[Xmca-l] Re: NYTimes.com: Why Do Americans Stink at Math?
Ed Wall
ewall@umich.edu
Fri Aug 1 08:54:55 PDT 2014
Greg and all
I could have stayed in K-12 teaching and I miss it; however, I decided to, in a sense, multiply myself by returning to the university/college because I felt a lot of teachers actually cared, but, perhaps because of pessimism (smile) or just unaware of possibilities (there are a lot of the latter at this workshop I'm attending), had gotten in a sort of rut. So I really wonder if the problems people are seeing aren't, to a degree, more with myself and others in teacher training. I do know some of my students (college students) are sometimes underwhelmed by us.
Ed
On Aug 1, 2014, at 11:16 AM, Greg Thompson <greg.a.thompson@gmail.com> wrote:
> Lovely conversation about the possibilities of meaning-fully engaging
> students-in-their-lives with math(s)-as-discourse. Seems like the same
> could be said of science. Some of you may know Jay Lemke (who is somewhere
> on the list serve). I have often heard him speak of the playful, creative,
> storytelling practice that science is as well - and Jay got his PhD in
> theoretical Physics.
>
> Unfortunately, with my kids (oldest is 12.5 year old boy), this hasn't been
> the case. With the exception of one year when we were at an affluent
> elementary school in San Diego where he had a particularly exceptional
> teacher, most of what my kids have been getting in school is the bad and
> lifeless math and science education that sees those fields ONLY as a set of
> skills to be mastered (i.e. Anna's "game to be played").
>
> Thus far, I've been able to convince my son that this is a worthwhile game
> and that there will come a time when he will be able to play with the
> discursive genres of math and science, but I don't know how much longer I
> can keep up that argument when it flies in the face of everything he is
> learning in school. My son has some advantages b.c. as a boy, there are
> certain expectations that he will do well in math and science (and I have
> done a fair bit of proleptically interpellating him as an engineer, but
> that could easily have the opposite effect at any point in his life...). I
> have also tried to provide examples of
> science-as-story-telling-and-problem-solving as I did when we went on a
> hike last weekend and I told him the story of the discovery of pheromones
> (Martha McClintock was a prof where I was in grad school so I knew her
> personal story as well as her story of discovery and was able to tell it in
> a compelling manner). But I do wonder if those few conversations, few and
> far between, are really going to amount to much compared to the day after
> day drilling of skills that he is getting in school. I hope so. And I also
> have three more girls coming up through the ranks in my household who will
> not have the advantage of being a gender that is socially recognized as
> being "good at math and science" - hopefully I can learn something from my
> son's experiences. So I really hope so with them as well. But for now I'm
> very anxious...
>
> -greg
>
>
>
> On Fri, Aug 1, 2014 at 5:57 AM, Bella Kotik-Friedgut <bella.kotik@gmail.com>
> wrote:
>
>> I want to retell a personal story of a student who shared it in my M.A.
>> Vygotsky class at HU some years ago. (Today he has Ph.D in education).
>> He always was recognized as a talented writer and poet, receiving
>> different literary prizes as a teenager. But he had some problems with
>> math and somebody explained him that these talents do not go together, that
>> his struggle with math is because of his literary talent. And in addition
>> "You belong to the Moroccans and this is not a good sign for math
>> capacities" So he received it verdict and graduated school without
>> matriculation exam in math, which is a serious obstacle for higher
>> education.
>> Being at the army service, he was lucky to meet a teacher who explained him
>> that who stopped him from studying math was just wrong: "A talented person
>> is talented in all he does" This became his new slogan and he studied and
>> successfully made the matriculation test in math and made education his
>> professional field.
>> So the social-cultural aspect here was working clearly.
>>
>>
>> Sincerely yours Bella Kotik-Friedgut
>>
>>
>> On Fri, Aug 1, 2014 at 11:30 AM, Helen Grimmett <helen.grimmett@monash.edu
>>>
>> wrote:
>>
>>> Thanks Anna, for both the reassurance and the citations.
>>>
>>> I've just been having a conversation with my kids in the car on the way
>>> home from school about this idea that maths is a form of story telling
>> and
>>> they both looked at me as though I was crazy! Yet when I mentioned the
>> idea
>>> at lunch to my maths education colleagues they both adamantly agreed.
>>> Clearly there is some secret here that mathematicians (and gifted maths
>>> educators) get that is not being passed on to the rest of us mere
>> mortals.
>>> I'm not saying that my kids and I are not "good" at maths (we've learnt
>> to
>>> play the old maths game quite well, but just don't like playing it) but
>> how
>>> interesting to think that there is a whole different way of seeing maths
>>> that could have changed our perspective of the game completely.
>>>
>>> Cheers,
>>> Helen
>>>
>>>
>>>
>>>
>>>
>>>
>>> Dr Helen Grimmett
>>> Lecturer, Student Adviser,
>>> Faculty of Education,
>>> Room G64F, Building 902
>>> Monash University, Berwick campus
>>> Phone: 9904 7171
>>>
>>> *New Book: *
>>> The Practice of Teachers' Professional Development: A Cultural-Historical
>>> Approach
>>> <
>>>
>> https://www.sensepublishers.com/catalogs/bookseries/professional-learning-1/the-practice-of-teachers-professional-development/
>>>>
>>> Helen Grimmett (2014) Sense Publishers
>>>
>>>
>>>
>>> <
>>>
>> http://monash.edu.au/education/news/50-years/?utm_source=staff-email&utm_medium=email-signature&utm_campaign=50th
>>>>
>>>
>>>
>>> On 1 August 2014 17:03, anna sfard <sfard@netvision.net.il> wrote:
>>>
>>>> Hi Helen,
>>>>
>>>>
>>>>
>>>> My daughter made a similar decision, once upon time. I already knew
>> then
>>>> that what she liked more than anything else was art, so I did not try
>> to
>>>> dissuade her. And artist did she become. Or designer, to be precise.
>> And
>>>> see what happened: design does require some technical/
>>>> scientific/mathematical thinking (math was a condition when she applied
>>> to
>>>> the Academy of Art, but the amount she had done was deemed sufficient,
>>>> considering her other strengths), and she was perfectly able to master
>>>> whatever mathematics was necessary whenever this learning was for some
>>>> "real" purpose.
>>>>
>>>>
>>>>
>>>> This said, i understand your worry, and must admit it is justified.
>> There
>>>> is a game being played out there, and either you play it or you may
>>> lose.
>>>> I do hope, though, that your daughter will only gain: first, she will
>>> earn
>>>> a few less stressful, happier years in school, and then she may find a
>>> way
>>>> among the hurdles just as my daughter did. And if she faces the real
>> need
>>>> for math latter in life, I'm sure she will cope. It will be a whole
>>>> different story then (it will be a story to begin with)! In any case, I
>>>> think the gains of your daughter's decision overweight the potential
>>>> losses, with one of the latter being her poor first-person identity,
>> lack
>>>> of self-confidence, etc, etc.
>>>>
>>>>
>>>>
>>>> And as to the refs you are asking for, the paper was originally written
>>> as
>>>> guest editorial for a math ed journal edited by students in Univ of
>>>> Georgia, Athens:
>>>>
>>>>
>>>>
>>>> Sfard, A. (2012). Why Mathematics? What Mathematics? - Guest editorial.
>>> *The
>>>> Mathematics Educator, 22*(1), 3-16.
>>>>
>>>>
>>>>
>>>> Then it was republished as a chapter in a book (and what I've sent are
>>> the
>>>> proofs of the chapter):
>>>>
>>>>
>>>>
>>>> Sfard, A. (2013). Why Mathematics? What Mathematics? In M. Pitici
>> (Ed.),
>>> *The
>>>> best writings on mathematics* (pp. 130-142). Princeton, NJ : Princeton
>>>> University Press
>>>>
>>>>
>>>>
>>>> anna
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> *From:* Helen Grimmett [mailto:helen.grimmett@monash.edu]
>>>> *Sent:* Friday, August 01, 2014 5:56 AM
>>>> *To:* eXtended Mind, Culture, Activity; sfard@netvision.net.il
>>>> *Subject:* Re: [Xmca-l] Re: NYTimes.com: Why Do Americans Stink at
>> Math?
>>>>
>>>>
>>>>
>>>> Thanks for sharing this editorial Anna. Can you please post the
>> citation
>>>> for it? I would like to share it with my maths colleagues, but it also
>>>> provides interesting reassurance for me about letting my daughter
>>>> discontinue maths at the end of this year (Year 10). She is a very high
>>>> achieving student but detests maths and science (she already dropped
>>>> science at the end of year 9 despite winning the Yr 9 Science prize in
>>> her
>>>> selective entry school) and has often said that she is only interested
>> in
>>>> subjects that let her tell stories (she includes music as one of
>> these).
>>>>
>>>>
>>>>
>>>> I must admit I've never thought of maths as a form of story telling
>>> before
>>>> and I wonder if her schooling had taken this approach to maths whether
>> it
>>>> would have managed to spark her interest and keep her engaged in the
>>>> subject. In her early secondary school years when science was
>> compulsory
>>>> she often mentioned that she thought it was possible that 'real'
>> science
>>>> would be quite interesting, but that 'school' science was intolerable.
>>> Her
>>>> stress levels about school have dropped considerably this year now that
>>> she
>>>> doesn't have to suffer through endless (and in her eyes pointless)
>>> science
>>>> homework and assignments. I appreciate that dropping maths will lead to
>>>> another huge reduction in any remaining school dissatisfaction and give
>>> her
>>>> more space to pursue the wide range of subjects that do fascinate her,
>>> yet
>>>> I still keep telling her I worry about her closing possible doors for
>>>> avenues of study in the future.
>>>>
>>>>
>>>>
>>>> Reading your editorial makes me realise that perhaps what I'm more
>>> worried
>>>> about is that "unofficial argument" that maths is a selection tool. In
>>> all
>>>> honesty my concern is perhaps more with what it says to others when she
>>>> says she dropped maths at Year 10, than with the doors it might close
>> or
>>>> with what she will miss out on knowing by not continuing maths into
>> Year
>>> 11
>>>> and 12. Naming this unofficial argument makes the hollowness of it very
>>>> transparent. I believe she is smart enough to have seen through this
>>>> argument (not just too naive to see it) and brave enough and gifted
>>> enough
>>>> to challenge it. I owe it to her to be brave too.
>>>>
>>>>
>>>>
>>>> It will indeed be a great day when school maths and science is
>> reimagined
>>>> in ways that do not do more harm than good for a huge number of
>> students.
>>>>
>>>>
>>>>
>>>> My thanks again,
>>>>
>>>> Helen
>>>>
>>>>
>>>>
>>>> Dr Helen Grimmett
>>>> Lecturer, Student Adviser,
>>>>
>>>> Faculty of Education,
>>>>
>>>> Room G64F, Building 902
>>>> Monash University, Berwick campus
>>>> Phone: 9904 7171
>>>>
>>>>
>>>>
>>>> *New Book: *
>>>>
>>>> The Practice of Teachers' Professional Development: A
>> Cultural-Historical
>>>> Approach
>>>> <
>>>
>> https://www.sensepublishers.com/catalogs/bookseries/professional-learning-1/the-practice-of-teachers-professional-development/
>>>>
>>>>
>>>> Helen Grimmett (2014) Sense Publishers
>>>>
>>>>
>>>>
>>>> [image: Image removed by sender.]
>>>> <
>>>
>> http://monash.edu.au/education/news/50-years/?utm_source=staff-email&utm_medium=email-signature&utm_campaign=50th
>>>>
>>>>
>>>>
>>>>
>>>> On 31 July 2014 23:47, anna sfard <sfard@netvision.net.il> wrote:
>>>>
>>>> " Doesn't it make sense that somebody should stand up and ask "why are
>> we
>>>> teaching mathematics?"
>>>>
>>>>
>>>> Already done, Michael - see the attached.
>>>>
>>>> anna
>>>>
>>>> PS. This is a fascinating conversation. I wish I could allow myself to
>>>> participate properly.
>>>>
>>>>
>>>>
>>>>
>>>> -----Original Message-----
>>>> From: xmca-l-bounces+sfard=netvision.net.il@mailman.ucsd.edu
>>>> [mailto:xmca-l-bounces+sfard=netvision.net.il@mailman.ucsd.edu] On
>>> Behalf
>>>> Of
>>>> Glassman, Michael
>>>>
>>>> Sent: Thursday, July 31, 2014 4:25 PM
>>>> To: eXtended Mind, Culture, Activity
>>>> Subject: [Xmca-l] Re: NYTimes.com: Why Do Americans Stink at Math?
>>>>
>>>>
>>>> So here is my question. We have gone through basically a century of
>>> this.
>>>> We teach mathematics and some people get it - the people in my
>> experience
>>>> really love mathematics - but most people don't. It's just something
>> you
>>>> do
>>>> to get some place else (I am reminded of my attitude towards statistics
>>>> courses in graduate school). So we keep banging our head against the
>>> wall
>>>> again and again. Doesn't it make sense that somebody should stand up
>> and
>>>> ask "why are we teaching mathematics?" - as a subject I mean, it is
>>> still
>>>> an important field of study. This is something we just made up mostly
>>> for
>>>> the sake of "efficiency" - although it is not very efficient. But
>> there
>>> is
>>>> nothing to suggest that this is a good idea, and there are a lot of
>>> things
>>>> to suggest that maybe we're on the wrong track here as far as education
>>> in
>>>> concerned. This was actually an argument about specific subjects in
>> the
>>>> 20s
>>>> and 30s, but we have been so unsuccessful and been so frustrated its
>>> pretty
>>>> amazing that it hasn't come up again. Why not let mathematics emerge
>> in
>>>> the course of what we do? Is the type of mathematics we learn in the
>>>> classroom transferable anyway?
>>>>
>>>>
>>>>
>>>> Maybe a bit heretical, but perhaps the idea should be raised every once
>>> in
>>>> a
>>>> while.
>>>>
>>>>
>>>>
>>>> Michael
>>>>
>>>> ________________________________________
>>>>
>>>> From: <mailto:xmca-l-bounces@mailman.ucsd.edu>
>>>>
>>>> xmca-l-bounces@mailman.ucsd.edu [xmca-l-bounces@mailman.ucsd.edu] on
>>>> behalf
>>>> of Ed Wall [ewall@umich.edu]
>>>>
>>>> Sent: Thursday, July 31, 2014 8:10 AM
>>>>
>>>> To: <mailto:lchcmike@gmail.com> lchcmike@gmail.com; eXtended Mind,
>>>> Culture,
>>>>
>>>> Activity
>>>>
>>>> Subject: [Xmca-l] Re: NYTimes.com: Why Do Americans Stink at Math?
>>>>
>>>>
>>>>
>>>> Mike
>>>>
>>>>
>>>>
>>>> As I said I am not a blissful optimist.
>>>>
>>>>
>>>>
>>>> Liping Ma made the point some time ago that, in fact, something
>>>> like
>>>> this would not be possible until a generation of students (perhaps two)
>>> had
>>>> been taught to reasonably (and what this means can be usefully debated)
>>>> understand what was going on (by the way, being able to do it in a rote
>>>> fashion indicates, at least, that one understands the procedure).
>> Parents
>>>> can help and hinder (most, if treated respectfully, want to help).
>>>>
>>>> Perhaps a story will indicate where I'm at. A number of years
>>> ago,
>>>> I
>>>> was at a conference sitting next to a young graduate student with a
>>> policy
>>>> background who was sort of interested in the mathematics mess. Finally,
>>> she
>>>> could stand no more and blurted out something like , "I can't
>> understand
>>>> why
>>>> you people are fussing about all this math teaching business, the kids
>> in
>>>> the inner city schools will never appreciate it." I turned to her and
>>> said
>>>> sadly something like, "You are possibly right, but I can't act as if I
>>>> believe so. Does that make sense?" She nodded yes.
>>>>
>>>>
>>>>
>>>> It is not just UCSD students who have problems with this. One of
>>> my
>>>> friends did something with fractions in his calculus class at UM
>>> (smile).
>>>> Part of the problem, I think, is that fractions in general have little
>>>> practical meaning for many people (unlike the natural numbers); they
>> are,
>>>> in
>>>> a sense, somewhat of a historical artifact. It is moderately easy to
>>>> intervene on this at certain points in the school curriculum although
>>>> asking
>>>> why is useful.
>>>>
>>>>
>>>>
>>>> Ed
>>>>
>>>>
>>>> On Jul 30, 2014, at 10:01 PM, mike cole < <mailto:lchcmike@gmail.com>
>>>>
>>>> lchcmike@gmail.com> wrote:
>>>>
>>>>
>>>>
>>>>> That all seems reasonable to me, Ed. But it strikes me as a real
>>>>
>>>>> problem when the average "top 12% of California high school
>> graduates"
>>>>
>>>>> cannot help a kid who has to figure out how to divide one fraction
>>>>
>>>>> into another. Or if they help its because they "teach the rule" (as
>>>>
>>>>> in, invert and multiply) but cannot explain why they do this.
>>>>
>>>>>
>>>>
>>>>> I think its a challenge to teachers and god bless those who can
>>>>
>>>>> emulate your approach. But its a challenge to parents, even UCSD
>>>>
>>>>> graduates aplenty, who cannot explain what they are doing in
>>>> understandable terms.
>>>>
>>>>>
>>>>
>>>>> That good teachers can teach it, give the opportunity I believe. That
>>>>
>>>>> this is, or is likely to become, the universally accepted norm for
>>>>
>>>>> everyone, I fear I doubt. But oh my goodness, how happy I would be to
>>> be
>>>> wrong!
>>>>
>>>>> mike
>>>>
>>>>>
>>>>
>>>>>
>>>>
>>>>> On Wed, Jul 30, 2014 at 12:46 PM, Ed Wall < <mailto:ewall@umich.edu>
>>>>
>>>> ewall@umich.edu> wrote:
>>>>
>>>>>
>>>>
>>>>>> Katherine
>>>>
>>>>>>
>>>>
>>>>>> I think yes to your next to last question. However, what
>>>>
>>>>>> sometimes concerns me (and we are perhaps back to optimism and
>>>>
>>>>>> pessimism) is that looking for a future which may or may not occur
>>>>
>>>>>> seems 'unfair' to the students of today. I'm for thoughtful baby
>>>>
>>>>>> steps (and babies do stumble) now on all fronts and, unlike Carol, I
>>>> don't yet know the 'right' answer.
>>>>
>>>>>> However, I would like to know (smile).
>>>>
>>>>>>
>>>>
>>>>>> Ed
>>>>
>>>>>>
>>>>
>>>>>> On Jul 30, 2014, at 3:32 PM, Katherine Wester Neal <
>>>>
>>>> <mailto:wester@uga.edu> wester@uga.edu> wrote:
>>>>
>>>>>>
>>>>
>>>>>>> I think we're all on to something here--just different parts of the
>>>>
>>>>>>> same
>>>>
>>>>>> thing. To put it all together, I'm thinking of a spiderweb. On
>>>>
>>>>>> individual strands, our spiderweb includes:
>>>>
>>>>>>>
>>>>
>>>>>>> 1. The differences in contact time and the difficulty of sustaining
>>>>
>>>>>> meaningful (or really any kind of) change when one is teaching 1,100
>>>> hours.
>>>>
>>>>>>> 2. The pressures of testing.
>>>>
>>>>>>> 3. The cultural value of childhood, teaching in general, elementary
>>>>
>>>>>> teachers, and testing as an educational goal in the U.S.
>>>>
>>>>>>> 4. Making changes in teachers' practices, the way schools work, the
>>>>
>>>>>> culture of testing, and how students' creative capacities are
>>> developed.
>>>>
>>>>>>> 5. Resistance from parents, teachers, and teacher educators to new
>>>>
>>>>>>> ways
>>>>
>>>>>> of learning/new ideas, which is often a result of deeply ingrained
>>>>
>>>>>> prior experiences.
>>>>
>>>>>>>
>>>>
>>>>>>> I probably didn't get everything that's been discussed, but these
>>>>
>>>>>>> are
>>>>
>>>>>> all issues that should be examined in concert because they are all
>>>>
>>>>>> connected as part of the same larger system. Although "system" isn't
>>>>
>>>>>> probably the word I should use with a Vygotskian framework (I'm
>> still
>>>>
>>>>>> learning), I use to say that I'm not sure how an individual could
>>>>
>>>>>> deal with one of these strands without affecting or needing to work
>>> with
>>>> the others.
>>>>
>>>>>> Does it take the effort of a collective, working on multiple strands
>>>>
>>>>>> simultaneously, to make more than a dent? Or to borrow Ed's words,
>>>>
>>>>>> how do we reshape the dent or make it bigger?
>>>>
>>>>>>>
>>>>
>>>>>>> Katie
>>>>
>>>>>>>
>>>>
>>>>>>> Katie Wester-Neal
>>>>
>>>>>>> University of Georgia
>>>>
>>>>>>>
>>>>
>>>>>>> ________________________________________
>>>>
>>>>>>> From: <mailto:xmca-l-bounces@mailman.ucsd.edu>
>>>> xmca-l-bounces@mailman.ucsd.edu
>>>>
>>>>>>> < <mailto:xmca-l-bounces@mailman.ucsd.edu>
>>>> xmca-l-bounces@mailman.ucsd.edu>
>>>>
>>>>>> on behalf of Ed Wall < <mailto:ewall@umich.edu> ewall@umich.edu>
>>>>
>>>>
>>>>>>> Sent: Wednesday, July 30, 2014 3:00 PM
>>>>
>>>>>>> To: eXtended Mind, Culture, Activity
>>>>
>>>>>>> Subject: [Xmca-l] Re: NYTimes.com: Why Do Americans Stink at Math?
>>>>
>>>>>>>
>>>>
>>>>>>> Greg
>>>>
>>>>>>>
>>>>
>>>>>>> I agree with much of what you write below. However, there may
>> be
>>>>
>>>>>>> a
>>>>
>>>>>> disjunct between what you think is happening (and in many instances
>> I
>>>>
>>>>>> agree with you) and the shape of the denting I am speaking about. I
>>>>
>>>>>> begin my methods courses talking about the commitments I bring to
>>>>
>>>>>> teaching (stressing they are mine and that teachers and pre-service
>>>>
>>>>>> teachers are welcome to push back)
>>>>
>>>>>>>
>>>>
>>>>>>> 1. I believe in promoting collective student and teacher engagement
>>>>
>>>>>> i(and I meant both!)
>>>>
>>>>>>> 2. I believe in having students do substantial mathematical work
>>>>
>>>>>>> (and
>>>>
>>>>>> that is where the constraints of the context can come into play -
>>>>
>>>>>> don't necessarily read into this 'new math' or tedious computations)
>>>>
>>>>>>> 3. I believe in taking my students' thinking seriously (this
>>>>
>>>>>>> includes
>>>>
>>>>>> (mis)understandings!!)
>>>>
>>>>>>>
>>>>
>>>>>>> I have yet, by the way, to find an instance (and that includes
>>>>
>>>>>>> school
>>>>
>>>>>> location and students, testing, whatever) where such commitments are
>>>>
>>>>>> impossible or, in a pragmatic sense, even moderately difficult (most
>>>>
>>>>>> often the difficulty is learning to value one's students which is
>>>>
>>>>>> more of a choice although one needs to be aware of the possibility).
>>>>
>>>>>> I would very much appreciate your suggesting some instances where
>>>>
>>>>>> such commitments were situationally impossible. My students and I
>>>>
>>>>>> (teachers and pre-service
>>>>
>>>>>> teachers) then spend a semester (and perhaps more) together - with
>>>>
>>>>>> feedback from classroom and field experiences - figuring out what
>>>>
>>>>>> kind of teaching (keeping in mind my commitments) can be sustained
>>>>
>>>>>> (and it will differ and they need to know this and accommodate to
>>>>
>>>>>> this). I am not unusual (perhaps read 'rare' - smile). In fact I
>> have
>>>>
>>>>>> a number of colleagues who are considerably more capable.
>>>>
>>>>>>>
>>>>
>>>>>>> Philip Jackson (or was it Dan Lortie) used to talk about the
>>>>
>>>>>> apprenticeship of observation. People, he argued, learn to teach -
>>>>
>>>>>> for the most part - by observing as students in regular classroom.
>>>>
>>>>>> That should give one pause for a variety of reasons. I have sat
>>>>
>>>>>> through numerous faculty meetings where students are mentioned in
>>>>
>>>>>> less than a respectful fashion (and have heard anecdotes where that
>>>>
>>>>>> carried into the college classroom). I have heard elementary
>> teachers
>>>>
>>>>>> spoken of quite disparagingly by faculty in Arts & Sciences and,
>>>>
>>>>>> while I agree their expertise is not always of the highest
>> 'academic'
>>>>
>>>>>> quality, it is not clear to me that, in their own field of study,
>>>>
>>>>>> they are not more capable than their detractors. I have also seen an
>>>>
>>>>>> instructor continually stress 'nice' or 'comfortable' rather than
>>>> 'challenging' or 'uncomfortable.'
>>>>
>>>>>>>
>>>>
>>>>>>> I admit my commitments have hooks in them; for instance, what
>> is
>>>>
>>>>>> substantial mathematics (you need to know some mathematics to figure
>>>>
>>>>>> this out); what is collective teacher and student engagement (you
>>>>
>>>>>> need to know some pedagogy to figure this out) and what does it mean
>>>>
>>>>>> to respect student thinking in view of the previous (you need to
>> know
>>>>
>>>>>> some mathematics and some pedagogy to figure this out). However,
>> they
>>>>
>>>>>> are a beginning and some of my students seem, in time, to grow into
>>> them
>>>> no matter the situation.
>>>>
>>>>>>>
>>>>
>>>>>>> Anyway, I can't say I'm blissfully optimistic, but I'm not
>>>>
>>>>>> pessimistic either. I do know that culturally we often don't work
>>>>
>>>>>> together; that we tend to get mired in the trivial; and we often
>>>>
>>>>>> 'demonize' the stranger. I hate to think that we will never choose
>>>>
>>>>>> otherwise. However, to choose otherwise seems very far from
>>>>
>>>>>> impossible in the formal schooling context.
>>>>
>>>>>>>
>>>>
>>>>>>> Ed
>>>>
>>>>>>>
>>>>
>>>>>>> On Jul 30, 2014, at 1:42 PM, Greg Thompson
>>>>
>>>>>>> < <mailto:greg.a.thompson@gmail.com> greg.a.thompson@gmail.com>
>>>>
>>>>
>>>>>> wrote:
>>>>
>>>>>>>
>>>>
>>>>>>>> Ed,
>>>>
>>>>>>>> Thanks for this wonderfully thoughtful reply. Very helpful.
>>>>
>>>>>>>>
>>>>
>>>>>>>> As for the teaching practices part, I entirely agree about the
>> need
>>>>
>>>>>>>> for thoughtful attention to teaching practices and agree that
>> great
>>>>
>>>>>>>> things
>>>>
>>>>>> can
>>>>
>>>>>>>> be accomplished locally. My sense, though, is that it takes great
>>>>
>>>>>> effort to
>>>>
>>>>>>>> sustain such smaller scale interventions (i.e. to make more than a
>>>>
>>>>>> dent).
>>>>
>>>>>>>> With regard to teaching practices, I would think that the way to
>>>>
>>>>>> approach a
>>>>
>>>>>>>> thoughtful teaching practice would be to start with the real
>>>>
>>>>>> constraints of
>>>>
>>>>>>>> context that teachers will regularly face and then try and figure
>>>>
>>>>>>>> out
>>>>
>>>>>> what
>>>>
>>>>>>>> kinds of teaching can be sustained given those constraints.
>>>>
>>>>>>>>
>>>>
>>>>>>>> That's where I'm most pessimistic. It is difficult for me to
>>>>
>>>>>>>> imagine developing responsible teaching practices that could be
>>>>
>>>>>>>> sustained on a larger scale given the cultural, institutional, and
>>>>
>>>>>>>> ideological context
>>>>
>>>>>> of
>>>>
>>>>>>>> schooling in the U.S. [and I might add that it seems like the
>>>>
>>>>>>>> history of teaching practice in the U.S. is a history where the
>>>>
>>>>>>>> same good ideas
>>>>
>>>>>> keep
>>>>
>>>>>>>> popping up and then fading from sight almost as quickly as they
>>>>
>>>>>> appeared].
>>>>
>>>>>>>>
>>>>
>>>>>>>> But I'm certainly open to ideas/suggestions for thoughtful
>>>>
>>>>>>>> pedagogical practices that are sustainable in the U.S. formal
>>>> schooling
>>>> context.
>>>>
>>>>>>>>
>>>>
>>>>>>>> -greg
>>>>
>>>>>>>>
>>>>
>>>>>>>>
>>>>
>>>>>>>> On Wed, Jul 30, 2014 at 10:11 AM, Ed Wall < <mailto:
>> ewall@umich.edu
>>>>
>>>>
>>>> ewall@umich.edu> wrote:
>>>>
>>>>>>>>
>>>>
>>>>>>>>> Comments below
>>>>
>>>>>>>>>
>>>>
>>>>>>>>> On Jul 30, 2014, at 11:33 AM, Greg Thompson
>>>>
>>>>>>>>> <greg.a.thompson@gmail.com
>>>>
>>>>>>>
>>>>
>>>>>>>>> wrote:
>>>>
>>>>>>>>>
>>>>
>>>>>>>>>> I was hoping that somebody might be able to comment on the
>>>>
>>>>>>>>>> situation
>>>>
>>>>>> of
>>>>
>>>>>>>>>> schooling in Japan and whether or not these hypotheses about the
>>>>
>>>>>> Japanese
>>>>
>>>>>>>>>> situation of schooling might bear out:
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>> 1. Teachers in Japan have time to develop their craft. 600
>> annual
>>>>
>>>>>> hours
>>>>
>>>>>>>>> of
>>>>
>>>>>>>>>> contact time for teachers in Japan vs. 1100 hours of contact
>> time
>>>>
>>>>>>>>>> in
>>>>
>>>>>> the
>>>>
>>>>>>>>>> U.S.
>>>>
>>>>>>>>>
>>>>
>>>>>>>>> Yes
>>>>
>>>>>>>>>
>>>>
>>>>>>>>>> 2. There is an ideology of childhood in Japan that values
>>>>
>>>>>>>>>> childhood
>>>>
>>>>>>>>> greatly
>>>>
>>>>>>>>>> and treats them as qualitatively distinct beings from
>> adolescents
>>>>
>>>>>>>>>> and adults, and thus suggests that they should be protected from
>>>>
>>>>>>>>>> the cruel
>>>>
>>>>>>>>> and
>>>>
>>>>>>>>>> harsh practice of "testing". But this also means that elementary
>>>>
>>>>>> school
>>>>
>>>>>>>>>> teachers are held in high regard.
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>
>>>>
>>>>>>>>> Yes. However, it doesn't necessarily follow that this is why
>>>>
>>>>>>>>> elementary school teachers are held in high regard
>>>>
>>>>>>>>>
>>>>
>>>>>>>>>> I guess the first seems a bit more factual but the second is
>> more
>>>>
>>>>>>>>>> of
>>>>
>>>>>> an
>>>>
>>>>>>>>>> hypothesis, but if they bear out as important factors for
>>>>
>>>>>>>>>> enabling the
>>>>
>>>>>>>>> kind
>>>>
>>>>>>>>>> of learning that Green describes, then it seems to me that even
>>>>
>>>>>>>>>> if
>>>>
>>>>>> there
>>>>
>>>>>>>>>> were to be a huge push for training teachers in the U.S.,
>>>>
>>>>>>>>>> teachers
>>>>
>>>>>> would
>>>>
>>>>>>>>>> quickly revert to what we currently lament about teaching in the
>>>> U.S.
>>>>
>>>>>> not
>>>>
>>>>>>>>>> because they are bad teachers or don't know how to teach in the
>>>>
>>>>>>>>>> more complex manner but rather simply because, with some rare
>>>>
>>>>>>>>>> exceptions,
>>>>
>>>>>> it
>>>>
>>>>>>>>> is
>>>>
>>>>>>>>>> IMPOSSIBLE to teach in the more desirable manner given the
>>>>
>>>>>>>>>> ridiculous amount of contact time and the fact that in the
>>>>
>>>>>>>>>> American ideology of childhood, the teaching of children is not
>>>> valued particularly highly.
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>
>>>>
>>>>>>>>> This doesn't follow. It is possible and it is possible in highly
>>>>
>>>>>>>>> urban areas (and I amy misunderstand you use of the word 'rare').
>>>>
>>>>>>>>> That
>>>>
>>>>>> doesn't
>>>>
>>>>>>>>> mean that it is necessarily valued or supported by the
>>>> powers-that-be.
>>>>
>>>>>>>>> There are a few more things to add to your facts: There is a
>>>>
>>>>>>>>> national curriculum in Japan and there is a reasonably effective
>>>>
>>>>>>>>> mentoring
>>>>
>>>>>> system
>>>>
>>>>>>>>> (largely teacher instigated). A 'fact' (and perhaps this is
>>>>
>>>>>>>>> anecdotal)
>>>>
>>>>>> is
>>>>
>>>>>>>>> that when it was first realized that some interesting things were
>>>>
>>>>>> happening
>>>>
>>>>>>>>> in Japanese schools (e.g. lesson study), the collegiate Japanese
>>>>
>>>>>> community
>>>>
>>>>>>>>> was caught, to a large degree, unaware. 'Master' lesson are
>>>>
>>>>>>>>> published
>>>>
>>>>>> by
>>>>
>>>>>>>>> teachers.
>>>>
>>>>>>>>>
>>>>
>>>>>>>>>> In light of this, it seems a Sisyphean feat to try to change
>>>> teachers'
>>>>
>>>>>>>>>> teaching practices without changing the cultural context in
>> which
>>>>
>>>>>> those
>>>>
>>>>>>>>>> teachers work. And changing cultural contexts is perhaps even
>>>>
>>>>>>>>>> more difficult still.
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>
>>>>
>>>>>>>>> That was why I suggested a look at the Netherlands (which seem to
>>>>
>>>>>>>>> do as well or better than the Japanese). Of course, some of this
>>>>
>>>>>>>>> can still be explained because of cultural differences and how
>>>> teachers are viewed.
>>>>
>>>>>>>>>
>>>>
>>>>>>>>>> Maybe we should stop looking to teaching practices in formal
>>>>
>>>>>> schooling in
>>>>
>>>>>>>>>> the U.S. as a site of change?
>>>>
>>>>>>>>>> Maybe better to look outside and beyond schools altogether?
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>
>>>>
>>>>>>>>> Perhaps we should do as you suggest (and, to a limited extent and
>>>>
>>>>>>>>> in a sense, something like this has been done). However, it might
>>>>
>>>>>>>>> also be a
>>>>
>>>>>> good
>>>>
>>>>>>>>> idea to look at teaching practices in a thoughtful way. I have
>>>>
>>>>>>>>> seen
>>>>
>>>>>> very
>>>>
>>>>>>>>> little of this happening over the years. I was just talking to a
>>>>
>>>>>> colleague
>>>>
>>>>>>>>> today and, although we love our work in urban areas, we admit to
>>>>
>>>>>>>>> making only a small dent. We also admit to being underwhelmed by
>>>>
>>>>>>>>> views of education prevalent in many schools of education. It is
>>>>
>>>>>>>>> getting
>>>>
>>>>>> steadily
>>>>
>>>>>>>>> worse.
>>>>
>>>>>>>>>
>>>>
>>>>>>>>>
>>>>
>>>>>>>>>> Too pessimistic?
>>>>
>>>>>>>>>> -greg
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>
>>>>
>>>>>>>>> Pessimism is fine, but simply pessimism can be self limiting;
>>>>
>>>>>>>>> however, that is an opinion and not a fact.
>>>>
>>>>>>>>>
>>>>
>>>>>>>>> Ed
>>>>
>>>>>>>>>
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>> On Wed, Jul 30, 2014 at 6:02 AM, Ed Wall < <mailto:
>>> ewall@umich.edu>
>>>>
>>>> ewall@umich.edu> wrote:
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>>> Perhaps something of interest re this thread.
>>>>
>>>>>>>>>>>
>>>>
>>>>>>>>>>> Ed Wall
>>>>
>>>>>>>>>>>
>>>>
>>>>>>>>>>>
>>>>
>>>>>>>>>>>
>>>>
>>>>>>>>>
>>>>
>>>>>> <
>>> http://www.nytimes.com/2014/07/29/opinion/joe-nocera-teaching-teachin
>>>>>
>>>>
>>>> http://www.nytimes.com/2014/07/29/opinion/joe-nocera-teaching-teachin
>>>>
>>>>
>>>>>> g.html?_r=0
>>>>
>>>>>>>>>>>> Some general comments (and I apologize for being so late to
>> the
>>>>
>>>>>>>>>>> conversation as I have been out of email contact)
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> Magdalen Lampert and Deborah Ball were both at Michigan State
>>>>
>>>>>>>>>>>> in the
>>>>
>>>>>>>>>>> late 80s. They both taught what might, in part, be an early
>>>>
>>>>>>>>>>> version
>>>>
>>>>>> of
>>>>
>>>>>>>>> the
>>>>
>>>>>>>>>>> Common Core to their students. I also taught math methods
>>>>
>>>>>>>>>>> beginning
>>>>
>>>>>> in
>>>>
>>>>>>>>> the
>>>>
>>>>>>>>>>> late 90s and also emphasized such an approach (I also did
>>>>
>>>>>>>>>>> similar as
>>>>
>>>>>> a
>>>>
>>>>>>>>> K-12
>>>>
>>>>>>>>>>> math teacher before moving onto college teaching). There is
>>>>
>>>>>>>>>>> little
>>>>
>>>>>> 'new'
>>>>
>>>>>>>>>>> math in the Common Core - perhaps a bit of 'old' math. However,
>>>>
>>>>>>>>>>> there
>>>>
>>>>>>>>> is a
>>>>
>>>>>>>>>>> very strong emphasis on kids making sense out of what they are
>>>>
>>>>>>>>>>> doing
>>>>
>>>>>> (I
>>>>
>>>>>>>>>>> apologize for being brief, but this is a moment between
>> meetings
>>>>
>>>>>>>>>>> at a conference devoted to such 'strange' notions as helping
>>>>
>>>>>>>>>>> kids making
>>>>
>>>>>>>>> sense).
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> There are problems with the Common Core as written down: it is
>>>>
>>>>>>>>>>>> being
>>>>
>>>>>>>>>>> forced down teachers' throats; it has been tied into high
>> stakes
>>>>
>>>>>> testing
>>>>
>>>>>>>>>>> (which, by the way, occurs at places in a student's life in
>>>>
>>>>>>>>>>> Japan);
>>>>
>>>>>>>>> there
>>>>
>>>>>>>>>>> are some debatable differences in the age sequencing of topics;
>>>>
>>>>>>>>> teachers to
>>>>
>>>>>>>>>>> be have often not been prepared for such teaching in their
>>>>
>>>>>>>>>>> college
>>>>
>>>>>>>>> courses;
>>>>
>>>>>>>>>>> and more.
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> Some of these problems may be ironed out with time; however,
>>>>
>>>>>>>>>>>> the
>>>>
>>>>>>>>>>> training and culture of teaching (see Jackson and Lortie, even
>>>>
>>>>>>>>>>> if
>>>>
>>>>>>>>> somewhat
>>>>
>>>>>>>>>>> dated) in the US is still a bit grim.
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> So a few summary points:
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> Teaching that is, more or less, in sync with the Common Core
>>>>
>>>>>>>>>>>> has
>>>>
>>>>>>>>>>> been practiced for years in the US. Teacher training that is in
>>>>
>>>>>>>>>>> sync
>>>>
>>>>>>>>> with
>>>>
>>>>>>>>>>> the Common Core has been available for years in the US. Lesson
>>>>
>>>>>>>>>>> study Japanese style may be more possible with an agreed upon
>>>>
>>>>>>>>>>> core
>>>>
>>>>>> (although
>>>>
>>>>>>>>> one
>>>>
>>>>>>>>>>> might look to the Netherlands to see what works well for them
>>>>
>>>>>>>>>>> rather
>>>>
>>>>>>>>> than
>>>>
>>>>>>>>>>> Japan).
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> An interesting question for those of us who are involved in
>>>>
>>>>>>>>>>>> teacher
>>>>
>>>>>>>>>>> training might be "Why do so many teachers find the Common Core
>>>>
>>>>>>>>> Standards
>>>>
>>>>>>>>>>> so threatening - factoring out the forcing and testing)?" What
>>>>
>>>>>>>>>>> (from
>>>>
>>>>>> the
>>>>
>>>>>>>>>>> 4th grade standards, for example):
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> . Use place value understanding and properties of operations
>>>>
>>>>>>>>>>>> to
>>>>
>>>>>>>>>>> perform multi-digit arithmetic.
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> . Make sense of problems and persevere in solving them
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> do some elementary teachers find difficult and threatening?
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> Again apologies for being very, very short about a very large
>>>>
>>>>>>>>>>>> and
>>>>
>>>>>> very
>>>>
>>>>>>>>>>> complex problem.
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> Ed
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>> On Jul 28, 2014, at 2:25 PM, Katherine Wester Neal
>>>>
>>>>>>>>>>>> < <mailto:wester@uga.edu> wester@uga.edu>
>>>>
>>>>
>>>>>>>>>>> wrote:
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>> What an interesting article! I am thinking about the lack of
>>>>
>>>>>>>>>>>>> focus
>>>>
>>>>>> on
>>>>
>>>>>>>>>>> specific contexts in the article's discussion of teaching and
>>>>
>>>>>> learning
>>>>
>>>>>>>>> to
>>>>
>>>>>>>>>>> teach as a practicing teacher. Is it possible to go about such
>>>>
>>>>>>>>>>> change
>>>>
>>>>>>>>> (from
>>>>
>>>>>>>>>>> "old" math to new math or Common Core math) with little/no
>>>>
>>>>>> consideration
>>>>
>>>>>>>>>>> for what kinds of teaching might work in a particular school
>>>>
>>>>>>>>>>> culture
>>>>
>>>>>> or
>>>>
>>>>>>>>> the
>>>>
>>>>>>>>>>> social context of a given classroom? I think less of a
>>>>
>>>>>>>>>>> standardized approach (here, everyone do this) and more focus
>> on
>>>>
>>>>>>>>>>> what works
>>>>
>>>>>> locally
>>>>
>>>>>>>>>>> (here are some ideas; now decide what might work for you) might
>>>>
>>>>>>>>>>> help teachers learn to teach Common Core math in a way that
>>>>
>>>>>>>>>>> actually
>>>>
>>>>>> works in
>>>>
>>>>>>>>>>> their particular context. To adapt phrase from Magdalene
>>>>
>>>>>>>>>>> Lampert, it
>>>>
>>>>>>>>> might
>>>>
>>>>>>>>>>> bring about more sustainable change as they are "re-learning
>>>>
>>>>>> teaching"
>>>>
>>>>>>>>> in
>>>>
>>>>>>>>>>> their schools.
>>>>
>>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>> Because Common Core math is so different, perhaps this
>>>>
>>>>>>>>>>>>> re-learning
>>>>
>>>>>>>>>>> teaching requires a radical new approach instead of the same
>> old
>>>>
>>>>>>>>>>> professional development. Learning through the Japanese
>>>>
>>>>>>>>>>> jugyokenkyu
>>>>
>>>>>>>>> method
>>>>
>>>>>>>>>>> sounds like it might be very useful, but there doesn't seem to
>>>>
>>>>>>>>>>> be a
>>>>
>>>>>> push
>>>>
>>>>>>>>>>> for reforming how teachers learn once they are in the field.
>>>>
>>>>>>>>>>> (Except
>>>>
>>>>>>>>> that
>>>>
>>>>>>>>>>> if enough of their students fail the Common Core-aligned tests,
>>>>
>>>>>>>>>>> they
>>>>
>>>>>>>>> will
>>>>
>>>>>>>>>>> eventually be out of a job.)
>>>>
>>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>> It seems nonsensical to implement incredibly high-stakes
>> tests
>>>>
>>>>>> without
>>>>
>>>>>>>>>>> significant investment in re-learning teaching and with, as far
>>>>
>>>>>>>>>>> as I
>>>>
>>>>>>>>> know,
>>>>
>>>>>>>>>>> no research on how to learn to teach Common Core as a
>> practicing
>>>>
>>>>>>>>> teacher.
>>>>
>>>>>>>>>>> I, too, wonder about how these issues are handled in Japan?
>>>>
>>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>> Katie
>>>>
>>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>> Katie Wester-Neal
>>>>
>>>>>>>>>>>>> University of Georgia
>>>>
>>>>>>>>>>>>> ________________________________________
>>>>
>>>>>>>>>>>>> From: <mailto:xmca-l-bounces@mailman.ucsd.edu>
>>>> xmca-l-bounces@mailman.ucsd.edu <
>>>>
>>>>>>>>> <mailto:xmca-l-bounces@mailman.ucsd.edu>
>>>> xmca-l-bounces@mailman.ucsd.edu>
>>>>
>>>>>>>>>>> on behalf of Huw Lloyd < <mailto:huw.softdesigns@gmail.com>
>>>>
>>>> huw.softdesigns@gmail.com>
>>>>
>>>>>>>>>>>>> Sent: Monday, July 28, 2014 12:58 PM
>>>>
>>>>>>>>>>>>> To: eXtended Mind, Culture, Activity
>>>>
>>>>>>>>>>>>> Subject: [Xmca-l] Re: Fwd: NYTimes.com: Why Do Americans
>> Stink
>>>>
>>>>>>>>>>>>> at
>>>>
>>>>>>>>> Math?
>>>>
>>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>> On 28 July 2014 16:46, Greg Thompson
>>>>
>>>>>>>>>>>>> < <mailto:greg.a.thompson@gmail.com>
>> greg.a.thompson@gmail.com
>>>>
>>>>
>>>>
>>>>>>>>> wrote:
>>>>
>>>>>>>>>>>>> [...]
>>>>
>>>>>>>>>>>>> These students had learned
>>>>
>>>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>>> incredibly well how to solve recipe Physics but they had no
>>>>
>>>>>>>>>>>>>> idea
>>>>
>>>>>>>>> about
>>>>
>>>>>>>>>>> how
>>>>
>>>>>>>>>>>>>> the basic principles of Physics worked.
>>>>
>>>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>> Greg,
>>>>
>>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>> I would say the ethics of the situation go deeper than simply
>>>>
>>>>>>>>> (un)learnt
>>>>
>>>>>>>>>>>>> capabilities, but rather to the development of the student's
>>>>
>>>>>> creative
>>>>
>>>>>>>>>>>>> capabilities (or, rather, the stunting of them).
>>>>
>>>>>>>>>>>>>
>>>>
>>>>>>>>>>>>> Best,
>>>>
>>>>>>>>>>>>> Huw
>>>>
>>>>>>>>>>>>
>>>>
>>>>>>>>>>>
>>>>
>>>>>>>>>>>
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>>
>>>>
>>>>>>>>>> --
>>>>
>>>>>>>>>> Gregory A. Thompson, Ph.D.
>>>>
>>>>>>>>>> Assistant Professor
>>>>
>>>>>>>>>> Department of Anthropology
>>>>
>>>>>>>>>> 883 Spencer W. Kimball Tower
>>>>
>>>>>>>>>> Brigham Young University
>>>>
>>>>>>>>>> Provo, UT 84602
>>>>
>>>>>>>>>> <http://byu.academia.edu/GregoryThompson>
>>>> http://byu.academia.edu/GregoryThompson
>>>>
>>>>>>>>>
>>>>
>>>>>>>>>
>>>>
>>>>>>>>>
>>>>
>>>>>>>>
>>>>
>>>>>>>>
>>>>
>>>>>>>> --
>>>>
>>>>>>>> Gregory A. Thompson, Ph.D.
>>>>
>>>>>>>> Assistant Professor
>>>>
>>>>>>>> Department of Anthropology
>>>>
>>>>>>>> 883 Spencer W. Kimball Tower
>>>>
>>>>>>>> Brigham Young University
>>>>
>>>>>>>> Provo, UT 84602
>>>>
>>>>>>>> <http://byu.academia.edu/GregoryThompson>
>>>>
>>>> http://byu.academia.edu/GregoryThompson
>>>>
>>>>>>>
>>>>
>>>>>>>
>>>>
>>>>>>
>>>>
>>>>>>
>>>>
>>>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>
>>
>
>
>
> --
> Gregory A. Thompson, Ph.D.
> Assistant Professor
> Department of Anthropology
> 883 Spencer W. Kimball Tower
> Brigham Young University
> Provo, UT 84602
> http://byu.academia.edu/GregoryThompson
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