[Xmca-l] Re: V. V. Davydov’s mathematics curriculum

[Baloncuk Tr]

The dialogue we have here is helping me clear some points about the
project.

Huw, you wrote that “content is a vehicle not the goal”. Because of the way
we teach a content, or a concept may lead to a type of concept which is
outdated or false (or in Vygotsky’s words everyday concepts) in a formal
discipline. As the students move to higher grades, the content or concepts
become more formal and abstract in the way they are handled in the
discipline itself.  Students may form misconceptions because of the way we
teach. They have difficulty learning the concepts in later grades. For
example, most students in Turkey do not want to take advanced math’s
courses. They fail in these courses because they cannot overcome their
misconceptions. They avoid the discipline altogether. For example, math’s
departments in universities have difficulty in getting students in Turkey.
Most students do not want to study math’s because they must study the
formal content at the university level. There is also the STEM (science,
technology, Engineering, Math’s) education, which is very popular now in
Turkey and all over the world. I think countries are in a race for
technological and scientific advancement. Even pre-K students are
encouraged to think like engineers. Even though I think taking things to
extreme points is unnecessary, conveying the content in the way a formal
discipline describes is the goal. As a teacher, I find it more difficult to
teach students who have false and uncomplete knowledge than students who
have no knowledge. Because I need to get them forget about their
misconceptions first.

    Best Ayşe

Huw Lloyd <huw.softdesigns@gmail.com>, 7 Eki 2019 Pzt, 12:45 tarihinde şunu
yazdı:

> "Nicolas Bourbaki" is a pseudonym for a group. I am not familiar with the
> details of their set-theoretic approach, however the emphasis on the
> approach taken by Davydov was (is) concrete -- the ideas are intended to be
> experienced. I doubt it is a good idea to associate the two as sharing a
> philosophy or core set of ideas. Davydov's approach entails a compact set
> of understandings pertaining to the history of ideas, a unit of analysis
> (of a domain), the presentation according to the participants (zpd etc),
> the appropriate orientation, and subject familiarity (expertise). This is
> all constellated in the experience, and might be considered a necessity for
> any developmental approach. The subject matter appearance might be viewed
> as abstract -- as a collection of notations about aspects of things -- but
> the point of the developmental approach is to foster transformations in
> ways of understanding, construing, thinking, etc. The emphasis is upon this
> transformation, which is the dialectical aspect. The formal content is a
> vehicle, it isn't the goal.
>
> Best,
> Huw
>
>
>
> On Sun, 6 Oct 2019 at 21:39, Baloncuk Tr <aysekan@gmail.com> wrote:
>
>> Thanks so much for the ideas on the project, Ed.
>>
>> I began to think that the project will be more difficult than I thought.
>> I think I need a math teacher who knows the mathematical theories very
>> well. But it is very difficult to find such a teacher. Math teachers take
>> math and education courses at the same time in Turkey. They may not know
>> the theories of the discipline they teach very well because of the
>> education they get in university. Knowing the recent developments in the
>> field you teach is very important for developmental teaching. As all you
>> know, quality of the content (scientific vs. everyday concepts) is
>> important in developmental teaching.
>>
>> Ed, what you said about the abandonment of Davydov’s curriculum because
>> of the teachers made me think about the “New Math” curriculum movement in
>> the USA. In articles and books about history of math education I read that
>> After Russia launched the Sputnik 1, American public experienced a period
>> of fear and anxiety about technological gap between the USA and Soviet
>> Union. In order to boost the science education, a group of American
>> mathematics professors prepared a new curriculum based on Bourbaki’s
>> extremely abstract and formal mathematical theory. At first public welcomed
>> the change. After a while, parents, teachers, policy makers opposed the
>> change because the new curriculum was too far outside of students' ordinary
>> experience. In the end, the curriculum was abandoned. By the way, Davydov
>> too used Bourbaki’s mathematical theory to design his curriculum.
>>
>> Ayşe Tokaç
>>
>> Edward Wall <ewall@umich.edu>, 6 Eki 2019 Paz, 00:33 tarihinde şunu
>> yazdı:
>>
>>>     Sorry as I saw this but was short of time. I recommend you take
>>> careful note of what Huw says about ‘instruction.’
>>>
>>>      Anyway, most of the attempts re the Davydov ‘curriculum’ in the US
>>> that I knew about have been abandoned because, it seems, ‘qualified’
>>> teachers were not readily available (and, in my opinion, that is very
>>> unlikely to change). Perhaps the most substantial attempt in recent times
>>> was at the University of Hawaii; there still may be some mention and a text
>>> was ‘promised', but I have never been able find out much and I have tried
>>> several times.
>>>     That said, there are elementary curricula/instruction - and I only
>>> mention this as an aside - that attempt to do substantial mathematics in a
>>> somewhat dialogic manner; NYC, Ann Arbor, and the Netherlands are sites.
>>> The difficult problem is that while one might argue - I don’t argue so -
>>> that we have a theory of learning re mathematics,  we don’t really have,
>>> and this is an opinion, a robust one - there are some reasonable ones, but
>>> they are anemic - about teaching or more importantly about studying (the
>>> intersection of teaching and learning) mathematics.
>>>
>>>       There are English translations of articles published here and
>>> there by Davydov and collaborators about, I assume the thoughts behind the
>>> curricula, the curriculum; e.g. 'The Object Source of the Concept of
>>> Fractions.' I think I even have a paper somewhere where Davydov explains
>>> some of the details of the curricular sequence. As regards instruction, I
>>> would assume Galina Zuckerman would be the person to contact and I suspect
>>> Anna Marjanovic-Shane would have useful things to say. Peg Griffin was the
>>> first to give me a sketch of classroom interactions (very helpful in my
>>> theorizing).
>>>
>>>       There are several private schools in Russia (or where when I last
>>> looked) and, while not touted as the most influential (which means little
>>> in the climate around mathematics instruction), there is, at least, one
>>> existent that still appears to follow Davydov.
>>>
>>>       If you get something off the ground in English and ramp it up in
>>> some reasonable manner, there are a lot of mathematical educators who
>>> likely would flock to your door :)
>>>
>>> Ed Wall
>>>
>>> Imagination was given to man to compensate him for what he is not, and a
>>> sense of humor was provided to console him for what he is.
>>>
>>> > On Oct 4, 2019, at  6:34 AM, Baloncuk Tr <aysekan@gmail.com> wrote:
>>> >
>>> > Hi,
>>> >
>>> > Thank you for taking the time and sending me the articles and the
>>> books.  They are great for the project because I did not have some of them.
>>> What I needed to find was the textbooks for elementary students written by
>>> Davydov and his associates. I guess I misworded my request. The citation
>>> for the books are:
>>> >
>>> >
>>> >
>>> > Davydov, V. V., Gorbov, S. F., Mikulina, G. G., and Saveleva, O. V.
>>> (1999). Mathematics: Class 1. Edited by J. Schmittau. Binghamton, NY: State
>>> University of New York.
>>> >
>>> > Davydov, V. V., Gorbov, S. F., Mikulina, G. G., and Saveleva, O. V.
>>> (2000). Mathematics: Class 2. Edited by J. Schmittau. Binghamton, NY: State
>>> University of New York. Davydov, V. V., Gorbov, S. F.,
>>> >
>>> > Mikulina, G. G., Savyelyeva, O. V., and Tabachnikova, N. L. (2001).
>>> Mathematics: 3rd Grade. Edited by J. Schmittau. Binghamton, NY: State
>>> University of New York.
>>> >
>>> >
>>> > These are English translations of the original books. I read Galina’s
>>> email and I will look at the website she mentioned with a Russian friend
>>> from my school. I could not understand anything right now because I don’t
>>> speak Russian. I will post you about what I find in the website. Thank you
>>> again for your immediate responses. I am happy to be part of this group.
>>> >
>>> > Lots of love from Turkey
>>> >
>>> > Ayşe Tokaç
>>> >
>>> > Selçuk University
>>> >
>>> >
>>> > Huw Lloyd <huw.softdesigns@gmail.com>, 4 Eki 2019 Cum, 14:24
>>> tarihinde şunu yazdı:
>>> > A result! Thank you, Galina.
>>> >
>>> > Attached is a coarse google translation of the first doc.
>>> >
>>> > On Fri, 4 Oct 2019 at 11:12, Galina Zuckerman <
>>> galina.zuckerman@gmail.com> wrote:
>>> > The publishing house "BINOM" recently published all math textbooks for
>>> elementary school children, designed by Davydov and his followers.
>>> > http://lbz.ru/books/936/
>>> > You can order the books through this  publishing house.
>>> > Manuals for teachers are available free:
>>> > http://lbz.ru/metodist/authors/elkonin-davydov/6/
>>> > Enjoy!
>>> >
>>> >
>>> >
>>> >
>>> > On Thu, Oct 3, 2019 at 11:04 PM Huw Lloyd <huw.softdesigns@gmail.com>
>>> wrote:
>>> > There are example fragments in Peter Moxhay's 2008 translation of
>>> "Problems of Developmental Instruction". There are example fragments in
>>> numerous JREEP papers too, from psychologists practicing developmental
>>> instruction (Kharkov school and others).
>>> >
>>> > Although not strictly part of a course "content', the core of this
>>> material is the completely different approach to "instruction"
>>> ("instruction" is perhaps a poor choice of label, given its connotations).
>>> In that respect, if one tried to transplant merely the curriculum to a
>>> conventional approach, it would be clear that one was not achieving
>>> developmental instruction. Hence, being able to work out an appropriate
>>> curriculum might be considered a minimum qualification for delivering it.
>>> >
>>> > A while back, Galina Zuckerman (cc'd), contributed a few emails
>>> pertaining to her work, which might be considered as continuing to carry
>>> the flag for Davydov's approach. My impression was that she had made
>>> advances on the dialogic side of things with respect to dynamics of
>>> engagement.
>>> >
>>> > Best,
>>> > Huw
>>> >
>>> >
>>> >
>>> > On Thu, 3 Oct 2019 at 16:58, Baloncuk Tr <aysekan@gmail.com> wrote:
>>> > Dear all,
>>> >
>>> > I am a lecturer at Selcuk University in Turkey. I am focused now on a
>>> curriculum project on math’s education in primary grades. I would
>>> appreciate it if you can tell me how to find V. V. Davydov’s mathematics
>>> curriculum and math books in English or Russian.
>>> >
>>> > Thanks, and I hope to hear from you.
>>> >
>>> > Ayse Tokac
>>> >
>>> > Selcuk University
>>> >
>>>
>>>
>>>
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