Innate Interest + rewarding exploration = math success

This is a response to a letter by Silvio Laccetti to the Mercury News on April 13, 2004.

He says math students need:

• Innate Interest, though few have it.
• The ability to think logically
• The dedication to practice
• The ability to grasp abstract ideas.

Where do students get these traits?

Innate interest.
All kids starts out with innate interest in math. Either it is nurtured or it wanes. The traditional "skill and drill" methods of traditional math teaching kills interest in math.

Logical thinking.
Logical thinking in math develops by exploring the physical world, counting every kind of thing, weighing, measuring, estimating, sorting, arranging, classifying. Kids especially need blocks and models for exploring their math. Exploring patterns and classifying, they can learn the set-theoretical aspects of logic.

Solving problems in groups nurtures logical thinking. In a group, students hear different perspectives and can be taught to think before they speak. They are motivated to look critically at their own ideas and get feedback from others. People learn when they need to. In groups, kids learn the need for logic and rigorous reasoning.

Dedication to practice.
Kids need dedication, but to work, not practice. And how do they learn dedication? They learn it by solving problems that are open-ended so their insights can be rewarded. They learn it by having their perspectives appreciated rather than learning "there is one right way." The problems need to be easy enough that the student can make headway, but hard enough so finding solutions are rewarding.

Developing insight and number sense are rewarding. Feelings of being knowledgeable and able are rewarding. Feeling confident is rewarding. Contributing is rewarding. There's little room in traditional math courses for these.

Success is rewarding and develops patience. Basic learning theory tells us that people will work harder and longer for less frequent rewards (the essence of patience) if the rewards keep coming. Programs that foster interest and these kinds of rewards turn out more students who choose science and engineering careers.

Skill-and-drill math classes have very limited rewards. Teaching kids to find answers quickly teaches them that patience just means they're failing. Traditional "exercises" are based on performance of skills just learned, not insight or valuable perspectives. There's no reward for conceptual understanding.

The ability to grasp abstract ideas.
People who study children find that kids develop this naturally as they age, but only in areas in which they are familiar. They need to count before they can add. They need to group their additions before they can add 2-digit numbers. They need to "take away" before they can subtract. They need to add repeatedly before they can multiply. They naturally build up abstract ideas based on experience.

Studies show that children are ready for (abstract) algebra anywhere from 6th to 10th grade. Pushing algebra on them earlier only frustrates them, again turning them off of math.

So while I liked Prof. Laccetti's sentiment, he doesn't uncover the real problems- why aren't we fostering these traits needed for math success? Those studying math teaching know why:

• Elementary school teachers are not taught how to teach math.
• For elementary schools, California state textbook money can only be used for very tradition "skill and drill" textbooks.
• California's poor math standards mandate learning a skill a week instead of learning deeply.

Professor Laccetti says "Every year America's public school students are tested on their math proficiency, and every year the results are unnacceptable." Perhaps it's time we stop doing the same old traditional math teaching. Perhaps it's time we look at programs that work and listen to the experts.

Two of California's three problems are easily solved.

• Make the book list recommended, not mandatory, and publish a list of books recommended by those who study math teaching.
• Throw out the California Math Standards and instead adopt those of the National Council of Teachers of Mathematics.

Currently, elementary school teachers in California who want to teach math well can't. Let's give them the freedom to do so, and begin to give others the training and support they need to teach math better.

Randy Strauss
Parent, Mathematician, Computer Scientist, Math Teaching Student