Attached is a 2004 article from THE MATHEMATICS EDUCATOR by Jean Schmittau and Anne Morris entitled, "The Development of Algebra in the Elementary Mathematics Curriculum of V. V. Davydov".
I look forward to hearing from Robert Hansen or any likeminded experts on mathematics teaching and learning to reveal the scam contained therein. For those with short memories, Robert stated that Davydov's work had been shown to be a scam. I never saw said demonstration of a scam, but I can't read EVERY post that's been flooding in on MIRA and Davydov's ideas: perhaps somewhere one of the usual suspects provided devastating proof of a scam. Or is it possible that we've got an example of antiprogressive channeling here? Seems like "scam" is a favorite word of another regular here at mathteach. Stranger things have happened in the Math Wars and in this forum. I'm not sure if any of Davydov's research colleagues (Gorbov, Mikulina, Saveleva, for example) are still gracing the top side of the planet. If so, I'm sure they wait with bated (not baited) breath to hear from the sharpeyed, sharptongued elementary mathematics education experts here on the "scam" they perpetrated (wherever exactly they did so). Maybe arrests will follow hard upon such an analysis. More likely, no one over in the land of NO! will read the piece. It's long, has big words, lots of references, and requires thought. Never appealing to those who would much rather simply bellow something dismissive, negative, and shallow about that which they don't know anything at all. Development of Algebra in Elementary Math by Schmittau.pdf (378K) Download Attachment 
MPG Posted: Mar 2, 2010 11:45 PM
>More likely, no one over in the land of NO! will read >the piece. It's long, has big words, lots of >references, and requires thought. Never appealing to >those who would much rather simply bellow something >dismissive, negative, and shallow about that which they >don't know anything at all. Michael, The piece is long and it does have big words. In fact, I need help. Would you please explain to me the following passage from page 61 paragraph 1: >Vygotsky distinguished between scientific or >theoretical concepts, which he contrasted with >spontaneous or everyday concepts. The latter are formed >through childrenâ€™s everyday encounters with their >environment, while the former, which transcend the >empirical level of interaction, require a theoretical >generalization and consequently, pedagogical mediation, >for their appropriation. I am especially interested in the meaning of "pedagogical mediation for their appropriation". Thanks in advance, Haim Keep The Change 
In reply to this post by Michael Paul Goldenberg
It means "teaching so they get it."

And likely in the context of the article, something much more
specific. I'm sure any intelligent, openminded reader can glean that from what went before and after. ANY intelligent, openminder reader. In the extremely heuristic book MAKING SENSE: Teaching and learning mathematics with understanding, by Hiebert, Carpenter, Fennema, Fuson, et al., the term "problematizing the mathematics" is used. I've almost certainly quoted at length from that book here on that particular issue. And I'm quite sure from my reading of the Schmittau article that that is some of what Davydov and colleagues, as well as Vygotsky, had in mind. However, I think they were focused on doing this in a particular way and with a particular age group. The article makes that clear. And what it also makes clear is that this is done by giving nothing but a series of problems that challenge students to stretch their thinking, use the resources they've gotten from previous work, and over time to abstract certain qualities from actual things they're working with (e.g., length of various cylinders) towards gaining a clearer notion of comparison along that particular dimension. If what's described is a fair representation of Davydov's problems, then students learn to make sense of greater than, less than, equal to, not equal to, then move from informal to standard symbols. And wind up able to solve problems in early elementary that involve algebraic reasoning. Regardless of whether one things this is true, or even feasible, the approach isn't exactly arcane, though it clearly goes against received wisdom and standard practice over here and in many other places. Instead of looking at this practice, however, it is 100% predictable what the usual voices of NO! will say. After all, received wisdom and practice "worked" for them. It follows that it MUST work for everyone; anyone for whom it doesn't work "lacks mathematical talent." Anyone who suggests that we should consider alternatives  be they Davydov's ideas, his specific curriculum (I know several researchers in the US who like his ideas but don't feel his exact problem set is the way to go, though I have not yet explored in any detail with them why. I do know that there are several folks, including a former member of this list from a long time ago, working on various versions of a measurementbased elementary curriculum, and that MEASURE UP! is one already in use. What has become of Jean Schmittau's translated books of the Davydov problems I am unable to find out, though I continue to follow various leads. Unfortunately, Dr. Schmittau herself is . . . uncommunicative. Unfortunately, the naysayers here already know how we should teach everyone. And since that clearly isn't working well, they blame schools of education, professors of education, teachers' unions, liberals, progressives, NCTM, calculators, computers, and of course Barack "Satan" Obama (I prefer to blame Arnie Duncan for any new horrors, but then I'm a pinko). Not sure if Jews and Communists in the pay of the Pope have been mentioned lately, nor the Gnomes of Zurich, the Protocols of the Elders of Zion, the Illuminati, the Triads, the Trilateral Commission, or my mom. But I'm sure each will get a fair turn here on mathteach from the usual suspects. That reminds me: How's your mom? Quoting Joshua Fisher <[hidden email]>: > It means "teaching so they get it." > > >   ************************** Michael Paul Goldenberg 6655 Jackson Rd Lot #136 Ann Arbor, MI 48103 734 6440975 (c) 734 7868425 (h) [hidden email] rationalmathed.blogspot.com It was when I found out I could make mistakes that I knew I was on to something.  Ornette Coleman ************************** 
In reply to this post by Michael Paul Goldenberg
Joshua Fisher Posted: Mar 3, 2010 3:21 PM
>It means "teaching so they get it." You think? But "pedagogical mediation" sounds much more serious, more...how can I say it?scientific. I mean, "teaching so they get it" sounds like something Professor Wayne Bishop (or I) might say. If Wayne and I have been Vygotskyans, or Davydovians, all along, where does that leave poor Michael?   Okay, so that was fun. I have not read something this horridly written in a long time (thank God). Less funny is that Michael thinks this article proves anything. The article begins with a glaring mistake. Schmittau and Morris assert in the introduction, >Currently in the United States we are concerned about >how to provide early algebra experiences for elementary >school children that will prepare them for the formal >study of algebra later at the secondary level. I do not know anybody who is concerned about providing early algebra EXPERIENCES [my caps] for elementary school children in order to prepare them for the formal study of algebra later. I do know a lot of people who are very concerned about educating young children in arithmetic, up to the arithmetic of common and decimal fractions, as preparation for the formal study of algebra at the secondary level. Early algebra "experiences" may well be on Davydov's agenda, but let's not pretend that large numbers of Americans have been waiting for such a "break through" like Shi'ites waiting for the Twelfth Imam. The central problem, however, is that the article does not rise even to the level of plausible assertion, to say nothing of proof. Schmittau and Morris describe the Davydovian agenda, they do a textual comparison to NCTM standards, and nothing more. Nothing more. There is, quite simply, none of the apparatus of a scientific investigation. No control groups. No longitudinal data (longitudinal as in what happens to the children some years after they leave the Davydovian matrix). And no statistics. As best I can tell from the bibliography, we have Schmittau and Davydov describing Davydov, and Morris reporting on her own work. In a word, this article is pure <expletive deleted>. And it is so badly written (OMG) it reminds me of an old, old joke. In a supermarket in Cambridge, MA an obvious student type wheels his overladen shopping cart into the "10 Items or Less" cashier's aisle. The gumsnapping cashier takes one look at the student, puts her hand on her hip, and quips, "Okay, which is it? You go to Harvard and you can't count or you go to MIT and you can't read?" In this case, the total absence of data suggests the authors are word smiths who can't count, but the awful writing suggests they are math types who can't write. I wonder which it is. Haim Keep The Change 
Mr. Pipik has previously promised to abandon upon request discussions
of math pedagogy as long as he wasn't made part of the discussion. I am formally requesting that he withdraw from this thread, as well as the ones on multiplication as repeated addition. He is not being made part of the discussion. I hope Mr. Pipik will honor his public promise to this list to withdraw. Quoting Haim <[hidden email]>: > Joshua Fisher Posted: Mar 3, 2010 3:21 PM > >> It means "teaching so they get it." > > You think? But "pedagogical mediation" sounds much more serious, > more...how can I say it?scientific. I mean, "teaching so they > get it" sounds like something Professor Wayne Bishop (or I) might > say. If Wayne and I have been Vygotskyans, or Davydovians, all > along, where does that leave poor Michael? >   > > Okay, so that was fun. I have not read something this horridly > written in a long time (thank God). Less funny is that Michael > thinks this article proves anything. > > The article begins with a glaring mistake. Schmittau and Morris > assert in the introduction, > >> Currently in the United States we are concerned about >> how to provide early algebra experiences for elementary >> school children that will prepare them for the formal >> study of algebra later at the secondary level. > > I do not know anybody who is concerned about providing early algebra > EXPERIENCES [my caps] for elementary school children in order to > prepare them for the formal study of algebra later. I do know a lot > of people who are very concerned about educating young children in > arithmetic, up to the arithmetic of common and decimal fractions, as > preparation for the formal study of algebra at the secondary level. > Early algebra "experiences" may well be on Davydov's agenda, but > let's not pretend that large numbers of Americans have been waiting > for such a "break through" like Shi'ites waiting for the Twelfth Imam. > > The central problem, however, is that the article does not rise > even to the level of plausible assertion, to say nothing of proof. > Schmittau and Morris describe the Davydovian agenda, they do a > textual comparison to NCTM standards, and nothing more. Nothing > more. There is, quite simply, none of the apparatus of a scientific > investigation. No control groups. No longitudinal data > (longitudinal as in what happens to the children some years after > they leave the Davydovian matrix). And no statistics. > > As best I can tell from the bibliography, we have Schmittau and > Davydov describing Davydov, and Morris reporting on her own work. > > In a word, this article is pure <expletive deleted>. And it is > so badly written (OMG) it reminds me of an old, old joke. > > In a supermarket in Cambridge, MA an obvious student type wheels > his overladen shopping cart into the "10 Items or Less" cashier's > aisle. The gumsnapping cashier takes one look at the student, puts > her hand on her hip, and quips, "Okay, which is it? You go to > Harvard and you can't count or you go to MIT and you can't read?" > > In this case, the total absence of data suggests the authors are > word smiths who can't count, but the awful writing suggests they are > math types who can't write. I wonder which it is. > > Haim > Keep The Change > > >   ************************** Michael Paul Goldenberg 6655 Jackson Rd Lot #136 Ann Arbor, MI 48103 734 6440975 (c) 734 7868425 (h) [hidden email] rationalmathed.blogspot.com It was when I found out I could make mistakes that I knew I was on to something.  Ornette Coleman ************************** 
In reply to this post by Michael Paul Goldenberg
MPG Posted: Mar 4, 2010 10:41 PM
>Mr. Pipik has previously promised to abandon upon >request discussions of math pedagogy as long as he >wasn't made part of the discussion. I am formally >requesting that he withdraw from this thread, as well >as the ones on multiplication as repeated addition. He >is not being made part of the discussion. I hope Mr. >Pipik will honor his public promise to this list to >withdraw. I withdraw from Davydov. And I look forward to reading your contributions to a long, fruitful, and illuminating discussion on math pedagogy. I will also withdraw from "Math As Repeated Addition", but I do so "without prejudice" and not on the basis of my Public Promise. "Math As Repeated Addition" is a discussion based on an article by Keith Devlin, who stated in plain English that he was making a mathematical point, not a pedagogical one. Necessarily, the discussion in this forum is primarily mathematical, and touches upon the teaching of small children only in the most superficial way. No reasonable person can view this discussion as a pedagogical one. Therefore, I am not bound by my Public Promise, and I withdraw purely as a matter of collegiality and professional courtesy. (Michael, those are just fancy words for acknowledging that you asked nicely.) Haim Keep The Change 
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