Perspectives on Math Education
The articles below were written by Dr. Eugene Maier, co-founder of The Math Learning Center and an Emeritus Professor of Mathematics at Portland State University. This first set has been published in downloadable book form as Gene's Corner and Other Nooks and Crannies.
Dr. Maier welcomes your comments via email.
Results of recent research in the field of math cognition, as reported by Stanislas Dehaene in The Number Sense: How the Mind Creates Mathematics, suggest "we should honor and nurture the vast amount of intuitive knowledge about numbers children bring to the education process."
Do we foster mathematical swindling—the too-common phenomena of students getting good grades in the subject, yet realizing they have minimal understanding—or the alternative: classroom practices that lead to true understanding?
An examination of the tenacity with which long division holds sway in the classroom and the prejudice against the acceptance of the calculator.
Meaning-enhancing math processes and curricula joust with misguided "standard" practices and an uninformed public.
Looking at the original meanings of such words as student, school, test, discipline, and educate, suggests a number of fresh and helpful images for educators.
Evidence of an innate mathematical spirit abounds. But often classroom practices stifle this inner mathematician. How can we avoid that, and how can a strangled spirit be resuscitated.
Expressions, such as "the real world" and "real-world problems," suggest that mathematics is not part of "the real world." The implications of this view are investigated.
Statistics show that 30 percent of U.S. workers earned less that $7.25 in 1995. Can these be the "well-paying," gratifying jobs students are told will be at the end of their educational trail? Might we better focus on the trail itself?
Creativity, in mathematics or any other area of life, entails an encounter between a highly-involved individual and some aspect of his or her world. How does one facilitate creativity in the mathematics classroom and also deal with the anxiety that can ensue?
We seldom reflect on the validity of our own long-held positions and can endlessly discount "evidence" that goes counter to these positions. Asking "What evidence will I (you) accept?" sidesteps an interminable and ultimately useless "Yes, but..." discussion.
Tremendously expensive both in money and time spent, state assessments deflect teachers from developing students' mathematical abilities to developing their test-taking abilities.
A widely-held misconception is that the basics of mathematics consist of rules for carrying out procedures, rules that must be mindlessly memorized and practiced. Confusion reigns when, years later, adults try to recall and use these procedures that carried no meaningful mathematical understandings.
Activities that foster understanding of the grouping-by-tens nature of our numeration system and help develop meaningful mental images need to precede children's work with multiplication facts.
The dangers inherent in focusing teaching on lists of (debatable) "basic mathematical skills."
Motivation for studying mathematics that focuses on future utility may, first of all, be untruthful and, secondly, belittle the innate intrigue and interest that the subject has for students.
How assessment reforms can deform education. Might not the considerable resources spent on state assessment be better used for transforming the classroom?
What I learned from a confident student with all the right answers—but not the words to describe how he got them.
"Why do we try to teach algebra to everyone?" may not be a question of "Why?" but "How?"
Teaching the "Christopher Columbus Stuff" of mathematics—procedures that one can learn by rote and test on successfully—doesn't develop students' mathematical common sense or perception.
In response to An Open Letter to Secretary of Education Richard Riley, we question the stress the letter writers put on algorithms.
Is mathematics a nice predictable world where things always behave in a sensible, logical fashion, as many think? Or is it actually a world of infinite possibilities and variety, where creativity and imagination are free to roam?
Are state assessments accomplishing something of value, or do they waste time and money? Aren't classroom teachers still the most qualified to assess their students' accomplishments?
Getting students to learn may not be possible, but other things are.
Problem solving is an essential part of all mathematics and not just another topic to be included in a school math curriculum.
Education ought to be viewed as an end in itself rather than preparation for a future many students will never realize.
Some fret about programs that want to make math fun. The concern ought to be math classes in which nobody is having any fun.
The news about math isn't favorable—and requiring more math won't change that.
The subconscious plays a significant, albeit mysterious role, in problem solving.
"Education" is a four-syllable word. If you had to pick another four-syllable word to describe the educational process, what word would you pick? The choice of the powers that be seems to be "competition." There must be a better word. My choice is "expedition."
Focusing on the future steals from the present.
The President's logic won't lead to acceptance of his national testing program.
Dealing with dropouts is more than an educational problem; it's a societal problem.
If you really want to know how well we're doing in mathematics education, talk with your mailman, or any other adult.
Equating education with job training doesn't serve life's circumstances.
A research study provides strong evidence that everyone's mad about math.
Sophisticated schemes come up short.
The fortuitous occurrence of two news stories in the same issue of the local paper lead to reflections on the relationship between education and the business world.
A reprint of an article on mathematics teaching that appeared in the September 1984 issue of the Oregon Mathematics Teacher.
The autobiographies of two colleagues at the turn of the last century reveal a radical difference in attitudes toward math attitudes that still prevail today.
Mathophobes—persons with an aversion to math—are easily produced in today's educational climate.
A granddaughter's description of her algebra class is dispiriting.
A popular metaphor for the role of manipulatives seems wanting.
Administrators, and others, learn to play the education game.
By request, the text from talk given April 22, 1999 at the 77th Annual NCTM Meeting in San Francisco, California.
The content of Dr. Maier's April 14, 2000 presentation at the 78th Annual NCTM Meeting in Chicago, Ilinois.
Other Articles by Gene Maier
Even with increasing scores, the current emphasis on testing foreshadows a gloomier day for education.
Who can object to teaching the basics? But the question is: What are they?
Years later, what is retained from those college math courses.