Case for brain based thinking and "whole math"
From: DNS BNA
Date sent: Thu, 15 Jan 1998 09:27:27 EST
To: email@example.com, firstname.lastname@example.org (E. David Thielk)
Subject: A Teacher Wanting Comments on His Ideas About Teaching Math
Organization: AOL (http://www.aol.com)
I've sent Mr. Thielk my comments, and offered to post to this list so he can
get more. If you'd like to comment, include his e-mail address in the to:
field as I will not forward comments sent only to education-consumers.
Subj: Brain based learning and math-long
Date: 98-01-13 18:55:49 EST
From: email@example.com (E. David Thielk)
Sender: CESNEWS@BROWNVM.BROWN.EDU (Coalition of Essential Schools News)
To: CESNEWS@BROWNVM.BROWN.EDU (Multiple recipients of list CESNEWS)
I am writing a series of newsletter articles on brain based learning for
a local newsletter. This is the fourth in the series. I am interested
in any feedback or response to some of the ideas posted. If you are
interested, please reply. If not, just delete.
The Forest, Trees, or the Ecosystem?
Gretchen and I pride ourselves on individualizing as much as we can.
We try to focus on individual student needs, assessing students as
individuals, and giving help and push where we feel it will create the
most learning. What we have found is that our teaching and assessment
have merged, and are often indistinguishable from one another. This is
particularly true when we are working with students on math and writing
skills. Generally this approach works well, but occasionally we have
students who frustrate us because we find ourselves spending a great
deal of time with someone who could do a great deal more to help
I have such a student in on of my math sessions. His modus operandi
to work intensely and frantically on math until he comes to a problem in
which he can't see a clear path from beginning to end. He has looked at
the sample problems in the book, but for some reason, the problem he is
facing is slightly different than the sample problem (oh, no . . . . it
requires some actual thinking). The other day, he was struggling with
a problem which, if following the sample problem given in the textbook,
required dividing by zero. He had learned some time ago that you can
never divide by zero, thus, he sensed a roadblock. The problem,
however, could easily be solved by drawing a quick sketch and "seeing"
a solution. Even more effectively, the problem could have been solved
by simply pushing back from the table, putting down the pencil, and
starting a short internal dialogue about the nature of the problem and
what the equation actually implied about the numbers.
Unfortunately, many students have not learned to appreciate this
approach to problem solving in math. When I asked this particular
student to put down his pencil, and proceeded to discuss the problem
with him, he quickly "saw" the solution. When we were done, I was a bit
amused by his question, "But can you find the answer this way? I
mean, can you just draw a picture and find the answer by looking at the
graph? Won't you get a different answer if you go through the math?" I
am not sure what he meant by "going through the math", but I do know
that stepping back to look at the trees for a moment is as important in
math as it is in art or literature.
Neurobiologists are discovering that the active brain, in a natural
setting, processes parts and wholes simultaneously, and taking time for
a view of the trees is one way to allow part and whole processing to
occur simultaneously. They have also discovered that learning involves
both focused attention and peripheral perception. For the math student
above, his math potential is very high. What he has missed is the
practice of engaging in "whole math" process at the same time he has
been asked to mechanically manipulate equations. He has become an
expert at blocking out the peripheral perception. He can describe the
bark of the tree in great detail, but he is looking so closely, he fails
to recognize a woodpecker hole when he encounters a small opening the
bark. Whole math, like whole language, means learning to place
numerical patterns in perspective, to view them and practice them in a
contextual setting. It means to develop skills in relationship to each
other and real world applications. It means learning to see the trees,
and the forest and to understand the relationship between them.
And of course, understanding the relationship between trees and forests
means understanding the ecosystem.
Perhaps it is time for teachers of mathematics to start the equivalent
of the whole language/phonics controversy enjoyed by teachers of
For mathematics teachers to implement what the neurobiologists are
telling us would mean a shift in the way we deliver math content.
Perhaps the word "delivery" would no longer be appropriate. Essentially
it would mean that students should experience mathematical equations in
context to real phenomenon. And more importantly, the patterns that
occur in nature and are readily observable by anyone should be used as a
basis for the manipulation of the mathematical symbols.
One way to promote this approach is for teachers of mathematics to look
at the inquiry model of learning used by some science teachers. In the
inquiry model, the student usually starts with an experience. The
experience could be something as simple as watching a toy car move along
the floor or observing symmetry in flowers. Of course it could be far
more complex, and ultimately should challenge the student to think,
compare, predict, analyze, etc. This grounding experience sets the
stage for the conceptual development to come later and experiences are
all the better if they shake some intuitive foundations the learner may
have about the natural world or in this case mathematical patterns.
But alas, this is a near impossible task. Our math curriculum is
designed entirely on the basis that we must do math this year to prepare
students for next year's math concepts. And of course, next year's math
program is designed to prepare students for the math that comes the year
after that. There is no time to stop and observe the roses (let alone
the forests) along the way unless we collectively agree to cover less.
Further, to look at the forest means changing the picture of what a math
student is actually doing when they are learning math. It means that
math curriculum must be fully integrated at the very least with history,
social and natural science.
Our district defines mathematics as 'the science and language of
patterns." I wonder how many of us reflect on this definition each day
as we work with students. Helping students see the forests along with
the trees will mean restructuring our math programs, and of all the
disciplines, math probably has the most barriers to change. We must ask
ourselves, Why we are teaching mathematics? Whose needs are we trying
to meet? Must we design our curriculum around college and college
professor's expectations, next year's teacher's expectations, moving
students to achieving calculus, student transcripts? All of these are
valid inputs in the process, but also are somewhat peripheral to the
more essential goal of giving students the ability to use mathematics to
explore and understand patterns. How many of our students truly see
math as the science and language of patterns? Perhaps the first step is
to truly incorporate the simple definition - the science and language of
patterns - into our classrooms and our own view of mathematics.
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