cheesemonkey wonders

cheesemonkey wonders

Monday, May 30, 2011

Unmediated Experience, part 2 —
another use of primary texts in the math classroom

While gathering problems for my logarithms and exponential functions unit from some of my favorite textbook sources, I noticed that John Napier's birth and death dates (1550-1617) looked kind of familiar — really familiar, in fact.

And they're awfully close to Galileo's birth and death dates too (1564-1642).

So why not at least mention the historical context of logarithms?

Saturday, May 28, 2011

Getting students writing and reflecting in math class

I used this idea in Algebra 2 during our polynomial graph sketching unit to support their conceptual understanding of end behavior, and it worked surprisingly well.

Most of my students had not had much truck with the idea of infinity, much less with the idea of approaching it, so we started by talking about how the graph of a function is a representation of a specific story — like a novel — or like the life story of a human being. Every person's life story is completely unique, yet everyone has an experience of both birth and death (the beginning and end being like end behavior). Everyone's birth story may be different -- some people are born in a taxi cab, some are born at home, some are born in a hospital, some are born under water, and yet every single one of these births has the very fact of having gone through birth in common. Similarly, death is the ultimate "end behavior" of life. We cannot know exactly how or when a specific person's death may come, but we do know that it is going to happen some time after they have been born and have lived for some duration of time.

We also talked about the movement of a function graph across the axis at its x-intercepts — how at certain key transformative moments, a person's life crosses from negative into positive territory -- or it may move in the opposite direction.

Friday, May 27, 2011

Unmediated Experience — part 1
the 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.