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.
_______________________________________________
xmca mailing list
xmca@weber.ucsd.edu
http://dss.ucsd.edu/mailman/listinfo/xmca
Received on Mon Mar 31 12:37 PDT 2008