This discussion is so far from reality in the present it has already violated the limit on the speed of light.

We're talking nonsense.

E.g., you wrote:

"You talk as if there were never test scores to think about before. There always have been."

Nonsense. We're in full agreement here.

Instead of some false disagreement, we need to move on to something constructive.

You wrote:

"'Engaging' is far, far more important than you realize."

Nonsense. In simple terms, you can't know what I "realize". For more, of COURSE 'engaging' is important.

My father was something of an expert in educational theory and practiced it as the educational theorist for a military technical school (electronics, welding, hydraulics, mechanicals, etc.) for years with over 40,000 students at once.

His main 'guidance' of my education was that I be 'engaged', and in some subjects I really was. I was engaged enough, but where I wasn't he didn't push; he likely thought that such pushing would be pointless and may have been correct. In the end I did well in school, went "all the way". Far and away, the best things I did in school were from my being 'engaged', although that's a bit too mild.

So, what about 'engaged' in the article by the third grade teacher?

(a) No teacher in K-12 'engaged' me in anything. Not once. Ever. Where I was most engaged, in plane geometry, more fun than eating caramel popcorn, the teacher was the ugliest person I've ever met, and I slept in class and refused to admit doing any of her assigned homework. So, she would have turned off many students but did not affect my level of 'engagement' at all.

Actually, I made sure to work every non-trivial problem in the book including the more challenging ones in the back. I was fully "engaged".

I got 'engaged' for the usual reasons: A desire to achieve the security of adult competence. The content of the media that emphasized science got me 'engaged' in science.

(b) As I outlined, there's not a lot taught in K-8. Given that, a lot of being 'engaged' is not necessary to that learning. So, it's a bit empty for her to say that she got her students 'engaged' in learning the standard stuff in the third grade.

(c) More directly, if she can get her students 'engaged', then let's see the results in student accomplishments:

So, maybe she gets some student engaged in math and they rush ahead and pass the AP calculus exam at the end of the third grade. If then she wants to say that she got the student 'engaged', then I can believe her and chalk up some credit for her getting a student 'engaged'.

Maybe she plays some music for the students and then has as a class guest the first chair violinist of the local symphony orchestra. The violinist gives a concert in class with everything from 'Twinkle Twinkle Little Star' to various pieces really easy to like to some dance pieces even easier to like like to various classic showpieces to some 'video backed show and tell', say, motifs from 'The Ring', with images as in, say,

http://www.youtube.com/watch?v=7prUFflX0_E

where the climax should get much of the class 'engaged', to something really 'engaging', the D major section of the Bach 'Chaconne':

Castelnuovo-Tedesco: "The Bach 'Chaconne' is the greatest piece of music ever written."

The central D major section is the easiest to like and has the climax of the piece. The Heifetz performance of the climax is especially 'engaging'.

A violin is such a magnificent piece of 'woodworking' that it is 'engaging' just to see one for the first time. Being just close to a violin being played for some of the best music by a good violinist is really 'engaging'.

I did that once: At Christmas at the farm I retired to an upstairs bedroom for some violin practice. Soon a niece about 8 came up to watch and listen. So, sure, soon I put my violin under her left chin, stood behind her, showed her how to hold the bow, and the next day her father asked me, "How much is a violin going to cost me?". Her mother had been trying to get the girl 'engaged' in music for years with no effect. I was successful in a few minutes. Part of the reason is that it is much easier to get a child engaged in something an adult is doing instead of something they are just saying. Having a really good musician in class will get a lot of students 'engaged'.

Next day, have a good concert pianist do much the same. Sure, start with some famous pieces some students in the class may be able to play already, e.g., the Bach C major "Prelude" from 'The Well Tempered Clavier', let the student get acknowledged, maybe get a 'master class' on this piece from the guest pianist, sitting beside him on the piano bench, get status in the class, and then get the rest of the class more eager to 'follow along' and be 'engaged'. Yes, the piece is in the movie 'Samantha: An American Girl Holiday' and there played very well. Net, Hollywood knows that third grade or so girls can like that piece.

Next day, a cellist. Sure, play something really easy to like, the 'Prelude' to the Bach first unaccompanied -- easy enough to like to be used in ad music, but the ascending chromatic scale climax near the end is one of the better moments in all of music.

Next day, have a guest outlining the math for satellite orbit determination as needed by GPS. So, get students 'engaged' in math and physics.

So, some student gets really 'engaged', checks out a violin, spends about half of each day in a back storeroom practicing, and by the end of the third grade plays the D major section of the Bach 'Chaconne'.

Now I'll give her credit for getting her students 'engaged'.

Some of the students like writing. Okay, have them start some blogs, write the initial posts, moderate the other posts, and respond, i.e., have them play the role of Fred Wilson at AVC.com. The teacher will get some chances to supervise the work and help with the writing, content, handling contentious issues, computer usage, grammar and spelling. At the end of the year, finally tell the world that the blog moderators were all of eight years old!

You wrote:

"The problem is not the taking of tests. The problem is focusing on tests at the expense of everything else."

The tests are not going to cover playing the Bach 'Chaconne' and, instead, just cover the basics of third grade material. Good students with good instruction can learn enough of the grade 1-8 material in a few months. Asking that the ordinary and normal students know the third grade material by the end of the third grade is asking very little.

For the "teaching to the test", that is presented as some sin but without details about the sinfulness. Go ahead: Teach to the test. Heck, most straight A students study just for the test and just as they perceive the teacher will write it anyway.

If the test is at all well constructed, then passing the test is a quite good indication of the learning. People have known how to write good tests for decades.

As we all know, tests are a central part of education, including via the examples I gave of CEEB, SAT, GRE, LSAT, MCAT, etc.

Net, these K-12 objections to "testing" with the vague sin of "teaching to the test" look like excuses less good than the classic "My dog ate my homework.".

One way I got back at my plane geometry teacher was what I did on the state test. I got back at all those teachers with my SAT scores, especially my math SAT score.

The SAT score was correct: I had not only a lot of 'engagement' and interest in math, I had some talent as subsequent events have shown: Yes, the grand hero of mathematical economics is K. Arrow. There is a famous paper by Arrow, Hurwicz, and Uzawa. Why poor Uzawa has not gotten his Nobel prize I don't know; maybe they give at most two per paper? There was a problem stated but not solved in the paper. There was also H. Whitney, long at Harvard, of the Whitney extension theorem. So I proved a result comparable with Whitney's, assumed a little less and got a little less, used my result to solve the Arrow, et al., problem, and published.

Net, that third grade teacher should (A) have her students do well on the tests and (B) have her students get fully engaged in much more that is not on tests but quite visible as I outlined.

I'll add one more important point: However much the AFT, NEA, Department of Education, Obama, The Chosen One, Blessed Be He, want all of US K-12 run directly from DC, it is still the case that local school boards run K-12 education. Bluntly, what such a school board wants, such a school board can get. If a teacher, principal, and school really get their students and parents 'engaged', e.g., parents of third grade see their children wanting freshman college texts on math and physics, a violin, piano, or cello, are listening to

http://www.youtube.com/watch?v=7prUFflX0_E

etc., then the school board can get 'engaged', provide what is needed for, e.g., getting a concert master into third grade classes, etc., and really go for it.

Net, that's much of just why we have local school boards.