Dean’s Reasoning Doesn’t Add Up

Orange County Superintendent of Schools John Dean tried to set the record straight regarding math scores (Orange County Voices, May 4). Now I’m doubly concerned.

I don’t mind that he personally doesn’t know the theory behind the operation of dividing a fraction by a fraction. It’s his belief that only professional mathematicians need to know this that’s nonsense. Our math teachers have to know it! One can’t help but wonder about their competence if the perspective of the administration is so seriously flawed. If that’s the prevailing mind-set it’s no wonder our colleges and universities need to provide remedial math courses.

The theory behind division of a fraction by a fraction is no more complicated than the fact that if both numerator and denominator are multiplied (or divided) by the same quantity the value of the fraction is unchanged. Any competent instructor can make that point and drive it home with a variety of well-chosen examples. It is necessary to understand this concept as subsequent math, technology and science courses often contain algebraic equations presented in the form of complex fractions.

We need to give our children the best education we can deliver. Testing our students for what they’ve been taught has validity only if they’ve been taught what they need to successfully further their education.

PHILIP CUTLER

Costa Mesa

* Superintendent of Schools John F. Dean offers us the reassurance that our fourth- and eighth-grade students really are not doing as poorly in mathematics as we might conclude from the results of the recent National Assessment of Educational Progress tests.

He cites results from a variety of other tests to back up his claim that students really are doing OK. Is it any wonder that 53% of the freshmen who enter the California State University system are unable to pass a simple test on high school algebra?

Dean admits that he is unfamiliar with the NAEP mathematics test even though NAEP has been in use since 1973 and is widely regarded as the only nationally representative, continuing assessment of what elementary and secondary students can do in a variety of subjects.

Given that this test has such a prestigious pedigree and that it forms the basis of our “National Report Card” on the quality of K-12 education, I’m more than a little surprised that our county superintendent of schools doesn’t seem to have a clue about it.

The NAEP math test examines a student’s conceptual understanding, procedural knowledge and problem solving ability at a very basic level.

This is not rocket science! The test examines the basic mathematical knowledge that a person needs to function in society: to be able to balance a checkbook, to decide if the interest on that credit card you are thinking about signing up for is more than you can afford, or to figure out if you are getting a good deal on your home mortgage.

The fact that California students do so poorly on the NAEP is an indication that both our curriculum and our teaching techniques are out of step with the rest of the country, and that our students are not learning the mathematical skills they need to be able to function in a society where the good jobs require at least some number sense.

MARK H. SHAPIRO

Professor of Physics

Cal State Fullerton

* As a volunteer tutor of community college mathematics students I wish to disagree with John Dean.

Our students are bad in mathematics. Many students from Orange County high schools are graduated without a useful understanding of basic mathematical concepts. If a student cannot explain his reason for using a particular procedure, how does he know that the result is correct? Dean treats the learning of “how and why” as exercises in committing facts to memory.

One person can only commit a few facts to memory. We compensate for that limitation by generalizing, by combining many facts into one concept. Mathematics is generalization. Learning and applying concepts requires much more than a good memory.

The process builds on previous concepts and expands the range of problems to which the concepts apply. Even history, which is often perceived as a study of facts, finds the reasons behind actions that produced historic events. We don’t serve our students well if we don’t have a system that teaches concepts, reasoning from concepts and applying concepts to problems.

To decide whether we are successful we must test the ability of every student to reason and explain. Our measure of success must withstand comparison with other states.

FRANCIS N. EASTMAN

Costa Mesa

* I was dismayed to read John Dean’s “defense” of mathematics education in Orange County schools, doubly so when I realized that these words were coming from the county schools superintendent. This type of trashing of mathematical reasoning is the precise reason test scores are low.

Dean belittles mathematical education altogether by implying that simple division is useless knowledge for the general public. He then suggests that only “serious, professional mathematicians” need to know how division works. I expect this sort of rationale from Talking Barbie, or perhaps Beavis, but not from an education professional.

We live in a technological society. Tools such as computers and calculators require more knowledge from the user, not less. The ability to divide a pair of fractions is a good thing to have; understanding why we “invert and multiply” is what separates a student from an electronic calculator; the ability to express that knowledge is what separates a good student from an average one (or from a superintendent of schools).

The purpose of tests such as the NAEP is to determine the depth of knowledge students are attaining. If a child can divide twelve by three, but can’t set up and solve a word problem requiring the same level of arithmetic skill, what has the child learned? The ability to recognize the nature of a problem is inherent to solving that problem.

JAMES REPKA

Laguna Beach