So it's been almost two years, but I'm
trying my hand at blogging again. I have lots of thoughts and
opinions about math education, and need to make the effort to get
them out there.
As a child, I hated math. I thought
that it was something that I simply wasn't good at, and wouldn't ever
really understand. I didn't really start to love math until I took
classes for my undergraduate degree at Southwestern University. I
learned constructivist teaching methods including Cognitively Guided
Instruction (CGI) and strategies to increase real numerical
understanding in Van de Walle's Student Centered Mathematics.
Through these constructivist approaches, I began to see math not as a
set of isolated procedures, as I had been taught in school, but as a
logical way to navigate a landscape of related figures.
Mathematical understanding is powerful,
and I find it incredibly rewarding to equip my students with this
power. I love being able to make a real difference in my students'
lives, but I've often been frustrated with the constraints of the
system I teach in, and not being able to have a bigger impact. I
believe that increasing students' abilities at math, including
critical thinking and problem solving, is good for them as
individuals, and good for our world. Being adept mathematicians and
problem solvers opens doors for students in careers in engineering,
technology, and science. And more engineers, mathematicians,
scientists, and citizens who are critical thinkers is what we need to
help solve the big problems our civilization is facing.
This blog started out as platform where
I could pitch my ideas about how to impact math education with
emerging technologies. I still want to do that, to some extent, but
I also want to address the other aspects of teaching that positively
impact students' mathematical understanding.
The most effective teaching happens
when I am working one-on-one or with a small group of students. I am
able to engage with each child, discover their understandings and
misunderstandings, and scaffold through purposeful questioning and
modeling. Teaching this way is a craft. It is not easy and often
does not come naturally. As teachers, we want our students to be
successful. It is easy just to show them the steps and teach short
cuts, but this does not lead to lasting understanding. We have to
let them struggle, find out what they know, and help them build
understanding from there. This can be a long, arduous and,
occasionally, frustrating process, but it builds deep and lasting
knowledge. I want to explore questions and strategies around this
type of teaching, especially problem solving, on this blog.
When I am working with a small group of
students, one of the biggest issues is how to best use the rest of
the students' time and attention. They usually work in small groups
on center activities, or on individual worksheets. This creates a
few problems. I cannot give them immediate feedback or help on what
they are doing. Of course, I have modeled the activities, and will
grade their work later, but that doesn't help them in the moment. I
don't understand why we are still using text books and worksheets in
classrooms. Why aren't our students working primarily on computers?
They could be participating in motivating, game-like programs that
individualize for the students' needs, give appropriate scaffolds
(such as models or number lines) when needed, and record data in real
time for the parents, teachers and administrators. Such programs
would not replace effective teachers, but allow them to better use
their time. Instead of spending hours grading worksheets after
school, with little useful data to gain from the effort, teachers
would automatically get data on student understanding. With this
information and with the saved time from individually grading,
teachers would be able to focus their time on better planning for the
next day's lessons. The ed tech industry is incredibly active and
vibrant, with new products and solutions constantly being presented.
I would like to spend time reviewing some of these solutions, and
proposing solutions of my own.
