You can't focus on words like progressive or even rigor because they are too open to interpretation and misuse (like liberal versus conservative). I like to look at things like:

1. What is the exact content (breadth and depth) that is taught?
2. What are the skills that are taught? (I don't mean only basic things like learning the multiplication tables.)
3. How well do they have to know the content and skills as seen by homework, quizzes, projects, and tests? Show me the problems the kids have to solve. How well do they understand the material?
4. What performance level do they have to achieve to progress to the next grade level?

I suppose it doesn't have to be, but I find that education that calls itself "progressive" tends to have lower expectations for these four items, which directly relate to rigor.

The link to the commentary "On Rigor" didn't tell me anything about how rigorously the kids were prepared. Then, I followed the link to find out that what she was talking about was Interactive Math Program (IMP). IMP is one of the new progressive reform math programs that many mathematicians, scientists, and engineers (myself included) say don't contain enough content, skills and rigor to properly prepare students for technical careers. See this site for more critical information about IMP.

http://www.math.nyu.edu/mfdd/braams/links/imp.html

I advise all students interested in a technical career to avoid IMP at all costs. It is perhaps reasonable for a high school to provide both IMP and the traditional (algebra, geometry, trig, calculus) route, but to provide only IMP and tell college prep students that IMP is all you need is quite arrogant and dangerous.

She starts by saying that:

"I have always wondered what rigorous means when it is used in terms of schooling."

I would hope she would know her subject well enough to know what rigor means. If the goal is to prepare kids for college programs in science, math, or engineering, there are clear expectations for preparation in high school. Look at the California content standards for grades K-12 for a good example.

http://www.cde.ca.gov/board/pdf/math.pdf

The following quote is quite revealing.

"A simple way of thinking about this is to realize the rub between the bench mathematician or scientist and the field mathematician or scientist. The bench scholars usually reside a lifetime in the university setting. They deal in right, wrong and proof, one best answer. The field fellow is out solving the problems that crop up with new ideas and applications. His solutions do not always have one right answer, but a best answer for the moment."

Progressives have this hang-up about one right answer versus some sort of "best answer for the moment" in math. After 30 years of applying math and computer science to real life engineering problems, her discussion of one right answer and "bench" versus "field" scientist is meaningless to me. This sounds like some sort of excuse to avoid being exact and rigorous. There is no dichotomy between the working engineer and the ivory tower professor, including what and how they need to be taught.

As for the one right answer hangup, I can't quite figure this out. Students need to know the different classes of problems to solve: M=N, MN where M is the number of variables and N is the number of equations. The M=N class has just one unique answer, but how good the answer is depends on the validity of the equations and the accuracy of the data. For the MN cases, there are a vast number of methods (real skills that students have to learn) that can be used to solve these problems. I could go on and on, but this idea of one right answer versus some vague sort of something else, is preposterous.

University professors may be interested in more exact, theoretical calculations that don't have an immediate, practical use, but this has nothing to do with one right answer. It has to do with progress and trying to find more accurate answers. Scientists and engineers working on computational fluid dynamics simulations know all about no one best answer. That isn't even the problem. It's all about verification and validation to within certain error tolerances. I have spent my whole career applying ivory tower theories to real life problems and there is no conflict or need to educate these people differently.

I find her comments on rigor to be trivially simplistic and scary coming from someone involved with preparing our future scientists, mathematicians and engineers.

"See, Progressivism and high academic standards aren't mutually exclusive!"

This may sound nice, but you have to be careful how you define rigor and high academic standards. Many people have quite different views on what they mean. The K-12 education community needs to come down from their ideological and pedagogical clouds and learn some real content and skills.

Oops. The greater than and less than signs were lost when talking about M = N, M less than N and M greater than N for the classes of problems to solve.

"The K-12 education community needs to come down from their ideological and pedagogical clouds and learn some real content and skills."

I will never forget the time a young teacher, steeped in the constructivist tradition (is that an oxymoron?), told me with a straight face that "Number lines are NOT conceptual."

What she was trying to do, apparently, was defend the staff's deselection of a traditional math text, with number lines in all their glory, because the text violated the pure constructivist "no diagrams" rule of education researchers like Constance Kamii.

Of course, a parent is then left with the STRONG impression that none of the teachers sitting in the room that day would recognize a mathematical concept even if it ran up and bit them.

As an Australian teacher, I find this US debate between progressive and traditional educators quite fascinating. We have no real similar debate here because what has happened is that we have developed a blend of the two over the last 20 years. Teachers here teach content and skills in a fairly balanced mixture of traditional and "progressive" style and then assess it by a variety of methods including testing, problem solving, various forms of oral/written presentations and real life scenarios. I cannot conceive of a classroom in my state where this does not go on. I was amazed last year when a visiting American educator showed us a power point display which showed students performing parts of The Crucible as a way into debating history, and presented it to us as if it were a world shattering discovery that such things could happen in a classroom. I don't want to appear to be denigrating US education, but it seemed to me that we are much further down the path of achieving a balance between the two poles. If I'm wrong, I'm willing to be corrected.

"... we have developed a blend of the two over the last 20 years."

It all depends on the blend, doesn't it? Does this mean that no one questions your blend? In the US, teachers are trained at teacher colleges that emphasize pedagogy far more than basic skills and content. They learn what I call a top-down approach to teaching and learning. They feel that all learning can be done in context - all content and skills can be learned and mastered by working on problems - rather than learning and mastering the basics (content and skills) and then applying them to increasingly difficult problems. The top-down approach often shows up as thematic learning, where a teacher might have the kids perform The Crucible as a basis of debating history. I suppose that this could work, but how much time is being used up and do the students know enough supporting history to make this debate anything more than just a silly exercise.

In this sense, it is not a matter of balance, but of process. For the the top-down (progressive) approach, there is the possibility for a lot talking and little learning and mastery of content and skills. For the bottom-up (traditional) approach, there is the possibility of boring the students to tears and not having enough time to apply their basic content and skills. My very strong opinion (I also taught college math and computer science for many years in the 1980s) is that it is much more difficult to achieve a balance or blend using the top-down approach than it is for the bottom-up approach. It is also much more difficult to achieve a proper coverage of content and mastery of basic skills.

As a parent, I expect my son to learn how to work on subjects where there isn't an immediate payoff. I don't want him to think that all learning has to be fun and interesting. As in learning the piano, I expect him to spend some time each day on scales and sight reading. Of course, you have to worry about boring the student to tears, but I expect the teacher to know the subject (content and skills) and to know how to inspire the students to do the difficult work. As I said before, you cannot talk about vague words like balance or blend, you have to look at the details.

OK. I'll look at the details. I guess I was trying to say a lot in not too many words and I didn't intend to be "vague", just brief. I believe teachers here generally do "know their stuff" and teach skills and content in a straightforward manner, with rote learning where it's needed, with regular testing, and they assess it frequently through a very comprehensive criteria based framework. However, they integrate into this relevant problem solving, practical application, and a variety of assessment tasks. Students are certainly not just kept entertained, but neither do they learn purely by rote, standardised pen and paper tests, state mandated text books, and a narrow assessment procedure. Our teacher training courses do not emphasise one method above another.
I don't want to sound too critical of American education, as I'm certain there are fine teachers there as here, doing a great job, and I wasn't meaning to get people's back up about it, but when I read about the emphasis on pen and paper tests, teaching to tests, state mandated texts, rigid assessment methods,etc, I can't help feeling that the "balance" isn't right.
I don't agree with you that you can't have a successful blend of the two methods. In the example I gave of The Crucible, that would be used as an application/extension activity after the basic knowledge and concepts had been taught, not in place of them. I believe students need to be taught what they need to know, by skilled operators, but they also need to be able to see how that knowledge fits into their world and how it can be used in other situations and why it's necessary to know things. I am definitely not a "progressive" but neither am I someone who believes that we still live in a world where students will simply accept what we dish out to them, in the same old way as we've been doing for decades. Surely it's only by exchanging ideas, rather than taking offence and being defensive, that we will all learn from each other.

Jean wrote ..
"I don't want to sound too critical of American education, ..."

That's OK, I'll do it for you, but it's not just about balance or blend. It's about exactly what you teach, how you teach, and what knowledge, skills and problems the kids have to solve before they move on to the next grade. (By the way, I have two masters degrees in engineering and have taught college math and computer science, but I am not allowed to teach K-12. However, I am talking here as a parent, not a teacher.)

There is a very wide range of approaches between "Progressive" and "Traditional" that can be called balanced. My complaint is that the progressive approach often throws in a little content and skills and then calls it balanced. Perhaps you don't quite appreciate how pervasive this attitude is in the US and how little the basics are emphasized in many US public schools. When educators talk about "balance" here in the US, parents are quite cynical about what kind of balance they are talking about.

Jean wrote:
"I am definitely not a "progressive" but neither am I someone who believes that we still live in a world where students will simply accept what we dish out to them, in the same old way as we've been doing for decades".

"Do you feel that you have to teach only what the students will accept? When you are teaching the kids basic knowledge and skills, do you feel that you are dishing it out to them? Does this mean that you always teach the basics in context? Don't you think that the kids should respect your knowledge, skills, experience and judgment and learn the material even though it may not be fun or relevant to their day to day life? Practicing scales on the piano is no fun, but those skills cannot be learned properly in context.

Jean wrote -
"I don't agree with you that you can't have a successful blend of the two methods."

I never said "can't". I said that you have to be careful about generalities and that it is much better to tackle analysis, problem solving, and connections to real life after teaching basic knowledge and skills. Learning content and skills in context will only waste a lot of time or just never get the job done.

As for standardized tests in the US, this follows my general rule that if you can't do it yourself, then the government (the ten ton gorilla) will come in and do it for you. Since the US K-12 teaching establishment couldn't seem to guarantee that high school graduates knew much of anything, the government is forcing the issue with its NCLB. The details are left up to the individual states, but these tests are after-the-fact (too late for the students), lowest-common-denominator tests that no school should use as a criterion of great teaching. As a parent, I have looked at these tests and I am completely unimpressed. If schools teach only to the test, then I want to know what they are doing for the rest of the school day. If some schools say that they waste time on teaching the material on the test, then they should look at the test again and explain to parents why our kids shouldn't know that material.

"it is much better to tackle analysis, problem solving, and connections to real life after teaching basic knowledge and skills."
If you read my post carefully, I think you'll fims that is exactly what I was saying that we do here. We don't have a National Curriculum, we don't have SAT tests, we don't have mandated texts, yet on the OECD PISA tests Australia scores very well on numeracy and literacy, so we must be doing something right. What we do allow for is a lot of professional judgement compared with other countries including the UK./

I enjoyed reading this exchange, as it highlights a dichotomy that disappears in the context of high-quality teaching. Just as the most extreme adoption of so-called "Progressive" methods result in a formless, mushy pseudo-education, so do the most extreme "Traditionalist" methods result in an education characterized by dogmatism, inflexibility and disconnection. Neither of these extremes result in a well-educated individual, who has both a rich array of information and knowledge, and the ability to organize and communicate it.
At its best, education IS a blend, truly. The best teachers have always known this. Any education prescription is doomed if it pretends the teacher is irrelevant (as in, use the right curriculum and methods and it's foolproof.) The best system is one in which (as it sounds like Jean describes) excellence is supported by allowing--and requiring!-- such quality teaching to happen.
I am the director of a small private school in Missoula, MT, growing to serve children Pre-K through 8th grade. Such a "blend" is our goal. I am a strong advocate of parental choice, but unfortunately, Montana does not currently have charter school legislation.