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## Doctors Must Have Been Middle-Schoolers

The January, 2008, issue of The Annals of Internal Medicine includes a study that should be informative to all mathematics teachers. The University of Cambridge researchers learned that doctors have trouble computing with ratios.

In a simulation of a medical emergency, 28 doctors were faced with a 5-year-old patient with a potentially fatal reaction to peanuts. The proper treatment was an immediate injection of 0.12 milligrams of epinephrine.

The doctors were given bottles of epinephrine with differing labels. For fourteen of the doctors, the lables read "1 milligram in 1 milliliter solution" while for the other fourteen doctors the labels read "1 milliliter of a 1:1000 solution." (NOTE: In "doctor-talk," the symbolic ratio 1:1000 means the same as 1000 micrograms of drug per milliliter saltwater, which is equivalent to 1 milligrams drug per milliter saltwater.)

Thus, both labels mean the same thing, but one involves a ratio and the other a concentration expression. In both cases, the doctors were to precribe a dosage of 0.12 milliliters with expediency.

The results: In the concentration group, eleven doctors prescribed the correct dosage, while in the ratio group, only two (that's right, TWO) doctors were correct. Furthermore, the doctors facing concentrations needed an average of 35.5 seconds, while the doctors facing ratios needed an average of more than two minutes (and most were still wrong).

Dr. Daniel Wheeler, the lead researcher, states: "Converting from ratios to milligrams per milliliter leads to muddles between hundreths and thousandths...All errors tend to be factors of 10--large and potentially dangerous."

Source: Simple Math Errors Can Imperil Patients," New York Times, January 22, 2008