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Mathematics and Memory2007, Lori MacKinder, M.A.
An
all too common scene in the home during the evening: a child sits at
the kitchen table, staring at math pages with their head held in their
hands. Time ticks by. Sometimes tears are involved in the scene,
sometimes even anger or rage, but the scene does not change. As
parents, we long to help our children, yet often feel inept or too far
removed from mathematics or teaching.
Students
who struggle often understand the math work while at school, or while
sitting with a tutor, but given time alone with the subject, they can
draw a blank. By taking a closer look at the relationship of memory
and mathematics, we can begin to unravel the mystery of why the
learning of mathematics does not always stick in the minds of those who
study it.
The
development of memory is of great importance to the advancement of
thought. This maturity of thought in conjunction is of great
significance to the ability to perform math. By first taking a look at
memory, we begin during the first three years of life, where memory
forms in three distinct ways: localized memory (movement memory),
rhythmical memory and picture memory. (The First Three Years of the Child, Karl König, 2004)
Localized
memory (movement memory) begins in the first year of life and is a
memory that is created out of our limbs. Infants use their arms,
hands, legs, feet and tongue to feel and to remember in this early
stage of life. Out of the bodily experiences of moving themselves and
the objects in their environment, up/down, left/right and
backwards/forwards they develop a sense of movement, of balance and of
the space around them. These bodily experiences lead to the ability to
move inwardly, through thought, and to remember. During the first
three years of life, if movement of the young child is overly
restricted or confined in some way, this faculty of memory may need
some additional strengthening work during the later school age years.
Long periods of time strapped in car seats, baby carriers and strollers
may hamper the natural development of this fundamental piece of memory
formation.
When it comes to mathematics, this underdevelopment
of movement memory may first show up in kindergarten or first grade.
The student will show difficulties with place value and the meaning of
a number, which is called number sense. This is because a child may not
have had enough bodily experiences of moving around various numbers of
objects, counting and sorting during earlier stages of development. It
may also become apparent in second grade where borrowing and carrying
begin. Around the third grade, weakness in localized memory is shown
when long division is presented. Without a very comfortable ability
to move their own bodies and the objects around them, students cannot
then move around comfortably within the context of all the operations
(multiplication, addition and subtraction) and locations (left/right,
above/below, forward/backward) in a long division math problem.
When
these challenges present themselves, it is suggested to then take the
child back into movement in order to strengthen the memory before
proceeding. Those may consist of the following: large bodily gross
motor movement (zoo exercise movements, jump rope, skipping, bean bag
tossing, etc.) and fine motor movements like the use of manipulative
(blocks, counting sticks, beads, bean, proper pencil grip, etc.)
This child with weak localized memory may benefit from learning math,
by moving every mathematical problem in a concrete form first using
their limbs and with objects that can represent the thoughts.
Secondly,
this child needs permission to stay at that stage of learning in order
to explore the objects that make the math true before moving to the
next stage. Luckily, in Waldorf Schools, many teachers recognize the
importance of movement in learning and memory formation and thus
support additional movement classes such as the Zoo Exercises in the
second grade, Extra Lesson sessions or exercises and Curative Eurythmy.
The
second step of memory formation is rhythmical memory formation. This
piece of memory is connected with the use of speech and song during our
second year of life. We see this clearly in a child's first words, "Ma
ma" for mother or "da da" for father or "ba ba" for bottle. Sometimes
this rhythm is stretched out further making the pattern more apparent:
"Ma ma ma ma..." Every new word is repeated and repeated. This is the
small child forming rhythmical memory. The person or object, in this
case mother, is remembered through this rhythm of the sounds in this
small monotone song. Later in school, this faculty of memory is called
upon when the child sings a song to support remembering the names for
the days of the week, states in a country or when creating a rhythm for
the multiplication tables to support memorization.
The
hazard of moving to the rhythmical memory state too early in school
learning environments is that if the child has not sufficiently touched
and moved with their limbs what is being now taught in rhythm, there is
little or nothing for the child to connect the rhythm to within himself
or herself. Thus the rhythm, while possibly fun, may not lead to
independent thought formation if presented to early. Although many
children may be able to get caught up in the classroom songs and
rhythms, when asked to later reproduce them independently, there is a
struggle and perhaps failure. Teachers often see this in the children
that are challenged with saying their multiplication tables forward and
backward on their own. While with the class, they participate fully in
the reciting and chanting of the tables, seemly grasping the math
facts, but without the group carrying them externally, they struggle
reproducing independently. This is a piece of information a parent or
teacher can glean from this situation and then take the child back to
the localized memory stage with work involving their limbs and object
able to be touched and manipulated followed by work with verses,
poetry, story and speech.
Picture memory is the third step of memory formation and can
be seen being developed in the small child through their use of
imagination and story telling or fantasy play in the third year of
life. This is where the inner movie screen comes into being or the
ability to see in our "mind's eye" develops. This faculty is of paramount importance in the study of higher mathematics where abstract ideas are worked with. Conditions that can bring about
deficiencies
in the creation of the picture memory are environments with screens
such as television and computer. Both of these screens provide
completely formed images to a child and therefore the need to inner
picture is superseded. Reading and pretending with children
consequently support the growth of picture memory. Beginning with
pre-algebra in the middle school years, this faculty of inner picturing
or lack there of becomes very apparent in the student. Once diagnosed,
a teacher can work with this deficiency in the math lesson through the
use of stories, images, and color-coding of the work to stimulate the
picture formation in the inner mind of the student.
Children
who struggle with the subject of mathematics are trying to tell us
something. Often it is not so simple as a dislike of the subject
matter itself. There is an underlying reason. When we use the
students struggle as information in a critical judgment free way, we
can therefore support and heal the child.... as is the purposeful path
of education.
I am a willow of the wilderness,
Loving the wind that bent me. All my hurts
My garden spade can heal. A woodland walk,
A quest of river-grapes, a mocking thrush,
A wild-rose, or rock-loving columbine,
Salve my worst wounds.
-Emerson, Ralph Waldo
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