# 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.

#### Number Sense/Number Sense

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."

#### Another Case of Swindling

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?

#### Long Division Dead as a Dodo Bird?

An examination of the tenacity with which long division holds sway in the classroom and the prejudice against the acceptance of the calculator.

#### A Modest Proposal: SOQME

Meaning-enhancing math processes and curricula joust with misguided "standard" practices and an uninformed public.

#### The Words of Education

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.

#### Inner Mathematician

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.

#### The Real World

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.

#### The End of the Trail

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?

#### What's Missing

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?

#### What Evidence Will You Accept?

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.

#### Influencing Instruction

Tremendously expensive both in money and time spent, state assessments deflect teachers from developing students' mathematical abilities to developing their test-taking abilities.

#### The PTA Does Fractions

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.

#### Those Times Tables

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.

#### What's Basic?

The dangers inherent in focusing teaching on lists of (debatable) "basic mathematical skills."

#### The Big Lie

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.

#### Reforming, Deforming, Transforming

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 Rusty

What I learned from a confident student with all the right answers—but not the words to describe how he got them.

#### A Question About Algebra

"Why do we try to teach algebra to everyone?" may not be a question of "Why?" but "How?"

#### The Christopher Columbus Stuff

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.

#### The Life of Riley

In response to An Open Letter to Secretary of Education Richard Riley, we question the stress the letter writers put on algorithms.

#### Not Fit For Human Consumption

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?

#### Assessing the Assessment

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?

#### Who Gets What

Getting students to learn may not be possible, but other things are.

#### Problem Solving

Problem solving is an essential part of all mathematics and not just another topic to be included in a school math curriculum.

#### Why Education?

Education ought to be viewed as an end in itself rather than preparation for a future many students will never realize.

#### For the Fun of It

Some fret about programs that want to make math fun. The concern ought to be math classes in which nobody is having any fun.

#### Math in the News

The news about math isn't favorable—and requiring more math won't change that.

#### Attending to the Subconscious

The subconscious plays a significant, albeit mysterious role, in problem solving.

#### Four-Syllable Words

"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."

#### Taking Thought for the Morrow

Focusing on the future steals from the present.

#### Testing the Logic

The President's logic won't lead to acceptance of his national testing program.

#### Dropping Out

Dealing with dropouts is more than an educational problem; it's a societal problem.

#### A Talk with the Mailman

If you really want to know how well we're doing in mathematics education, talk with your mailman, or any other adult.

#### It Doesn't Make Sense

Equating education with job training doesn't serve life's circumstances.

#### Everybody's Mad About Math

A research study provides strong evidence that everyone's mad about math.

#### College Football, the Postal Service, and Bush-era Education

Sophisticated schemes come up short.

#### The Education/Business Connection

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.

#### Note to Myself—Some Reflections on Teaching

A reprint of an article on mathematics teaching that appeared in the September 1984 issue of the Oregon Mathematics Teacher.

#### Math in the Lives of Two English Professors

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.

#### How to Make a Mathophobe

Mathophobes—persons with an aversion to math—are easily produced in today's educational climate.

#### The Algebra Blues

A granddaughter's description of her algebra class is dispiriting.

#### Manipulatives and Metaphors

A popular metaphor for the role of manipulatives seems wanting.

#### Playing By The Rules

Administrators, and others, learn to play the education game.

#### How The Mind Deals with Math (Special Presentation)

By request, the text from talk given April 22, 1999 at the 77th Annual NCTM Meeting in San Francisco, California.

#### What They Say About Math and What We can Learn From It

The content of Dr. Maier's April 14, 2000 presentation at the 78th Annual NCTM Meeting in Chicago, Ilinois.

### Other Articles by Gene Maier

#### The Testing Pall

Even with increasing scores, the current emphasis on testing foreshadows a gloomier day for education.

#### Teaching the Basics

Who can object to teaching the basics? But the question is: What are they?

#### What Did You Get Out of That?

Years later, what is retained from those college math courses.