conceptualization" into math has lead to reliance on calculators and kids arriving at hs literally not knowing their multiplication tables ...

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I really cannot tell who is advocating what - or if there is any difference in what the two of you are saying - I agree with both.

As a now retired High School math teacher (retired in Oct) I can vouch for the fact that most students arrive at the 11th grade without knowing their multiplication facts - they have been allowed, even taught, to use their calculators for everything. This is wrong - very wrong. I have seen students actually using calculators to multiply a number by 1 - or even zero.

When a multiplication is seen as nothing more than a series of keystrokes, it is difficult to establish a habit of looking for common factors.

I used to always have at least one warmup problem where I would post a division problem with the exact same numbers (factors) in the numerator as the denominator and ask them to find the quotient. I would have enough factors to multiply that the calculator would have to resort to scientific notation to present the answer.

I never once had a student look at the problem and just write down the obvious answer "= 1"

It is difficult to establish a sense for factorization and simplification when these concepts are totally foreign to their basic understandings of how things work.

So - I applaud any concentration on concepts and understanding over mechanical skills, but I also insist on having basic knowledge of simple multiplication and addition facts - WITHOUT a calculator.