One step forward, two steps back?
In “Back to Basics for the ‘Division Clueless,’” Lisa Watts reports on Krieger School mathematics professor W. Stephen Wilson’s lament about how the “new-old-new” math has ruined elementary students’ grasp of numeracy [Wholly Hopkins, Winter 2010]. The substitution of technology for memory and understanding eventually affects SAT scores and undergraduate performance, according to Wilson’s analysis.
Several recent news articles attest to related phenomena. For example, a December Baltimore Sun article called “Study: One-quarter Fail Army’s Entrance Exam” described a study of high school graduates applying for the military. According to the study, many graduates lack the reading, math, science, and problem-solving skills needed to pass the enlistment exam.
Are we being led down the path to utter destruction by a “Sputnik revival”? Are we putting too much faith in a regeneration of computer-based instruction? Do we really believe that a test teaches content? Have we substituted digital glitz for basic skills mastery? Have we once again created an either-or situation when what we need is both technology and old-fashioned learning?
I have a copy of the 1923 Maryland State Department of Education Annual Report. Though the graphs are only pen and ink, they communicate information as well as the modern computer-generated, colorful, pictorial, animated, 3-D charts. Though the prose appears in primitive font, it is written with a clarity, precision, and syntax that I wish we emulated in our current documents.
The more we progress, the less we move forward? I hope not!
Gary Brager
Former Adjunct Professor, School of Education; Supervisor of Research, Baltimore County Public Schools
Number sense
I suspect that most readers of this magazine may be initially inclined to agree with W. Stephen Wilson about continuing to include long division in the school curriculum. After all, isn’t long division a part of “basic math,” something that you learned in third grade and can still do, if given pencil and paper and enough time? No, I say it is not.
As a professor who has taught all levels of mathematics, I share some—but not all—of Wilson’s concerns about students’ overdependence on calculators. I wince when I see my students reach for their calculators to do computations that can be performed mentally, such as 10 percent of 35,000 or 27 – 22.
This is a problem for two reasons. First, mental arithmetic is a very useful skill. In some situations, it is the most efficient means of computation; in other situations, it is critical for checking the reasonableness of machine-generated answers. Second, doing mental arithmetic helps develop “number sense.” Number sense is about making sense of numbers and understanding why and how they behave the way they do. For example, using number sense I know that a 0.75-liter bottle of wine priced at $7.18 is a better deal than a 1.5-liter bottle of the same wine priced at $14.50.
However, my mental arithmetic goes only so far. For instance, I cannot do 2,375 ÷ 67 mentally. I can estimate that the answer is above 30 and I can—but do not want to—use long division to compute the exact answer. This leads to my disagreement with Wilson. These days, there are essentially three ways to do computations: mentally, with paper and pencil, or by machine. I suggest that paper-and-pencil work is important primarily for the purpose of developing number sense and mental arithmetic. In contrast, Wilson argues in favor of long division, presumably for such paper-and-pencil problems as 2,375 ÷ 67. Why? He argues that there is a cause-and-effect relationship between knowing how to do long division and learning Calculus III. I doubt it. I think there are more plausible explanations, such as students’ levels of self-discipline, or their tolerance for authority, or an underlying correlation with number sense.
Long division provides students with experience in doing multi-step problems, which is a good thing. However, I would argue that students’ time would be better spent learning mental arithmetic, grasping key number principles, and doing multi-step applications. Based on over 30 years of teaching experience, I am convinced that the average college student is deficient in all of these areas.
For all of these reasons, I think that long division is in the same category as the slide rule and will disappear from the curriculum eventually—unless those who wish to keep it come up with good research and powerful reasons to do otherwise.
Betsy Darken
Professor of Mathematics, University of Tennessee at Chattanooga
The “division clueless”
Regarding “Back to Basics for the ‘Division Clueless,’” if one looks at the math competency in this country nicely illustrated by the collapse of the financial industry and the low ratings of our country compared to others, one could deduce that we have little understanding of math and little ability to teach it. With the education system crushing the morale and creative spirit of our teachers, we have little hope of making a turnaround in the next five or 10 years. Math is a way of thinking, a way of solving problems, and a way of organizing that is applicable to any field of study. In my own case, I was able to grow in this infertile soil because of a nurtured curiosity, intelligent and caring parents, and inspiration from a teacher here and there.
When one looks at how children are being taught today, one can only cry out how intellectually undernourished they are. I gave my fifth-grade grandson a division problem of six digits divided by three, which I could do in less than a minute. Ten minutes later, he was incorrectly one-third of the way through the problem, with lattice multiplication scratch work all over the paper and multiple cumulative guesses honing in on the correct digit with absolutely no understanding of what he was doing. What was missing? He did not know how to do mental arithmetic!
In our great educational wisdom, we are removing the teaching of basic computational skills. I grew up and was part of the technology revolution and understood the intellectual and financial limits of it. We have used that technology to undermine good teaching and learning. Education has become enormously expensive and ineffective. Good education exercises the mind and helps you develop insight and techniques to study and is very inexpensive.
Irvin M. Miller, Engr ’59, A&S ’64 (PhD)
President and Director, Math and Physics Exploration
Poughkeepsie, New York
Preserving history in the digital age
I am writing this short missive concerning two articles that appeared in your Winter 2010 edition.
One of the articles was titled “The Welch Goes Digital” [Wholly Hopkins]. In it, the quote that caught my eye and made my heart sink was, “The library’s future will have arrived when its shelves are empty, its books are gone, and its librarians have become ‘embedded informationists.’”
The second article highlights Elliott Hinkes’ success in preserving “rare books, pamphlets, and articles of science” [“Atoms, Genes, and Everything In Between”].
I am not sure if it was a stroke of genius or serendipity, but the inclusion of these two articles in the same edition of the magazine provided a glimpse of the future if the Welch does go all digital.
If the goal of all digital had been achieved in the 1950s, instead of a photograph of the original Nature journals incorporating Watson and Crick’s writings and drawings, a photograph of a CD or hard drive would have had to suffice in the Hinkes article.
I do not agree with the all-digital plan for the Welch and tossing the books and print journals into “bright yellow fabric bins . . . to be recycled.” One of the most exciting times of my studies at Hopkins was walking into the Welch, feeling the books and bound journals, and communing with the spirits of all those who had come before me.
I do hope a compromise can be reached that accommodates both the computer age and the thread of history.
Curtis Chubb, SPH ’78 (PhD)
Milano, Texas
Promoting global health
Dale Keiger’s piece [“The Buck Goes Here,” Spring 2010] listing eight places to put global health money clearly expresses a problem: Doing things to people is what we do and then justify, as Randall Packard does with his concluding remark, “You do something because you can do it. People are dying and you can’t allow that to happen.” But I suspect Packard was being ironic because Keiger also quotes him as saying, “You only really solve these problems when people are able to protect themselves and governments are able to provide their own support and not depend on international aid.”
Packard also points out that the list of eight priorities discussed in the article addresses neither poverty nor war. Yet he says the list is a good place to start. I doubt it; this strategy is what we’ve been about for years. More likely it’s a good place to stop and think not about what we can do, but what might really help.
I’m not suggesting that it’s our job to end poverty or war, but there are things we could be doing. Here are four:
1. Educating women is probably the single most powerful global health intervention.
2. Preventing protein-calorie undernutrition in 0- to 5-year-olds. Children don’t just die of measles or pertussis; it’s the malnutrition that kills them. Helping moms grow what they need to feed their families saves lives and builds self-sufficiency.
3. Birth spacing saves lives and improves the quality of lives of surviving children and their mothers.
4. Integrating prevention with cure strengthens both: Meeting universally felt needs for basic primary care builds the trust necessary for sustained prevention . . . including all the eight priorities discussed in Keiger’s article.
Nicholas Cunningham, Med ’55, SPH ’77 (DrPH)
Emeritus Professor of Clinical Pediatrics and Clinical Public Health, Columbia University
Corrections:
In the Winter 2010 issue of the magazine, “Outbreak Agents,” about the federal Epidemic Intelligence Service, incorrectly stated when mass measles vaccinations began. The vaccine was first licensed and used in 1963.
In our Winter 2010 “Shelf Life” review of Bruce Parker’s The Power of the Sea: Tsunamis, Storm Surges, Rogue Waves, and Our Quest to Predict Disasters, we misreported the number of casualties in the 2004 Indian Ocean tsunami. The correct number is nearly 300,000 people.