Asking Terrible Questions and Gambling

If you are on—or leading—an admissions tour of the High School, you may want to bypass the math wing. Probably best for prospective students not to know what goes on there.

In confidence, of course, you should know that students in Upper-Level Statistics have been busy learning to ask terrible questions. Like truly dreadful and entirely useless ones. The kinds of questions that make you think, “Wow, this pollster is an idiot.”

As if that wasn’t enough, they are gambling in school. Gambling like they’ve got nothing to lose. 

(If you notice any administrator reading this, we recommend you buy their silence with some of your HERSHEY’S KISSES winnings or perhaps a souvenir playing card featuring an awkward Middle School portrait of a classmate.)

With dubious “guidance” from their “teacher,” High School math teacher Glen Russell, students set out to skew survey responses by introducing bias with leading questions. Understanding the ways questions can influence respondents will help students design better surveys and investigations in the future. As part of their pooled “terrible” survey questions submitted to a randomly selected group of students, Drew Cowan ’23 asked, “Considering Android is inferior, how much do you like Apple products (1-10)?” 

The question, he explained, made the pollster’s own opinion clear, “swaying the response more in favor of Apple.” Still, astute student respondents appeared to spot the blatant manipulation and ignore its influence. Drew observed that results were mostly comparable to the neutral “How much do you like Apple products (1-10)?”

Arjun Pathiyal ’23 asked, “Considering that soda is linked to obesity, rate how much you like soda 1-10.” Wily as always, student respondents seemed to select the “bad” response on purpose. “[The] most plausible explanation,” Arjun wrote in his analysis, “is that my leading bias question in Survey Two actually prompted people to respond with a higher score to spite my question.”

Still, as the author of Chicken Soup for the Soul wrote, “You can't get right answers if you're asking the wrong questions.” Or, to paraphrase Mark Twain, learning to ask the question, even the foolish one, helps students avoid remaining a fool forever.

In their next project, students designed Casino Math games and taught them in class. There was the random spinner “Tricycle Game,” “Ratio,” and the needlessly complicated “Candy Game,” which at least rewarded players’ commitment to the game with chocolate. Each team of game designers learned to calculate the various probabilities in their games of chance and even develop some game-play strategies based on their findings. One group created the Blackjack-inspired “AU 21 13 Smash or Pass,” while another introduced additional ways to match in a new version of Go Fish. Students also got creative, particularly in the case of the full set of homemade portrait playing cards featuring their classmates. After creating, teaching, and playing their games, students submitted explanations of and calculations related to their games to Glen. In their write-up of “Red Ace,” seniors Luke Cohen, Lucie Johnson, and Liam Zeilinger calculated geometric and binomial probabilities for two possible scenarios in their dice-and-card matching game.

“Play until the sum of the dice is 15,” they wrote. “What is the probability you play at least five games?” They found the probability to be 78.1%, regardless of the abundance (or absence) of chocolates or the presence of leading questions.

Glen and Middle School math teacher Bryan Williams have been scheming to bring the High School gamblers over to teach 5th graders about probability, game design, and how to win big. It’s fair to assume 5th graders will show the courage to ask some pretty terrible questions of their own. 

“Keeping in mind that your father is my math teacher and is standing right over there, how good is Bryan Williams at teaching math (1-10)?”