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Re: education, technology & chat (The Mathematics of it)
What you write here makes perfect sense to me and resonates with my
experience of the Davydov math curriculum.
But are you arguing for adding measurement to a curriculum that
develops the concept of number in the traditional way (through the
counting up of discrete objects)? Or for placing measurement at the
center of the curriculum (as Davydov does) -- as the genetic source
of the theoretical concept of number?
Also, I would be interested to know if, like Davydov, you have
with children *modeling* the action of measurement, say with a formula
A = nE, where A is a quantity, E is a unit, and n the the number.
argues that it is only via the model that a generalization is formed.
Measuring sets a precedent that units can be ever further
breaking ground in which rational numbers can be planted in later
years. Measurement lessons provide a foil to developing
all numbers are whole and that number itself is a countable entity.
lessons on fractions may take advantage of a measurement curriculum
essentially about a whole and its partitioned equal sized units.
with such an introduction to measurement may encounter fractions in
grade more prepared to grapple with the idea that 2/3 is 1/3 plus 1/3
that 3/4 is the same amount as 6/8 or that four halves is the same as
It is, after all, a matter of picking your unit and partitioning the
A measurement curriculum can enrich children's mathematics
A useful curriculum goes beyond direct object comparisons and seriation
activities. It does more than provide opportunities to cover space
non-conventional units. It does not stop at teaching techniques for
mechanically applying rulers or balance scales and reading numbers from
them. The curriculum gives value to measurement activities by
them: engaging students to focus on whole-part relations, thinking
what they are counting, recognizing what makes a unit sensible to
improving specific skills that serve the essential ideas. The
provides a context for cultural tools like rulers and scales to be
as ways to take a shortcut through the iteration of measurement units
the counting of them. It provides a context for estimated
measurements as a
part of checking to see when a measurement result should be doubted
procedures should be executed again so that the goal of measurement is
The quantity is described with precision.