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[Xmca-l] Re: NYTimes.com: Why Do Americans Stink at Math?


        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. 


On Jul 30, 2014, at 10:01 PM, mike cole <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 <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 <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: xmca-l-bounces@mailman.ucsd.edu <xmca-l-bounces@mailman.ucsd.edu>
>> on behalf of Ed Wall <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 <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 <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 <ewall@umich.edu> wrote:
>>>>>>> Perhaps something of interest re this thread.
>>>>>>> Ed Wall
>> http://www.nytimes.com/2014/07/29/opinion/joe-nocera-teaching-teaching.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 <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: xmca-l-bounces@mailman.ucsd.edu <
>>>>> xmca-l-bounces@mailman.ucsd.edu>
>>>>>>> on behalf of Huw Lloyd <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 <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
>>>> --
>>>> 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