Unmediated Experience — part 1the case for using primary texts in the math classroom

Because I was a literary historian before I became a math teacher, it bothers me to see how little direct contact our math students have with primary source documents.

It bothers me a lot.

In the humanities, primary sources are the lifeblood of the curriculum. We don't limit students to reading about  historical or cultural artifacts, events, or texts. We bring students directly into relationship with those texts themselves.

What kinds of distorted ideas might a person develop if she or he had never wrestled with the original text of the preamble to the Declaration of Independence —

When in the course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.

Or the original text of the preamble to the U.S. Constitution —

We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America.

Pedagogically, in the humanities, we find great value in connecting directly with the words and thoughts, hopes and dreams, and even biases and delusions of those who came before us. When we do so, we connect with what is most powerful — and most human — in the enterprises and events we choose to investigate.

So why, I wonder, do we not do the same thing in the math classroom — at least from time to time?

Mathematics is a cultural and historical phenomenon. Acts of mathematics are performed by human beings who were born and who lived in times that were both similar to and different from our own. Giving students some experience of direct access to primary texts is an easy and cost-effective way to give them a basis — and context — for their own relationships with mathematics.

At least, that's one of the things that helped me the most when I first decided to cultivate my own relationship with math teaching and learning.

I think this is one of the most compelling — and least well-articulated — benefits of Dan Meyer's WCYDWT pedagogy.
His videos and 'captivating image' lesson starters are primary source documents that put students into direct relationship with mathematical questions. To make sense of their experience of the videos and the activities, students have to wrestle with the mathematics of what they are experiencing. And in so doing, they find their own very personal way into mathematical thinking and success with mathematical thinking.

I saw this in my Algebra 1 class this past winter when I used Dan's original sequence of Graphing Stories videos. Each student was given a sheet of blank graphing grids and, with each little video story, was invited to investigate ways in which we could sketch graphs these stories — i.e., how we can use algebraic geometry to represent a relationship between, say, distance and time.

Despite being a deeply discouraged bunch of math learners, most of my kids were riveted to this activity. Many of them had light bulb moments about why a distance-versus-time graph can never just shoot straight up ("Oh, I get it — you would need a time machine for that!"), what repeated actions look like graphically, and what lack of motion looks like ("Hey, time keeps passing... even when the guy isn't moving!").

Because this was a direct encounter with primary source texts (i.e., Dan's short videos), students had not choice but to enter into relationship with the texts themselves. After all, my role in this process was to be "less helpful." No way was I going to mediate this experience for them!

As a result, these encounters wove together conceptual understanding with procedural fluency in a way that is not generally possible using secondary source materials such as textbooks.

 The fact that these primary texts (the videos) are simple, clear, and direct enough for even the most discouraged math learners makes them all the more compelling as curricular materials or lesson-starters.

But I can't help thinking that their greatest value derives from the fact that they encourage our students to see the world — and their own experience of it — as their primary, unmediated math textbook.