them. I worked at this camp for many years and eventually became its program director.
Over the years, my experience at camp really became part of me and helped me understand
both kids and myself.
Many other things contributed to my learning how to teach as well. As far as I can remem-
ber, I always had an ability to explain things, to break down problems so other people could
understand them. As a student teacher, I learned to plan, execute, and evaluate lessons, but I
have to say that I do not think I was adequate as a teacher until I had 5 years of experience. By
then, I had a sense of the broader picture and understood how all the lessons in the curricu-
lum hung together. I was no longer teaching individual lessons; I was teaching a system of rea-
soning. It also took that long to understand where the kids were coming from, what they un-
derstood, and why they acted the ways that they did. It can be hard, but a teacher cannot take
every action or statement by a student personally. You have to remember that people often
act out of frustration and their behavior may have nothing to do with you.
One of the things that helped me become an effective teacher was figuring out the pur-
pose of tests. There are people who make up tests that are “ball busters.” I always ask them,
“What are you trying to do? Is the purpose of a test to show students how much you know
and how much they don’t?” Eventually I learned to construct tests that build up kids and
show them if they do the work they can learn the things they need to know. As a teacher,
your mind always has to be creative. You are constantly looking for new ways to teach a
topic in case someone in your class is not getting it.
As a teacher you cannot invent everything yourself and I am always willing to “borrow”
from another teacher. If I observe someone and I see something interesting, I try to use it in
my class. My son is in elementary school and his teacher gave him a science review sheet
called “Things to Know.” For example, one thing to know was the difference between a verte-
brate and an invertebrate. I thought this was a great idea and I changed my review sheets so
they list important ideas as well as provide practice problems. Of course, borrowing must be
mutual. I lend out my handouts to other teachers and I let people use my tests.
I think a lot about why it is so difficult for many students to understand math. A major
part of the problem is that students start off believing that they cannot do well. It is in-
grained in them throughout school. They think you are either born with math ability or not.
Because of this, they give up on themselves and end up failing. These and other problems
are compounded when teachers act as if certain groups of students will never be able to
learn math. When I grew up, like almost everybody else, I accepted that boys were better
than girls in math. That is another notion that must be challenged.
One way to help students understand math is to draw connections between math and the
world around us. I do not mean saying something like, “If you’re going to be a gardener, this is
the math you need to know.” I think the most important part of math is learning its logic: how
the whole thing fits together. The ability to solve problems that students learn in math carries
through in many other areas in both school and life. In all secondary school math classes, stu-
dents and teachers are really doing two things. We are learning to think logically and to see
how smaller pieces fit together to form a broader picture in the mathematical world.
A good example of this approach to mathematics is the study of plane geometry. It is a
system of reasoning where you accept certain postulates about the universe, and based on
these postulates, you can develop and prove other ideas. But in geometry, if you change a
single postulate, you change the whole system.
When we postulate that the universe is two dimensional or flat and looks like a piece of
paper, if you have a point (C) that is not on a line (AB), one and only one line can be drawn
through the point (C) that is parallel (II) to the line (AB). But the universe we live in is three
dimensional. If we define parallel lines as two lines that never intersect, in a three-di-
54 CHAPTER 2