My adventures in medication math.

I did my first med-math problems when my wife was in nursing school. She's pretty sharp and no math weenie, but some problems proved frustrating and she'd say, "Okay Mr. Math Guy, see if you can solve this one." I'd do the old bing-bang-boom, and offer up the (correct) answer. Once I got the old, "Ha! You're wrong, the answer key says it's ..." to which I helpfully replied, "When you go to class tomorrow be sure to let your instructor know her answer key needs correction."

Somehow I gave the impression of being some sort of math whiz, which I knew not to be the case, but damned if I was going to admit it to her—I didn't want her thinking she was smarter than me in everything! Unfortunately, at the time, I didn't pay any attention to how nursing students were being taught to do med-math, and she, asking only for the answer, paid no attention to how I so easily and annoyingly came up with the right answer every time. As it happened, during her first year she was taught the traditional (for nurses) approach using ratios, proportions, and formulas. Then during her second year, the school switched over to the new fangled (for nurses) approach based on dimensional analysis.

A couple of years later our daughter started nursing school (I started the next year), and I got to hear all the med-math horror stories about how many did or didn't pass the latest med-math quiz (these were given throughout the year after everyone had passed the 8-week med-math class) and had to attend remedial classes (on the dreaded titration quiz only two students in her class passed the first time!). Unfortunately, once again, I didn't look into how she and other nursing students were being taught to do dimensional analysis. I just thought there was something about med-math problems that made them incredibly difficult to solve.

I should have known that there was something horribly wrong. I had learned to do dimensional analysis (DA) some thirty years earlier when I was taking a lot of chemistry classes. I've happily used DA ever since and had never encountered an applied math problem in chemistry, physics, or engineering that DA couldn't readily dispatch, and yet I was willing to assume that med-math problems, with the exception of the ones I had done myself, were somehow different and intrinsically harder. I'm such a bloody moron!

It wasn't until I started nursing school and took the obligatory med-math class that I finally realized what was going on. I had an hour or so to kill before the first class, so I opened the textbook to glance through it. Before class began, I had realized, with growing shock and disbelief, that the authors of the textbook didn't understand the technique they were attempting to teach to nursing students. There were serious errors of omission—things you really need to know to do DA right and well. And there were serious errors of commission—using techniques and the language of math so badly as to give the text a distinct air of innumeracy. I was convinced that if I had had to learn DA from this book, I would be at serious risk of not passing the class. My next thought was, "Hmm, wonder where the instructor learned to do DA?"

So here I was in an 8-week class with nothing to do apart from memorizing a few abbreviations and conversion factors. The instructor made a good show of pretending she knew what the textbook was talking about. Instead of risking doing problems on the board herself, she deftly had students, a half dozen or so at a time, come up to the board to do problems from the text. Then she would point to each problem in turn and ask if everyone got the same answer. If anyone thought the answer wrong, they got to explain how they came up with the right answer. This actually worked out rather well as several students had enough sense to ignore the textbook and figure out how to do the problems in spite of the book.

Since I had a lot of spare time, I decide to see if I could do something to improve the situation. Perhaps a critique of the text with suggested corrections would help. Better, I could explain how I was taught to do DA with the gentle hint that maybe the Ph.D. chemist who taught me understood DA better than the nurses who wrote the textbook. I got started, getting my thoughts together in writing that first week of class.

Part of the situation was that here's a freshman nursing student, O ye of zero credibility, seriously thinking about calling into question the mathematical acuity of textbook authors with advanced degrees (in nursing), and implying that those teaching or who have taught the class, having learned DA from the book, didn't quite know what they were doing either. I needed to be careful and make sure I knew what I was doing. My first reality check was to mention my assessment of the textbook to a fellow student known to have a good grounding in science and math. He immediately agreed that the authors were confused, but as he was doing fine, he didn't seem interested in offering any corrections—a wiser man than I.

The only students to get in serious trouble were the ones who spent way too much time reading the book. I recall two who had taken the class over the summer and had failed it. They were taking it again and knew they'd be dropped from the program if they failed again. The pressure was on, and they just weren't getting it. The instructor tried without success then asked me to tutor them. I assured them I could help, but that I wasn't going to teach them to do DA the book way. They thanked me for the offer, but decided not to risk being confused any more than they already were, and to tough it out in the hope that, with enough effort, they would at last master med-math by the book. Sadly, these were the two who were dropped from the nursing program because they couldn't pass med-math.

There were others more willing to let me confuse them, but all reported that my clairifications were helpful. One student asked me a couple of days before the final how to pick a starting factor (something the text fails to mention), and reported the next day that she tried my technique out on various problems the night before and that it worked! She later mentioned getting 100% on the final.

As the hours put in to the project began to mount up, I thought of spinning my work into an Honor's Project, which would involve some faculty involvement and oversight. I was given the nod to go ahead, but from there on I pretty much did my own thing. At the end there would be an Honor's Colloquium, and I'd invite all the faculty listen to my presentation.

I realized that I was at best being presumptuous, and even I found it difficult to consider the possibility that I might be right. I needed to consult with someone whose mathematical acuity was beyond reasonable doubt, someone whose judgement I could completely trust. Ideally I wanted someone whose math ability was off the scale. Steven Hawking was too busy, or so he claimed, working on another project—something about a theory of everything, so I had to find someone else.

I emailed Jef Raskin about my problem who replied that he was a strong supporter of DA and was willing to help. Jef Raskin may not be a household name, but Jef is the creator of the Macintosh computer and was lead designer of the Mac OS. Prior to that he was a professor of computer science at UCSD, and since then, apart from being known widely as a human interface guru, he has written over 300 articles and books on science, math, and technology issues. I really like this guy, and as a bonus his wife is a nurse with advanced degrees (which is what made me think he'd take an interest).

I sent Jef copies of the textbook, those portions I found questionable, so he could form his own opinion. Basically he agreed that the authors' presentation of DA was "illogical and incorrect." But he went on to explain that gifted scientists and mathematicians use a different technique, namely none at all. Problems are approached from first principles and reasoned through to the answer that makes sense. This approach, the think-it-through technique, is slow and error is a risk, but the aim is to understand deeply and not merely crank out the right answer using some superficial technique. Of course, for those of us less gifted folk, superficial technique that gives us the right answer every time looks pretty darn good. It was a pleasure and a privilege to correspond with Jef.

I didn't mention my correspondence with Jef to my project mentor or other faculty. I felt that my critique and suggestions should stand on their own merit. I was prepared to argue my points based on evidence and reason, and felt that to play the Authority Card to gain credibility would be in bad form. In hindsight I probably should have in order to gain enough credibility to be listened to in the first place.

When all the students at the college who had done Honor's Projects were scheduled to present, I was the only nursing student on the list. I personally invited the Director of Nursing and any faculty who might be interested to attend. My presentation went well and was well received by the 30 or so academics present. Unfortunately, due to schedule conflicts, no one from the nursing department was able to attend.

On the off chance that someone out there in cyber land would be interested in my work, I posted some stuff on a Web site. I hope someone out there is being helped.

As my first year of nursing school came to a close, I told the Director of Nursing I would be willing to meet with her and any interested faculty to explain my concerns about the med-math program at a time of their convenience. She said she'd let me know, and here I must note that I detected or imagined some annoyance on her part that I was bringing up the subject yet again. At any rate she never called and I never offered again.

At the end of my final year of nursing school I felt I had an ethical responsibly to try again. I contacted by email the instructor currently teaching med-math (not the one I had had), and shamelessly played the Authority Card. This got me a meeting. She was receptive, mentioning straight off that she had already come to the conclusion that there was something not quite right with the textbook, but had yet to determine what it was. Needless to say I had plenty to say on that point. I was given time to make my case, felt I was listened to, and that all points were taken. I don't know if med-math students are doing any better as a result, but one can always hope.

Eric Lee, RN

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