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*To*: "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Subject*: Re: [xmca] a minus times a plus*From*: Andy Blunden <ablunden@mira.net>*Date*: Tue, 26 May 2009 11:31:33 +1000*Delivered-to*: xmca@weber.ucsd.edu*In-reply-to*: <30364f990905251757q6cc33970q7fc3e68d4f18fee9@mail.gmail.com>*List-archive*: <http://dss.ucsd.edu/mailman/private/xmca>*List-help*: <mailto:xmca-request@weber.ucsd.edu?subject=help>*List-id*: "eXtended Mind, Culture, Activity" <xmca.weber.ucsd.edu>*List-post*: <mailto:xmca@weber.ucsd.edu>*List-subscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=subscribe>*List-unsubscribe*: <http://dss.ucsd.edu/mailman/listinfo/xmca>, <mailto:xmca-request@weber.ucsd.edu?subject=unsubscribe>*References*: <000c01c9cc09$551bb160$ff531420$@edu> <Pine.SOL.4.60L.0905031215550.12267@copland.udel.edu> <30364f990905031137g6fa02a15r3eec7512e4f5803c@mail.gmail.com> <005201c9cc4e$0abf89d0$203e9d70$@edu> <49FE597C.60904@mira.net> <30364f990905251757q6cc33970q7fc3e68d4f18fee9@mail.gmail.com>*Reply-to*: ablunden@mira.net, "eXtended Mind, Culture, Activity" <xmca@weber.ucsd.edu>*Sender*: xmca-bounces@weber.ucsd.edu*User-agent*: Thunderbird 2.0.0.14 (Windows/20080421)

Well I think it's a risky approach because I think it's fortuitous that you get the right answer. There are only two possible answers you had a 50-50 chance anyway! In (-5) the - is firmly adhered to the 5. I -[(5)*-7] the - applied to the result of the first multiplication. Applying the minus to one of the multiplicands is happens to give the same answer as applying the minus to the product. The laws of association for sense, i.e. A*(B*C) = (A*B)*C is a later lesson surely! Andy Mike Cole wrote:

Andy-- Until getting back to this exchange, i had made it only as far as:5* (-7) is (-7 seven times down the line) which seems pretty easy torepresent and communicate about.But when we move to (-5) * (-5) I can understand it better myself (hah!)if I rewrite the problem as-[(5)*-7]. So inside the bracket I do what i did in the 5*(-7) exampleand then treat - as "do the opposite," an operator.I am sure this is all lousy thinking, but that is how far I have gotten. mike 2009/5/3 Andy Blunden <ablunden@mira.net <mailto:ablunden@mira.net>> Thanks for those observations Eugene. Can I just throw a couple of things on to the heap? Your translation of разпредмечивание as de-objectivization is right I think. Someone I have read recently, maybe Kozulin, made a big deal of Vygotsky's use of the idea, and also ascribed it to Hegel, which I am not at all sure about. As a civil engineering student we were taught to imagine ourselves as a building. Complex structures are formally indeterminate mathematically, you have to use successive approximation to calculate stresses and even then the point is to design in advance, not calculate afterwards. So far and away the best approach is to imagine yourself as the building and "feel" where the stresses are and how you have to adjust your position to bear the weight, and then sketh it in in steel. But how to de-objectivize -x-=+? I am actually of the view that it is better to postpone the justification of the rule till after a child has had experience in using it, but I am not the teacher here. So I wouldn't try explaining the deeper meaning of multiplication which unites it with various non-arithmetic operations until after the child can multiply arithmetically. Arithmetic is actually the richest domain in all of mathematics; all other domains are sub-parts of arithmetic! Learn arithmetic and everything else opens to you. But .... Multiplication is compounding. It is "of" rather than "and". In primary school we were actually taught "of" as an additional operations over and above "multiply". Odd. So -2x-3 is -2 of -3, whereas -2+-3 is -2 and -3. So if a child is linguistically well-developed, that might help. Andy Eugene Matusov wrote: Dear Mike-Let me try to tackle yours and Sophie's math problem since I'm verysympathetic to it, "I am working and thinking about Sophie's brave efforts to understand -2*6. The use of multiplication as repeated addition helps, but when I get to -2*-6 I feel as if I am only part way there and want something like Jerry's mirror approach."1) In my view, to understand a math model and a mathproblem means to subjectivize it - namely to translate it back to the bodily experiences and social relations. There is a useful Russian term "разпредмечивание" that I do not know how to translate (de-objectivization?). A person has to find a human experience ("переживание"), in which the math model and the problem make sense for the person. Nunes talks about "embodied cognition" - I like this term. Dividing pizza on equal parts is an example of such subjectivization of fractional division. When I was in high school, I realized that calculus is "geometry for blind people" - it really helped me to understand bizarreness of calculus. The problem is to find such subjectivizition for -2*-6. 2) In math, the minus represents undesired human values (bad) like debt, enemies, hole, absence, past, death, decay, giving away, cold, poor, prison, and so on, while plus represents desired human values (good) like income, friends, surplus, presence, future, life, growth, receiving, hot, rich, freedom and so on. Of course, these values can be relative to a person: what is good for one is bad for another and vice versa. They are also relative to cultures: 3) In math, the procedure of multiplication usually means "application". For example, 2 multiply by 3 means that each of the 2 Units (e.g., people, places, boxes) we apply (=give) 3 unites (e.g., applies, objects, dollars). The questions is how many unites we have now. 4) Application of "good" to "good" (i.e., multiplication of positive numbers) is always good in the math model (+1)*(+1)=+1, which is not always true in the reality. For example, kind people are good, eating is good as well, however, if we apply too much eating to kind people, the result is not necessary good because too much eating might lead to obesity, which is bad (-1), thus, (+1)*(+1)=-1. Mathematical model ALWAYS have limited power and we should watch out for how we use them. However, there are objects that might fit our mathematical models and thus mathematical models can be helpful. 5) If we apply good to the bad, the bad will increase (-1)*(+1)=-1. Again, it is not always true. For example, sometimes when we are kind to bad people, they soften and become kinder, not worse, thus, (-1)*(+1)=+1. But in many cases, they become worse as the math model predicts. For example, while Western nations were kinder to Hitler's Germany, it became more powerful and dangerous (worse). If you help (+1) to bad side (-1), it is getting stronger in making bad things (=-1). 6) Similarly, if you apply bad to the good, the good becomes worse (+1)*(-1)=-1. As you expect, it is not always true. Taking dramatic examples, when some good people are wrongly accused and get to jail, some of them became stronger spiritually (e.g., boxer Hurricane) - in these cases, (+1)*(-1)=+1. But in many cases, when bad things are applied to the good, the good usually suffers (-1), what the math model predicts. 7) Finally, when bad is applied to the bad (-1)*(-1), it usually weakens the bad and strengthens the good (-1)*(-1)=+1. For example, enemy (-1) of your enemy (-1) can become your ally (+1). Or in Christianity, death (-1) is applied to death (-1) creates the life of resurrection (+1). Punishment (-1) of a criminal (-1) is retribution=justice (+1). Again this mathematical model does not always work: enemy of your enemy can still be your enemy; death applied to death might result in a zombie; punishment applied to a criminal might lead to hardening his or her heart and to recidivism (in all these example, (-1)*(-1)=-1). ALL mathematical models have limitations and we should be careful in using them and explore when they might stop working for us and our objects. Even as familiar math model as 2+2=4 do not work always: two friends plus two friends are not always four friends! (for my family, 1+1=3, my wife and I have one son ;-). 8) So, here are several of my subjectivizations of -2*-6: a. Each of your two enemies (-2 for you) has six their own enemies (-6 for your enemies). How many potential allies you might have? b. Sad reality but for long time, Eugene has been paying $2 to a bank a year (-2 for Eugene) for his college debt (alas!). How richer was Eugene six years ago (-6 years)? Negative income (=debt) times negative time (=past) equals past treasure:. (This is a heartbreaking math task for me!) c. On more optimistic note, when I put my yogurt into my freezer, its temperature drops 2 degrees each hour (-2 degrees for yogurt). How warmer my yogurt was 6 hours ago (-6 hours)? 9) Thinking about a minus times a minus multiplication, I found that it is less common for our everyday experiences than many other math procedures. I have developed many examples but they were so contrived that one would wonder it is not math for life but life for math:Mike, I wonder if you organize your discussion with Sophiearound these subjectivizations and limitations of math models, it might help her. Let me know if you decide to do that: I wonder if there are other and better subjectivizations of (-1)*(-1)=1:. Of course, there is a pure math proof that -2*-6=12 but I'm not sure it can be useful for Sophie.What do you think?EugeneFrom: Mike Cole [mailto:lchcmike@gmail.com<mailto:lchcmike@gmail.com>] Sent: Sunday, May 03, 2009 2:38 PM To: Tony Whitson Cc: Eugene Matusov; eXtended Mind, Culture, Activity; PIG; backontrack@wwscholars.org <mailto:backontrack@wwscholars.org>; Zoi Philippakos Subject: Re: [UD-PIG] What good for kids seems dangerous for adultsEugene, Tony, et al.Firstly, I would like to follow up with the discussion of binaries which I think is important, and allied items that came up in those notes. But Eugene and I can do that off line or when we (finally!) get to see each other, or whenever. Unless the issues are of import to others who would seek clarification or tell us how we are both wrong headed, or whatever. I also want to write seriously about the issue of youth desired activities and adult sanctioned activities as these influence our work and general understanding. But this is also a large issue and will take time and should not be discussed if of narrow interest. So I would prefer to hear other voices chime in, as has happened incredibly with the minus/plus math discussion. (Another version of "what do you all think" rented from Eugene). And a way of dealing with urgent need to respond to a very large number of student fieldnotes before morning!!!). Tony-- Your take on the issue Eugene raised is not what we are talking about, but not unrelated. To me a really major manifestation of the phenomenon you are writing about is that in 1983 Sheila and I could write a text where Barker and Wright's *One Boy's Day* was relevant, if antique. But you will not find that empirical example (nor a lot else) in the current version of that textbook. I rode the streets of LA and climbed around its sewer system at a kid, and sold papers on a street corner in west LA in the late 40's when "Midwest" was still a going mid-western town. NO NO NO now. So old fashioned it might make the current generation titter as they twitter. More on that later. I am working and thinking about Sophie's brave efforts to understand -2*6. The use of multiplication as repeated addition helps, but when I get to -2*-6 I feel as if I am only part way there and want something like Jerry's mirror approach. What makes it so strange is that at another level I have no trouble with the contents of figure 1. Something about commognition going it seems. Gotta study Ng's pic too. Now, gotta go back to my local students until I have given them the feedback they need for this coming week of work/learning/fun. Kotbegmot willing, I will be back here with you-all ere too long mike On Sun, May 3, 2009 at 9:32 AM, Tony Whitson <twhitson@udel.edu <mailto:twhitson@udel.edu>> wrote: I am eager to hear what Mike has to say. At the risk of commenting on something that may be different from Mike and/or Eugene's meaning: I think this has become more and more prevalent over the course of my lifetime, at least in the US. I went to school through 12th grade in Iowa, where there wasn't anyplace to go, really, even after age 16 when you could drive (although there were all kinds of adventures possible by bicycle). When I moved to Boston at 18, one thing that seemed really exciting to me was the way kids had free reign of that marvellous city, inexpensively via the MTA. When I lived in Chinatown, I saw diverse groups of kids (mixing, for example, Chinese and Italian from the North End) freely roaming the city on the Boston subway system. That seemed to change at the time of the conflict over busing, when politicians like Louise Day Hicks http://en.wikipedia.org/wiki/Louise_Day_Hicks fanned the flames of fear and suspicion among population groups. Then, of course, came the paranoia over "Mr. Stranger Danger" http://en.wikipedia.org/wiki/Stranger_danger -- which although perhaps overreaction, was not totally without basis in reality. Now I live in an apartment complex with one entry from a suburban street to the lanes and parking lots within our complex. School buses pick kids up and drop kids off at that entry. At an age when I was riding my bike all over town in Illinois and then in Iowa, the kids today are watched over by their parents until they're on the bus, and then greeted by parents waiting for them when they're dropped off when they get home. I expect that Eugene and probably Mike were referring to things that are meaningful intellectually, aesthetically, etc.; but I think the problem, in the US at least, goes way beyond that. What do you think? On Sun, 3 May 2009, Eugene Matusov wrote: Dear Mike- Many years ago, you made a very good point in one of our private phone conversations that unfortunately, I did not write down after you. You said something like, "Often what is meaningful for kids seems to be dangerous for adults." Is my memory correct? Can you elaborate on that? Have ever written on that? By now, I have so many observations and examples of this sad point. I wish somebody studied this phenomenon on a systematic basis. I saw so many cases when adults literally suck the life out of kids because of their concerns about kids' safety and well-being. What do you think? Eugene --------------------- Eugene Matusov, Ph.D. Professor of Education School of Education University of Delaware Newark, DE 19716, USA email: ematusov@udel.edu <mailto:ematusov@udel.edu> fax: 1-(302)-831-4110 website: <http://ematusov.soe.udel.edu/> http://ematusov.soe.udel.edu publications: <http://ematusov.soe.udel.edu/vita/publications.htm> http://ematusov.soe.udel.edu/vita/publications.htm Dialogic Pedagogy Forum: <http://diaped.soe.udel.edu/> http://diaped.soe.udel.edu --------------------- Tony Whitson UD School of Education NEWARK DE 19716 twhitson@udel.edu <mailto:twhitson@udel.edu> _______________________________ "those who fail to reread are obliged to read the same story everywhere" -- Roland Barthes, S/Z (1970)__________ Information from ESET NOD32 Antivirus, version ofvirus signature database 4049 (20090501) __________The message was checked by ESET NOD32 Antivirus.http://www.eset.com_______________________________________________ xmca mailing list xmca@weber.ucsd.edu <mailto:xmca@weber.ucsd.edu> http://dss.ucsd.edu/mailman/listinfo/xmca--------------------------------------------------------------------------Andy Blunden http://home.mira.net/~andy/ <http://home.mira.net/%7Eandy/> Hegel's Logic with a Foreword by Andy Blunden: >From Erythro's Press and Media <http://www.erythrospress.com/>. _______________________________________________ xmca mailing list xmca@weber.ucsd.edu <mailto:xmca@weber.ucsd.edu> http://dss.ucsd.edu/mailman/listinfo/xmca

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**Follow-Ups**:**Re: [xmca] a minus times a plus***From:*Mike Cole <lchcmike@gmail.com>

**References**:**[xmca] What good for kids seems dangerous for adults***From:*"Eugene Matusov" <ematusov@UDel.Edu>

**[xmca] Re: [UD-PIG] What good for kids seems dangerous for adults***From:*Tony Whitson <twhitson@UDel.Edu>

**[xmca] Re: [UD-PIG] What good for kids seems dangerous for adults***From:*Mike Cole <lchcmike@gmail.com>

**Re: [xmca] a minus times a plus***From:*"Eugene Matusov" <ematusov@UDel.Edu>

**Re: [xmca] a minus times a plus***From:*Andy Blunden <ablunden@mira.net>

**Re: [xmca] a minus times a plus***From:*Mike Cole <lchcmike@gmail.com>

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