>We teach teachers to teach the adding and subtracting of >fractions...
You mistake my meaning. Haim's Challenge is not about Paul Tanner and any particular hobby horse that he may like to ride. It is about open questions in pedagogy (strictly speaking, math pedagogy, but I had long since relaxed that constraint) that are INTERESTING TO THE EDUCATION COMMUNITY. To meet Haim's Challenge, you would have to either point to an ongoing discussion on pedagogy, or start one.
A moribund thread with half the comments not even on point hardly rises to the challenge. Wayne cocks a snook at you, Richard cocks a snook at me, and Kirby talks curriculum, not pedagogy. On the adding and subtracting of fractions, the ostensible subject of your discussion thread, you are mainly talking to yourself. By no reasonable interpretation of the concept, does your thread even come close to meeting Haim's Challenge.
To put it another way, a question that is interesting to you and to nobody else does not meet the challenge. Now, you may be right in that the question ought to be interesting to others, but it isn't. And that is my point with Haim's Challenge.
Haim's Challenge began with the observation that no one is discussing pedagogy. At the time, I even briefly surveyed the education literature and I found a great deal on racial and "gender" equity and other stuff, mainly issues of social engineering, but nothing on pedagogy. It was from this vacuum that I hypothesized that people are not discussing pedagogy because there are no interesting questions to discuss.
I admit to being a little provocative. Plainly, the observation that no one is discussing pedagogy does not necessarily imply that there are no open questions in pedagogy. However, we can infer that the education community believes that there are other, more interesting and more important, questions to explore about education.
As it happens, I fall into that latter camp. Curriculum is mildly interesting to me, but discussions on pedagogy and textbooks, especially textbooks (the favorite hobby horse of my friends on the right side of the education debate), are worse than a waste of time. (Like a fever, bad textbooks are a symptom, not a cause.) I think it is much more important to discuss who are teaching fractions than exploring the minutiae of exactly how they are doing it. Discussing your formula method for adding fractions with someone who mainly fears and loathes mathematics (a good characterization of most elementary school teachers) strikes me as the height of futility.