Re: [xmca] a minus times a plus

[Mike Cole <lchcmike@gmail.com>]

I am still working on this issue, Eugene. I think about it almost daily
because even when I am not with kids who are worrying about "right answers"
in math terms, i am worrying about my own slippery understandings, having
been very thoroughly socialized into very dumb ways of thinking about math
and "getting by."

I think your suggestions border on Anna's ideas about commognition. The
difficulty is that when we
move to everyday experiences of this kind and away from, for example,
Davydov's approach, we
become prey to wrong conclusions (your example of the the enemy of your
enemy being your friend,
a very dangerous idea in my experience).

Thanks for your suggestions. There seems to be a research (dare I say it)
experiment growing in this
discussion. If one cared to do so, it would be interesting to compare the
VVD approach to razpredmechivanie.

In a related bemusement: opredmechivanie=reification. So, razpredmechivanie
is kind of like
"dispersed objectification" (?).  (Razbros) (Chin  chintsi raznochintsi)
(?). The interlinguistic "thawing" of our concepts never ceases to amaze me
with its potential for opening up the possibilities of
razpredmechivanie.

raz dva tri, too.
:-)
mike

2009/5/3 Eugene Matusov <ematusov@udel.edu>

>  Dear Mike--
>
>
>
> Let me try to tackle yours and Sophie's math problem since I'm very
> sympathetic 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 math problem 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 Sophie around 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?
>
>
>
> Eugene
>
>
>
> *From:* Mike Cole [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; Zoi Philippakos
> *Subject:* Re: [UD-PIG] What good for kids seems dangerous for adults
>
>
>
> Eugene, 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> 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
>
> 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
> _______________________________
>
> "those who fail to reread
>  are obliged to read the same story everywhere"
>                  -- Roland Barthes, S/Z (1970)
>
>
>
>
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