2006, Lori MacKinder, M.A.
Interestingly enough, some of my best insights come forth in the midst of my greatest struggles. Take for example the school year that my youngest daughter began first grade. For
reasons that I did not understand at that time, I could not keep her
well. She suffered ear infection after ear infection with high fever
throughout the 10 months of school. This was a stressful time for us
both as I was a Waldorf High School Mathematics Teacher and Chair of
the Math Department at that time. Together we missed many school days
while nursing her back to health. On some of these stay
at home days, I lamented about my mathematically challenged students
back at the high school who were waiting for my return in order to take
up fully their next section material. Invariably, upon my return to the classroom, my students would call for the details of my absence. After
one of these accountings of my nonattendance, one of the students began
to recall his childhood journey through multiple ear infections. His story sparked that of another student who then told her tale of childhood ear illnesses. That story then sparked the memory of another student and then another and then another. I
felt as though I was being bombarded with some universal phenomena
relating childhood ear troubles with adolescent math struggles.
The ear is a very fascinating organ. That it could be related to math deficiencies is down right exciting! It turns out that 2/3 of my mathematically challenged students suffered from ear infections during their younger years. Hearing is of course very important for learning in school. If
a child cannot hear well due to a fluid filled middle ear or swollen
eardrum they cannot take up the teacher’s instruction. If the eardrum
cannot vibrate, the students cannot hear clearly and then has a hard
time learning. However, hearing impediments are not the only difficulty to be aware of in terms of the ear. The ear is also important because it is the main source for our sense of balance and sense of movement.
This
is how the sense of movement and the balancing mechanism in the ear
works. Within the inner ear are the utricle and the saccule (see figure
below). These organs both contain fine hairs and an amount of viscose
fluid. They are designed to detect head orientation and
linear acceleration. When we tilt our head, gravity pulls on the fluid
that is in these two organs. This fluid moves over the
hair cells, which then send electrical signals to our brain to inform
it of the head's new orientation. Similarly, when we start or stop
moving in a straight line, the fluid inside the utricle and the saccule
sloshes around, affecting the hair cells further.
The
semicircular canals (see figure to right) in the inner ear control
balance. The canals detect angular acceleration, or turning movements
of the head. There are three roughly D-shaped canals in each ear; they
are all perpendicular to each other so that they can detect turning in
any axis, for example, nodding your head up and down, shaking it left
to right, or tilting it from side to side. These canals also work by
affecting hair cells through the movement of fluid inside the
semicircular canals as the movement occurs. When you rotate your head,
the fluid in the canals aligns in the direction of the movement,
thereby stimulating the hair cells. The hair cells sense the movement
and communicate to the brain that there is head movement. When spinning
around and around, the fluid may keep moving, even for a time after the
spinning has stopped. The hair cells keep telling the brain that you
are still moving, even when you are not, which is why you get very
dizzy and fall down!
The
brain then takes all the inputs from these organs, the up, down, side
and so forth and sorts them out to know how we’re oriented and which
way we’re moving. Hence, the sense of balance and sense of movement are
created. (© 2006 Howard Hughes Medical Institute. 4000 Jones Bridge Road Chevy Chase, MD 20815-6789 | (301) 215-8500 | e-mail: webmaster@hhmi.org )
In Man as a Being of Sense and Perception, (1981, page 18) Rudolf Steiner writes, “Now let us consider mathematical truths. A superficial observer would say: Oh yes, of course man gets his mathematics out of his head. But it is not so. Mathematics
derives from an altogether different sphere. And if you study the human
being, you will get to know the sphere from which mathematics comes. It is from the sense of movement and the sense of balance.” As
mentioned above, our sense of movement and sense of balance are both
derived from this fluid moving over the hair cells in our inner ear.
Our balance and movement in our body or our experience of the dimensions of space around our body is mirrored in our thinking. It
is commonly known that when a hindrance exits in being able to think
something through, moving it with our body is often the remedy. In this
same vein, when our thinking is underdeveloped in some area, we may
look to an area of our body that may also be underdeveloped. When we then develop the body, the thinking commonly will follow suit, such the slogan suggests: “The hand educates the brain.” Where
math is concerned, to be able to move to the right and left of the
equal sign as in, 3 + 4 = 7, requires that we have an amount of
flexibility in moving to the right and left in our body as well as in
our thinking. To move above and below the fraction bar,
such as with 144/12 requires the same ability to move up and down in
our body as well as in our thinking. This is not to mean that a person unable to physically move will not be able to move in their thinking either. However, some correlation does exist between physical movements and thinking movements.
To further explain, in
order to fluidly move around or with a longer mathematical problem,
such as long division, requires that our sense of movement is strong
and flexible, and that we can hold on to where we began and where we
are moving towards likened to out body following a path. If
our inner sense of movement is weakened, this ability to move around or
in an equation is also often weakened. If our sense of balance is
diminished it becomes more difficult to balance a spreadsheet or work
with equivalencies as well. We sometimes cannot experience in our thinking what we cannot experience in our bodies first. If
our sense of balance or sense of movement is impaired, we may have a
more difficult time with those same qualities in our thinking. Therefore,
as math is connected to movement and balance, and movement and balance
are connected to ear health, we can deduce that ear health is important
to math.
From the work of Audury McAllen and The Extra Lesson, we can read what she suggests supports for the sense of balance and the sense of movement. She
has written that games where children spin around, swing, spend time on
balance boards or one-legged stools and any activity that gets the head
hanging down for 30-60 seconds followed by a slow rise are beneficial
for these two senses. (page 116 , 2004).
Students
that need support with these two senses can be spotted in the classroom
by their frequent ear infections, difficulties in fluid moving thinking
with math, frequent need to re-adjust in their chair or inability to
sit still for lengthy periods of time. These are also
often the students that will sit with a leg or two tucked under them
while in a chair or push back in the chair, wobbling on only one or two
of the four available chair legs. These students may also regularly lay their head down on the desk during the daily lesson as well. All
of these latter mentioned tactics in the classroom are simply ways in
which the students are attempting to get the fluid moving in the ear
canal to stimulate the hair cells again.
In
other words, when the sense of movement and sense of balance is
underdeveloped due to illness or the like, the body will begin to
stimulate those senses in attempts to develop them further. Unfortunately,
those attempts by the body to develop in the middle of a class lesson
can result in distraction to neighboring students and to lack of focus
or concentration by the student. The forces of the
student with the ear illnesses are being used to stimulate the ear
system in order to integrate the sense of balance and the sense of
movement instead of being used in learning.
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