Lines in the
Curriculum: A persistent obstruction to Achievement
connecting Algebra and Geometry
11
AM, March 29, 2010: Conference Room at MIND Institute
To understand the ambitions of this talk it helps to know this. The
topic of lines in the
curriculum has conceptual teaching difficulties that you can't solve only by applying the typical blue-ribon interventions:
- better prepared teachers; and
- assuring students have perfect educational beginnings.
My talk starts by showing that the subject matter, lines,
is approached astonishingly differently in moving from one class to
another. So differently, that
a student's ultimate success in using math concepts to
interpret data cannot be the result of a great 3rd grade
teacher, or sound understanding of the number line.
Rather, it requires an
epiphany later in teenage life, assuming students can stay in there
long enough for such a possibility. There should be a longer discourse
on why relying on #1 and #2 will fail. We don't do it here.
We use a particularly
resonant example (lines), to show there is a wipeout problem that isn't
covered by blaming the system of classes, locally at some magic spot.
That an epiphany is possible with administrators (at least an
enlightened one like Dennis Galligani) is documented in
http://www.math.uci.edu/~mfried/edlist-tech/gold02-08-98.html
. This is the story of Howard Thompson, who appears in my
talk, and my interaction with an administrator who got the point of
that story almost immediately.
That an epiphany is possible with older students – not necessary one
readily identified as exceptional – is documented in this paper.
Interactive E-Mail Assessment, MAA Vol. on Assessment, B. Gold, S.Z.
Keith, and W.A. Marion, eds., Assessment in Undergraduate Mathematics,
MAA Notes #49, Wash. DC, 1999, 80--84. http://www.math.uci.edu/~mfried/edlist-tech/gold02-08-98.pdf
This part of the story depended on technology to gather information
from an ordinary class, run by an ordinary instructor. The technology
is called I(nteractive)
Q(uestionnaire)s
(IQs). For
this, the style of programming was less critical than the
style of questioning. That is, the nature of the curricular assessment
is the crucial matter.
The talk does not discuss anything about IQs, or the
epiphanies that came to me from them. For more on them see http://www.math.uci.edu/~mfried/edlist-tech.html.