In a non-STEM oriented degree programs, the terminal class in mathematics often involves practical training in finance, statistics, and applications thereof. It is what I would describe as a survey course, skimming the tops of these fields and trading depth for width. For this reason, the topic of percents comes up directly and in context with interest rates, mortgages, and amortization. Questions of working with statements involving percents have taken up to about 2 weeks of coursework; after this period I was curious what my students thought about the following “paradox”:
“You have 100 lb of potatoes, which are 99 percent water by weight. You let them dehydrate until they’re 98 percent water. How much do they weigh now?”
The classification scheme of Quine specifies that this is indeed a solved problem though with a seemingly absurd solution. The interesting educational result lies in how absurd it is for my freshmen college students after 2 weeks of percent training. I prompted them with the above question and left them a short write-in box to record their responses.
The results of student answers to the Potato Paradox; answer is on top of each tab.
Response Analysis
42% of students were fooled into the more “intuitive” response of 98 or 99 with 45.5% superseding that with the correct answer. Interestingly, the response of 99 pounds was more common than 98 pounds, which I can only explain as picking one of the visible numbers in the problem statement as the answer. Amusingly, the answer of 100 (or more!) pounds was nonzero indicating a lack of engagement with the problem itself for those 3 students. The students who did not answer correctly seemed to agree on my argument for 50 pounds and linked it to how we had been solving things for those two weeks. Perhaps adjusting the way percent questions are presented can bring this blue.
Pedagogical Insights
Using variable names in percent questions can be tricky, I will tag the variable with a percent sign as x%. In this question though the unknown is not a percent
“Let x be the new weight of the potatoes ”
Those who solved the paradox seemed to go this route of setting the question up. Whereas those who did not suggested 100 - 2 = 98 as their approach which mixes the units on numbers. Due to this, I think an insight can be gleaned:
“Treat percents as a unit in and of themselves. Those who solved the paradox seemed to think of the given percent information as a unit similar to pounds. ”