You are here: Home / Archives for understanding

Math teacher: I don’t know enough math

March 31, 2012 by

After earning an applied math degree and teaching math for years, Darren realized he doesn’t really understand math as well as he should.

In college,  he “could calculate my butt off, but so often didn’t fully understand what I was doing.”

As an example, in differential equations I could calculate eigenvalues all day long, but to this day I don’t know what an eigenvalue is or what it does for me or why I need to calculate it. I’ve taught myself plenty –sometimes just days before I had to teach it to my students.

He told a student bound for Cal Poly “not to make the mistake I made; ask the questions, go for the deeper understanding.” And Darren decided to go for it himself.

I’ve never understood the Fundamental Theorem of Calculus. Why, exactly, are an integral and an antiderivative the same thing? I’ve followed the steps in my calculus books, and understood each step, but never really understood how they all fit together. So today I pulled a different calculus book out of my closet and I started studying. I found one that provided a very user-friendly explanation, which then allowed me to understand the very rigorous (read: dry and difficult) proof in a second text. It took a few minutes to replace decades of deficit.

In the fall, Darren will start a masters program in Teaching Math through the University of Idaho’s Engineering Outreach Program.

Most of us never have the courage to face our eigenvalues, much less blog about it.

 

Filed Under: Education Tagged With: , , ,

The myth about traditional math education

September 24, 2011 by

“The traditional method of teaching math has failed thousands of students,” claim new math proponents. That’s a myth, writes Barry Garelick in Education News.

Garelick looked at math books and methods used in the ’40s, ’50s and ’60s.

Mathematical algorithms and procedures were not taught in isolation in a rote manner as is frequently alleged. Concepts and understanding were an important part of the texts.

Then and now, nobody argues for memorization without understanding, he adds.

Traditional math education was working reasonably well, Garelick argues. In Iowa, test scores rose steadily until about 1965, and then declined dramatically for a decade.  This pattern was repeated in Minnesota and Indiana.

 

Source: Congressional Budget Office (1986)

Some researchers blame increased drug use and the rise in divorce and single-parent families for the decline. Garelick blames progressive education which called for student-centered, needs-based courses.

After taking not-so-early retirement, Garelick is now a student math teacher at a California junior high school.

 

 

Filed Under: Education Tagged With: , , ,

The secret of Singapore Math

October 8, 2010 by

Last week, I asked if the New York Times story on Singapore Math described the program accurately. Barry Garelick, co-founder of the U.S. Coalition for World Class Math, answers the question on the Core Knowledge Blog: No way.

(The Times) described a program that strangely sounded like the math programs being promoted by reformers of math education, relying on the cherished staples of reform: manipulatives, open-ended problems, and classroom discussion of problems. 

. . . Those of us familiar with Singapore Math from having used it with our children are wondering just what program the article was describing.  Spending a week on the numbers 1 and 2 in Kindergarten?  Spending an entire 4th grade classroom period discussing the place value ramifications of the number 82,566?

Singapore Math books provide pictures, examples and problems, but doesn’t tell teachers how to teach, he writes.  If a kindergarten teacher is spending a week on the numbers 1 and 2, that’s the teacher’s choice.

Singapore Math uses traditional approaches to math education, such as “explicit instruction and giving students many problems to solve,” Garelick writes. This is not what math reformers advocate. Nor does Singapore Math rely heavily on manipulatives.  It does use “bar modeling” to help children solve problems.  

 Singapore’s strength is the logical consistency of the development of mathematical concepts. And much to the chagrin of educators who may have learned differently, mastery of number facts and arithmetic procedures is part and parcel of conceptual understanding.  Starting with conceptual understanding and using procedures to underscore it is an invitation to disaster—such approach is making profits for  outfits like Sylvan, Huntington and Kumon.

The underlying message in articles such as the Times’ is that math education is bad in the U.S. because it is not being taught according to the ideals of reformers—and the reason it is successful in Singapore is because it is being taught that way.  Never considered is the possibility that the reform minded methods and textbooks written to implement them are one of the root causes of poor math education in this country.  Katharine Beals in her blog “Out in Left Field” does an excellent job describing this.

Garelick plans to start his career as a math teacher next year, after he retires from the Environmental Protection Agency, where he’s an analyst.

Filed Under: Education Tagged With: , , , , ,