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

Wed Oct 9 09:40:02 PDT 2019

Yes, one would certainly want to consistently foster the same approach
across a whole curriculum, and not merely subject-specific approaches.

There is evidence in Davydov's texts in addition to many other translated
papers. But the necessity for the agent to be active in their own
transformation is often overlooked.

The motivating force for any such undertaking, however, is liable to
originate from personal experience. One does not need to read one hundred
papers to appreciate the virtue of this approach. Personal experience can
reveal this. The papers are useful for showing the systematic nature of the
process.

It is not an easy situation. For instance, my own children go to a
conventional school, and no one else in my close familiar shares these
appreciations.

However, I have also had some experiences that put the whole project of
"cognitive development" within a wider context, that relate, for example,
some of my personal discoveries to texts in the Upanishads. And so I find
myself being more open to a plurality of supportive environments and
allowing for hazard and circumstance in which agencies are able to find
their appropriate place.

Best,
Huw

On Wed, 9 Oct 2019 at 09:37, Baloncuk Tr <aysekan@gmail.com> wrote:

> Huw, I agree with you. Students shouldn’t be a passive audience in
> instruction. But there are always several competing theories about concepts
> in formal disciplines and one of these theories becomes dominant in
> directing practice. Choosing one of them in shaping the instruction and
> curriculum is unavoidable.  I know that choosing the most dominant one is
> not always good. My question is or the thing I am confused about is: Which
> one should we choose as developmental educators? How can we choose the one
> which can potentially encourage the kind of development we want in
> students?  how can be sure that we are using the correct one?
>
>
> Best
>
> Ayşe
>
> Huw Lloyd <huw.softdesigns@gmail.com>, 7 Eki 2019 Pzt, 21:55 tarihinde
> şunu yazdı:
>
>> Misconceptions may be actively used by engendering situations in which
>> genuine thinking may begin. This is to distinguish the "juicy" vs "dry"
>> pedagogy, commonly ascribed to STEM topics from outside (from an abstracted
>> position). The learning is concrete because it is the situation that
>> provides everything necessary. The experience of the problem provides its
>> own answers. One has to learn to read the situation. But when I say "the
>> situation provides everything", this situation is contingent upon the
>> agent's impressing the circumstances upon themselves, i.e. the impressing
>> is part of the situation. This cannot be achieved by merely showing up and
>> becoming a passive audience.
>>
>> The real emphasis in developmental education entails this autonomy (both
>> personal and shared), initiative and directed-ness, which of course need
>> not be about mathematics, but something of relevance and interest. This is
>> opposite to conventional schooling in which "learning to think" is treated
>> as a side-effect. In developmental education, acquiring competence with the
>> subject matter is a side-effect of, amongst other things, learning to
>> objectively read situations.
>>
>> I suspect that the STEM commonalities emphasised are really about
>> assimilating a model or paradigm which does not necessarily bring one into
>> contact with the information (the informing) latent within situations, but
>> amongst competent STEM practitioners there are of course those who take an
>> active interest in how things work, and acquire more nuanced knowledge
>> about the nature of their knowing.
>>
>> Hopefully these pointers are helpful. I don't mean to imply that these
>> concerns are foreign to you, Ayşe. Rather it seems sensible to help keep
>> things clear for other readers.
>>
>> Best,
>> Huw
>>
>>
>>
>>
>>
>> On Mon, 7 Oct 2019 at 16:35, Baloncuk Tr <aysekan@gmail.com> wrote:
>>
>>> 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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