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:
  1. better prepared teachers; and
  2. 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.