This free Information Age Education Newsletter is written by David
Moursund and Bob Sylwester, and produced by Ken Loge. The newsletter is
one component of the Information Age Education project. See
http://iae-pedia.org/
and the end of this newsletter.
Stress and Education Part 3: Stressors in Math Education
"What science can there be
more noble, more excellent, more useful for men, more admirably high
and demonstrative, than this of mathematics?" (Benjamin Franklin.)
"We cannot hope that many children will learn mathematics unless we
find a way to share our enjoyment and show them its beauty as well as
its utility." (Mary Beth Ruskai; Tufts University.)
This is the third of a sequence of IAE newsletters dealing with stress
and education. We know that chronic stress impairs both one’s brain and
one’s health. The first article discussed stress in general, while the
second focused on stress in education.
Many students find that school math is particularly stressful. This may
be why so many adults claim: “I hate math” and “I can’t do math.” This
IAE Newsletter explores various aspects of stress in our math education
system.
Math and the Human Brain
An intact human brain has is very good at learning oral communication in natural languages. Keith Devlin’s book (2000),
The Math Gene,
argues that anyone who can learn a natural language can learn math.
However, he believes that learning math is much more challenging than
learning to read.
Stanislas Dehaene (2010) indicates that:
Among the three big R’s of
our school education—reading, ‘riting, and ’rithmetic—the knowledge of
mathematics is perhaps the most complex. Calculation is easy to test,
but what does it mean to master the concept of “number”? When can a
child be said to grasp” a mathematical notion?
Howard Gardner includes Logical/Mathematical as one of nine human multiple intelligences.
Logical-mathematical intelligence
consists of the capacity to analyze problems logically, carry out
mathematical operations, and investigate issues scientifically. In
Howard Gardner's words, it entails the ability to detect patterns,
reason deductively and think logically. This intelligence is most often
associated with scientific and mathematical thinking. (Gardner, n.d).
Many people consider math to be a language. It is a special purpose
(discipline-specific) language. Communication in the language of
mathematics not only requires learning a great many math words and
ideas, it requires a level of precision far above what is typically
used in ordinary natural language communication (Moursund and Ricketts,
n.d.).
Some Math Learning Challenges
Here are a few challenges students face in learning math. Each can be quite stressful.
- Math is a vertically structured discipline. New topics build on
topics a student has previously studied. Failure to adequately
understand and remember the prerequisite knowledge and skills places a
learner in a potentially very stressful learning situation.
- In math education, we want students to learn to solve challenging
problems. We expect them to show details of their work. We expect them
to find correct answers and to demonstrate (prove) the correctness of
their answers. These types of demands are stressful partly because they
are so different from the types of cognitive challenges children face
in their daily lives outside of school. They are also stressful because
they require a sequence of steps in which the smallest of errors can
lead to incorrect results.
- Math is a language, but most people do not use the language
routinely enough to develop and maintain fluency. In the “use it of
lose it” paradigm, “lose it” is a common outcome. Students tend to be
taught math as an isolated discipline. By the upper elementary grades,
many students find that much of the math being taught seems unrelated
to their lives outside of school and their lives in the non-math
courses they take in school.
- The language and ideas of math tend to be relatively abstract. A
variety of versions of cognitive development theory posit that as a
brain grows toward full maturity (achieved by about age 25 for most
people), a steadily increasing ability to deal with abstraction occurs.
See Moursund’s article on Math Maturity (Moursund, 2010). Many people
argue that much of the school math is taught at too high a level on a
cognitive development scale. A great many students are expected to
learn the topics ratio, proportion, probability, and fractions well
before their cognitive development level is adequate to the task. This
is stressful and often leads to a “memorize, regurgitate, and forget”
approach to math learning.
- Transfer of learning is a major and not well understood cognitive
challenge (Moursund, n.d.). Math is useful in many different
disciplines. To a large extent, our math education system fails to
provide students with adequate help in transferring their school math
knowledge and skills either to other academic disciplines or to the
math-related problems and tasks they encounter outside of school. Many
students find it stressful when their teachers in non-math classes
expect them to make use of math.
- Many elementary school teachers who teach math have quite limited
math content knowledge and skills, and are fearful of math. They find
math to be stressful and students can pick up on this stress. A similar
statement holds for many parents and other adult caregivers in the home
environments of students.
- Math is a component of the high stakes state and national tests.
There is considerable pressure on students to perform well on these
tests. This situation has moved math education in a direction of the
major goal is to learn math in a manner that leads to being able to do
well on these math tests. This is stressful for both teachers and
students.
- Many students have a strong need for instant gratification. This
internal want/need for instant gratification poses a major challenge
when such students study algebra and other demanding components of
math. Success in dealing with challenging math problems often
requires persistent effort over an extended period of time.
While the list can be extended, it is now long enough to support a
contention that math education has the potential to be quite stressful
on many students. The amount of research that has been done on
these various topics varies. Your authors find the last of the bulleted
items particularly interesting. Read about marshmallow experiments in
Lehrer (2009). Quoting from the article:
Angela Lee Duckworth, an
assistant professor of psychology at the University of Pennsylvania]
first grew interested in the subject after working as a high-school
math teacher. “For the most part, it was an incredibly frustrating
experience,” she says. “I gradually became convinced that trying to
teach a teen-ager algebra when they don’t have self-control is a pretty
futile exercise.” And so, at the age of thirty-two, Duckworth decided
to become a psychologist. One of her main research projects looked at
the relationship between self-control and grade-point average. She
found that the ability to delay gratification—eighth graders were given
a choice between a dollar right away or two dollars the following
week—was a far better predictor of academic performance than I.Q.
She said that her study shows that “intelligence is really important,
but it’s still not as important as self-control.” [Bold added for
emphasis.]
Math Anxiety
Math anxiety is a type of stressor. A recent Google search
of the quoted phrase “math anxiety” produced nearly 200,000 hits. Sarah
Sparks (2011) summarizes some of the current research reported in a May
2011 Learning and the Brain conference. Here are a few quotes
from the article:
Mathematics anxiety is
more than just disliking math, however; someone with math anxiety feels
negative emotions when engaging in an activity that requires numerical
or math skills. In one forthcoming study by Ms. Beilock, simply
suggesting to college students that they would be asked to take a math
test triggered a stress response in the hypothalamus of students with
high math anxiety.
Anxiety can literally cut off the working memory needed to learn and
solve problems, according to Dr. Judy Willis, a Santa Barbara,
Calif.-based neurologist, former middle school teacher, and author of
the 2010 book
Learning to Love Math.
In a
series of studies
Mr. Ansari and his colleagues at the Numerical Cognition Laboratory
have found that adults with high math anxiety are more likely to have
lower-than-typical ability to quickly recognize differences in
numerical magnitude, or the total number of items in a set, which is
considered a form of dyscalculia.
“When engaged in mathematical problem-solving, highly math-anxious
individuals suffer from intrusive thoughts and ruminations,” said
Daniel Ansari, the principal investigator for the Numerical Cognition
Laboratory at the University of Western Ontario, in London, Ontario.
“This takes up some of their processing and working memory. It’s very
much as though individuals with math anxiety use up the brainpower they
need for the problem” on worrying.
Final Remarks
Several of the participants in the Learning and the Brain
conference pointed out that we have an intergenerational problem in
math education. Parents and teachers with high levels of math anxiety
can inadvertently foster the growth of math anxiety in the children
they work with. It is suggested that this occurs relatively frequently
in elementary school, as many elementary school teachers have high
levels of math anxiety.
References
Devlin, Keith (2000). The math gene: How mathematical thinking evolved and who numbers are like gossip. Basic Books. See also http://i-a-e.org/iae-blog/the-math-brain-keith-devlins-chapter-in-the-book-mind-brain-and-education.html.
Gardner, Howard (n.d.). Howard Gardner, multiple intelligences and education. Infed. Retrieved 5/22/2011 from http://www.infed.org/thinkers/gardner.htm.
Lehrer, Jonah (2009). Don’t. The New Yorker. Retrieved 5/23/2011 from http://www.newyorker.com/reporting/2009/05/18/090518fa_fact_lehrer?currentPage=all.
View short videos at http://www.youtube.com/watch?v=xNvvL9j_SIs and at
http://www.youtube.com/watch?v=6EjJsPylEOY.
Moursund, David (n.d.). Transfer of learning. Retrieved 5/22/2011 from http://iae-pedia.org/Transfer_of_Learning.
Moursund, David (2010). Math maturity. Retrieved 5/22/2011 from http://iae-pedia.org/Math_Maturity.
Moursund, David and Ricketts, Dick (n.d.). Communicating in the language of mathematics. Retrieved 5/22/2011 from http://iae-pedia.org/Communicating_in_the_Language_of_Mathematics.
Sousa, David A, Editor (2010). Mind, brain, & education. Chapter 9: The calculating brain. Bloomington, Indiana: Solution Tree Press.
Sparks, Sarah D. (5/16/2011). Researchers probe causes of math anxiety. Education Week. Retrieved 5/22/2011 from http://www.edweek.org/ew/articles/2011/05/18/31math_ep.h30.html?tkn=PZCCgIX4PjXZW2XdpIIG1LKJMVCQUHHr57gf&cmp=clp-sb-ascd.
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