Information Age Education
   Issue Number 66
May, 2011   

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.

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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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