“If Not Now, When?”:
Teaching Remedial Mathematics
By Lori MacKinder, M.A. 2005
Mathematics
is everywhere. Math is found in the construction of the
bee’s honeycomb, the pattern of the pine cone, the construction of
homes, the symmetry of bones, the smallest of particles and the
greatest regions of outer space. It is a door into our own body as well as into the mysteries of the universe. It surrounds us, it is us, whether we realize it or not. To deny math or to push math away is like pretending we do not breath.
The study of mathematics cultivates clear logical thinking. It
is similar to lifting weights to strengthen the muscular body or
cutting weeds to create a walking path. Working with math teaches
problem solving and develops inner flexibility by requiring movement
above, below, left, right, forward and backward in thought. The activities of problem solving and having flexibility in thought are very important tools for our adult world. It
is how we multi-task and stay organized amidst our daily
responsibilities. It may not be that we pull out the quadratic
equation at the grocery store, but we do use the neurological pathways
we created in working with higher mathematics each time we encounter
one of our everyday problems.
According
to a study published in the San Francisco Chronicle, less than
two-thirds (63%) of the students entering college have proficiency in
mathematics. (Wednesday, January 29, 2003, page A-15, Kelly St. John,)
That means 37% of these young adults have underdeveloped problem
solving skills and deficiencies in flexibility of logical thinking. Not
all students enter college; so therefore, the number of actual high
school students without proficiency in math is even greater. Why is this so? Who are these students and what can be done to change this? What impact might this deficiency have on the student's future?
On
a typical afternoon at a high school, students who do not like math or
who are not high achievers in the subject can be spotted right away.
They can be seen dragging their feet on their way to class. Mention
“word problems” and hear these students groan, refer to fractions and
watch them cringe, speak of decimals and see them roll their eyes.
These are the students attending courses commonly referred to as: the
B-group, remedial class, lower level, slower paced math, offerings for
those with learning difficulties, and sadly even "dumb math" or "stupid
math" by fellow students. For the purpose of this article, we'll just
call them "the lower level". The courses these students attend usually
have small class sizes, averaging around 10 students per class and are
taught at a slower pace beginning with Algebra in the 9th grade and
ending with Algebra II or Trigonometry in the 12th grade. As
with higher level classes, these lower level classes are taught with
the intention of cultivating college bound students. However, the
students in these modified classes tend to be drawn to art and
humanities based universities or choose careers not requiring a college
education. In other words, these are classes attended by normal,
intelligent students who happen to struggle with mathematics. |
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Teaching these students in a meaningful and productive way is a challenge. Many wonderful and qualified teachers seem to avoid teaching these lower level classes. Perhaps
this is because the same teaching methods and styles that produce
quality learning in higher level math students generate very little
understanding or enjoyment among the lower level students. The
advanced groups are filled with math-loving students who
enthusiastically take on the next topic just as fast as the teacher can
dish it out; they are self-teachers, to a large extent. The lower level
students, however, require a very different style and classroom
environment. In order to teach math effectively to lower
level students, a teacher must acquire a fundamental understanding of
who they are and what makes them different from other math students. There are three distinct qualities to these students: they are feeling-based, intuitive, and picture-image-learners.
By
using the phrase "feeling-based" to describe high school math
students, we are describing the center from which their reactive
decisions originate. For these students, judgment is centered in
feeling more than in thinking or willing. Whereas other
students can be influenced by their feeling life, these students are
inundated by it. Many things affect an emotional state:
sleep, nutrition, exercise, conflict, stress, menstrual cycle, etc. It is as if these students lack the ability to put aside their emotional and sensing life to focus on thinking. Their openness or receptivity to new material is predicated on how well they feel.
The lower level math student often understands math by means other than pencil and paper. They
typically do poorly on standardized test and instead have great verbal
and visual abilities and a "knowing" outside of ordinary textbook
modalities. Whereas lower level math students may not be
able to perform rigorous steps to solve an equation, they can quickly
blurt out a correct answer to a math problem. Such students may not
know where that answer came from or how they know it is true.
This group of students also has a knack of being in tune with their surroundings. They
can effortlessly sense the state of their classroom environment, their
peers’ emotional state and the mood of their teacher. Their intuitive ability, coupled with a strong personal feeling life, affects their ability to stay focused and on task. Their
attention can easily be drawn into a conversation half a room away, to
a bird flying by the window, or to a friend’s emotional state. These
students seem to have antennae stretching out from their bodies. They
can quickly become overloaded by these sense impressions and lose the
ability to concentrate.
Finally,
these students are picture-image-learners. This means that, more often
than not, they need to associate a mental picture or image with a math
problem in order to understand it. Many of the students in the lower
level high school math courses performed well in and enjoyed
grade-school mathematics. It is not unheard of for
students to have struggles once algebra begins in the 7th grade.
Algebra work is performed largely in the abstract. For
most students, moving into Algebra, and thus the abstract, is a welcome
change for which they are developmentally ready. However, some students
cannot easily create imaginations of abstract concepts. These
students require scaffolding to support the visualization of the
advanced mathematical topics in order for learning to continue
advancing.
"Whoso
neglects learning, loses the past and is dead for the future",
according to Euripides (485 - 406 B.C.). If we ignore the importance of
an education rich in mathematics, it is as if we are ignoring the gift
of clear thinking and the beauty of math in all that surrounds us. A
life without math is a one-sided existence. For this reason, it is of
vital importance to understand our students and to find a connecting
method of teaching. It is also of great consequence that as individuals
we take up math for our own future. Very late in life,
when he was studying geometry, some one said to Diogenes Laërtius (fl.
early 3d cent.), "Is it then a time for you to be learning now?"
"If it is not," he replied, "when will it be?"
Published on Autumn 2005 for:
Research Bulletin
The Research Institute for Waldorf Education
P.O. Box 307, Wilton, NH 03086
(603) 654-2566 fax: (603) 654-5258
http://www.waldorflibrary.org/ResearchBulletin.htm#V9N2 |
