From: Karen Wieckert <wieckertk who-is-at mail.belmont.edu>

Date: Tue Apr 01 2008 - 10:57:28 PDT

Date: Tue Apr 01 2008 - 10:57:28 PDT

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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*

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*>
*

*>
*

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Received on Tue Apr 1 10:57 PDT 2008

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