RE: [xmca] National Mathematics Advisory Panel

I believe there is a group at the University of Oregon that has had
enormous influence on the current U.S. administration's approach to these
matters. Maybe somebody can fill us in on that.

On Tue, 1 Apr 2008, Karen Wieckert wrote:

> Peter,
>
> I "googled" you and found that you are involved in a mathematics program in
> Portland Maine called The Theoretical Learning approach to mathematics.
> Let's take that program as an example.
>
> Is this a program in all of Portland schools? Do you treat it as a
> formative experiment? How do you evaluate the approach, and at what levels?
> What is the population? Etc.
>
> It is possible that you have all of the "data" to meet the report's
> criteria. If you do, it might be worth the effort to "market" the work so
> it would need to be considered along with the other work the Panel
> considered.
>
> If you do not, it might be worth the effort to ask why it cannot meet the
> criteria. For example, the criteria could intentionally be constructed so as
> to EXCLUDE your work. How and why does it do that? If each program asked
> this question, I wonder what would be found lacking -- the programs or the
> criteria?
>
> KEW
>
> -----Original Message-----
> From: xmca-bounces@weber.ucsd.edu [mailto:xmca-bounces@weber.ucsd.edu] On
> Behalf Of Peter Moxhay
> Sent: Monday, March 31, 2008 5:08 PM
> To: 'eXtended Mind, Culture, Activity' Subject: Re: [xmca] National
> Mathematics Advisory Panel
>
> Karen,
>
> I am especially interested in the "study methods," as you gave in the
> list from the report:
>
>> 4. Study methods
>> a) Randomized experiments or quasi-experiments with techniques to
>> control for bias
>> (matching, statistical control) or demonstration of initial
>> equivalence on important
>> pretest variables.
>> b) Attrition of less than 20% or evidence that the remaining sample
>> is equivalent to the
>> original sample on important variables
>
> My question is basically this -- I think of a formative experiment as
> something that is
> intended to create something new, something that does not yet exist.
> For example,
> the El'konin-Davydov program, which has tried to create, or project,
> a new type of thinking
> (theoretical thinking) in primary school children that did not exist
> previously (or existed
> only weakly). But what this new type of thinking looks like at any
> given age level, or the
> form of instruction required to achieve it, is not known before one
> conducts the experiment.
>
> Davydov writes somewhere, I think, of the formative experiment as
> related
> to a "projecting" type of science, which tries to "project" or "plan"
> something new
> (as in Plato's ideal republic), as opposed to the"verificational"
> type of science that
> has predominated since the scientific revolution.
>
> I am wondering whether or not a formative experiment type of pedagogical
> intervention can *ever* satisfy the criteria listed above. How can
> you talk
> about statistical controls or pretest variables if the result of the
> experiment is
> a kind of moving target?
>
> What does everyone think?
>
> Peter
>
>> Peter,
>>
>> What a very good question! I am not an educational researcher per
>> se, but a designer of information technologies. I am however
>> acquainted with the world of educational research from a long time
>> affiliation with my spouse! The use of "design experiments" which
>> may differ from what you suggest as "formative experiments" I
>> believe would need to fit within the criteria developed by report's
>> Subcommittee on Standards Of Evidence.
>>
>>> From Page. 7-9 from the REPORT OF THE SUBCOMMITTEE ON STANDARDS OF
>>> EVIDENCE—DRAFT 3//6/08
>> C. Instructional Practices Task Group
>> 1. Topics and content
>> a) Effects of instructional practice, teaching strategies, and
>> instructional materials on
>> mathematics achievement.
>> 2. Coverage
>> a) Published in a peer-reviewed journal or government report.
>> b) Published in English, 1976 or after.
>> 3. Study samples
>> a) Children, kindergarten through high school level.
>> 4. Study methods
>> a) Randomized experiments or quasi-experiments with techniques to
>> control for bias
>> (matching, statistical control) or demonstration of initial
>> equivalence on important
>> pretest variables.
>> b) Attrition of less than 20% or evidence that the remaining sample
>> is equivalent to the
>> original sample on important variables.
>>
>> Ka:ren
>>
>> -----Original Message-----
>> From: xmca-bounces@weber.ucsd.edu [mailto:xmca-
>> bounces@weber.ucsd.edu] On Behalf Of Peter Moxhay
>> Sent: Monday, March 31, 2008 12:14 PM
>> To: xmca@weber.ucsd.edu
>> Subject: Re: [xmca] National Mathematics Advisory Panel
>>
>> Karen, Mike and all:
>>
>> I have a couple of comments/questions on the panel's report, from a
>> Vygotskian point of view:
>>
>> 1) It seems to me that any discussion of the child's conceptual
>> understanding of number (see the excerpt below) refers to some aspects
>> of a merely empirical concept of number that is vaguely called "number
>> sense." Davydov's did his work on developing the child's true
>> concept of
>> number as early as the 1960's, or late 1950's, and provided some clear
>> and easily administered assessments for determining the level of
>> development of a child's concept of number. Why has Davydov's work had
>> virtually no effect on what educators mean by the concept of number,
>> even after so many decades? I agree with Mike that Jean Schmittau's
>> research is a big exception and well worth looking at.
>>
>> 2) On the "research criteria" quoted by Karen: Do such criteria
>> virtually rule out the formative experiment as a valid type of
>> research.
>> Or not?
>>
>> Regards,
>>
>> Peter
>>
>> [From the report:]
>> "Fluency with Whole Numbers
>> By the end of the elementary grades, children should have a robust
>> sense
>> of number. This sense of number must include understanding place
>> value,
>> and the ability to compose and decompose whole numbers. It must
>> clearly
>> include a grasp of the meaning of the basic operations of addition,
>> subtraction, multipli¬cation, and division, including use of the
>> commutative, associative, and distributive properties; the ability to
>> perform these operations efficiently; and the knowledge of how to
>> apply
>> the operations to problem solving. Computational facility rests on the
>> automatic recall of addition and related subtraction facts, and of
>> multiplication and related division facts. It requires fluency with
>> the
>> standard algorithms for addition, subtraction, multiplication, and
>> division. Fluent use of the algorithms not only depends on the
>> automatic
>> recall of number facts but also reinforces it. A strong sense of
>> number
>> also includes the ability to estimate the results of computations and
>> thereby to estimate orders of magnitude, e.g., how many people fit
>> into
>> a stadium, or how many gallons of water are needed to fill a pool."
>>
>> [And a snippet on research methods:]
>> "In general, these principles call for strongest confidence to be
>> placed in
>> studies that
>> . Test hypotheses
>> . Meet the highest methodological standards (internal validity)
>> . Have been replicated with diverse samples of students under
>> conditions that warrant generalization (external validity)"
>>
>> *** Please Note: ***
>> This email and its attachments may be confidential and are intended
>> solely for the use of the individual to whom it was addressed. Any
>> views or opinions expressed are solely those of the author and do not
>> necessarily represent those of the Portland Public School Department.
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>
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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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Received on Tue Apr 1 11:21 PDT 2008