Abstract

Citation

Researchers should cite this work as follows:

• Winkel, B. (2023). 2013-Brian_Winkel-Reflecting_On_Walls. SIMIODE, QUBES Educational Resources. doi:10.25334/VJQT-7A47

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Article Context

Description

Introduction

We reflect on our passion for teaching mathematics, useful mathematics, by
considering our understandings of just what a wall is and what a wall means to
us. Walls separate and keep out. They keep in, but allow for breath through air
circulation. Walls seal out things in insulation, yet keep in things like smells.
They act as supports. Walls are strong, lest they crumble, but they are also
flexible. Walls are to lean upon personally and to organize our space. Simply
put, walls are all around us and they shape our world. So why not think of how
the notion of a wall can shape our teaching?

In a speech near the Brandenburg Gate on 12 June 1987 President Ronald
Reagan, said to the leader of the Soviet Union, Mikhail Gorbachev, “Tear down
this wall!”[12]. We build walls for many purposes. In the case of the Berlin
Wall it was to contain and separate the East German population from the West
German population and keep ideas from flowing. We do not like walls to keep
people from moving about, exchanging ideas, or engaging in commerce.
As we pass a new construction site we see the stark concrete of the basement
walls in the foundation for the building which is to come. We need walls to
support structures and to serve as a foundation. Thus we are not against walls,
although we often lean against them!

Robert Frost, in his powerful poem, Mending Wall[4, p. 47] opens with this
line, “Something there is that doesn’t love a wall.” In Frost’s Yankee contrariness
and practicality he is saying we may not love walls, but we know we need them
in our lives.

At the beginning of the calculus reform effort [3] in the late 1980’s we used
the phrase “leaner and livelier”[3] and yet calculus texts are anything but leaner.
The lively engagement envisioned by reformers has subsided as we have slipped
back into the oblivion of grinding exercises, unengaging prose, an occasional
tack-on project activity, and a treatment of our students as juveniles wherein
we say, “Just learn this stuff so you can see how it is useful somewhere else,
somewhere down the road, in another subject area.” Thus our structural wall
has to be solid in order