communication resources, and digital video technology that can be used to capture outstanding
examples of effective practices. My personal experiences suggest that many outstanding technologists
residing in advanced economies would welcome the opportunity to take on this challenge.
A virtue of equal educational opportunity is that it often expands the size of the pie in ways that generate
breakthrough conceptualizations of educational that benefit everyone. Here, at the risk of being
excessively self-centered, permit me to call upon my own experiences verify this claim.
A decade ago, I spent a sabbatical year teaching mathematics in a religious-based middle school that
enrolled a large population of English language learners, from many different countries. Nearly all lived in
poor households, and many were living in the US without the official permission of governmental
authorities. Naturally, as an “eleventh-generation non-voluntary migrant minority US resident”, I
identified personally with the obstacles these students would be encountering.
I quickly discovered that the standard mathematics textbook was pedagogically useless. In my
desperate search for a alternative to the textbook I asked my students to supply me with drawings,
pictures, maps, tapestries, and other iconic representations used in their homes and communities. We
then proceeded to collectively identify strategies for using these naturally occurring representations to
create mathematics problems. Because I am a typical mono-lingual American academic, I relied upon
my students, and they upon each other, to determine the nature of these new pedagogical strategies.
Somehow, we collectively managed to cobble together a set of representation-rich mathematics
curriculum materials that proved to be remarkably effective in helping them benefit more fully from the
English-medium curriculum materials we were required to use. A surprisingly high proportion of my
students achieved normative levels of mathematically proficiency by drawing their skills in “reading” and
interpreting a multitude of naturally occurring representations to reduce the mathematics learning gap
between themselves and their more linguistically advantaged students.
Due to these experiences, I challenge the prospective teachers of high school mathematics and science
enrolled in my classes at the University of California at Berkeley to use similar representation-rich
materials to support native speakers of English. These future teachers tell me that materials have proven
to be as beneficial to mainstream students as they were for the language minority students I learned so
much from a decade ago.
Imagine what lessons might be leaned if it were possible to explore similar exercises in curriculum design
with other language minority groups in other geopolitical settings. My hunch is that were it possible for
geographically dispersed mathematics teachers, working in geopolitically and linguistically diverse
educational settings to share their experiences, many, many important lessons would be generated.
The use of easy navigable digital video, distributable over the Internet, would make these lessons
available to everyone. Moreover, the availability of lessons in this format would reduce the importance
of textual accounts of these lessons, while also giving those creating and using these lessons to retrieve
and re-interpret their significance continuously.