Subtraction: How the Hunted Became the Hunter
I have been listening to various versions of the phrase, “Damn kids these days, can’t even make change without a calculator,” for what has felt like my entire life. Kids, in this phrase, is a synecdoche for young people that work at, with, or behind a cash register or till. By the way, whether the register/till is at a grocery store, convenience store, drug store, movie theatre, restaurant, coffee shop, pub, bar, retail outlet, gas station, or wherever, it doesn’t matter. What matters is that these young people and their inability to make simple change behind the till is seen as a measuring stick for the rapid decline of the teaching and learning of mathematics in our schools and our society as a whole. There’s a lot to unpack here.
I should point out that I am not immune from the above conversation. In 2000, the nice lady conducting my interview for a bartending position at The Birchwood Motor Hotel (an hour north of Winnipeg on Manitoba Highway 59) pointed out that she was impressed that I had a BSc in mathematics. So impressed, actually, that she said that I would have no problem with the most important question of the interview. She asked, “If a bottle of beer costs $2.95 and a customer gave you a $5 bill, how much change do they get?” I promptly replied, “$3.05.” Oops. Shocking, I know… a bottle of beer used to cost $2.95! Oh, I see, you’re laughing at my incorrect answer. Stop laughing. Quizzically, the interviewer looked up from her sheet, but before she could look up the whole way I was able to tweak my answer to the correct amount of $2.05. We had a good laugh about me giving away the hard-earned money of the hotel owner, which was followed up by a series of questions involving the price of 2, 3, 5, and 7 beers, and the change that would be given back for various denominations of bills. Good news: I nailed this remaining portion of the interview and got the job.
I should also point out that at the time, I wasn’t the prototypical whippersnapper that most picture behind the till when they start to wax poetically about young peoples’ inability to make change, and how this is a sign that the world is quickly going to hell in a hand basket. Quite the opposite. At the time of the interview, I was in my early-to-mid-twenties (which, yes, I did consider old at the time), had majored in mathematics at university, was very confident in my arithmetic (and mathematical) abilities, and, perhaps most importantly, was not fazed by and was able to catch little errors that arose during my mental math moments. Barring certain notable servers, one in particular, my mental math behind the bar would soon become the stuff of legend at the Birchwood Motor Hotel. It wasn’t just the speed with which I could calculate the cost for big orders; rather, it was the confidence that I had in my answers that impressed my colleagues. That’s enough about me.
I contend that when we talk about peoples’ inability to make change, we have been too restrictive of the individuals under scrutiny. Ageist, if you will. Given the way our society is structured, it’s true that there are predominantly young people behind the tills. The reason for this, for the most part, is simple: young people can get paid less. (This notion was expressed eloquently by podcaster Adam Carrola, who said that we live in a “minimum wage gilded cage.”) The change-making ability of older individuals that work with/behind a cash register must be better. And, keeping in line with the current mathematics education zeitgeist in Saskatchewan and across Canada, there is a dominant working theory about why this must be so: given that the change-making individuals are older, they will have been taught mathematics properly — that is, in a traditional fashion. All of those lectures, worksheets, Mad Minutes, homework questions, quizzes, and tests concerning elementary arithmetic (adding, subtracting, multiplying and dividing) mean that elder folks should have no issues when tasked with elementary arithmetic tasks… The thing is, I have found quite the opposite to be true.
Albeit unofficially, I have been testing the numeracy skills, specifically subtraction, of liquor store employees ever since I turned 19 years old (the legal age to purchase alcohol in British Columbia). Well, not exactly ever since. The years during which I conducted my research were 1996, 2000–2006, and 2010–2016. The years during which I did not conduct my research were 1997–1999 and 2007–2009. If you have spotted the pattern, then you know that I am not conducting my experiment this year, 2017, and for the next few years, 2018 and 2019. If I’m being honest, I’m not sure I am even going to pick the experiment back up in 2020–2026, because I’m not sure that I’m going to like the results. As I have alluded to, my experiment is a test in subtraction, but I would be remiss not to mention that it is also an exercise in pushing back against authority.
For a very long time, I was nervous about handing over my identification to a liquor store employee so that they could determine whether or not I could purchase alcohol (mostly beer). This stems, in part, from my efforts to buy beer (and coolers) before I was legally allowed to make these purchases. My nervousness manifested itself physically with an elevated heart rate, and sometimes, my palms would start to get a bit clammy. Mostly, though, my nerves would be exposed through the awkward back-and-forth exchanges with the employee that stood between me and the purchase of my alcohol. “Did you find what you were looking for?” the employee would ask as I slid my purchase across the counter, to which I would sheepishly reply, “Fine, thanks.” My odd replies to questions that were not asked of me were a tell. They told the employees that I was nervous, which meant that I might be trying to purchase alcohol as a minor. “Can I see your ID?” the clerk would ask next. For whatever reason, perhaps due to a deep-seated fear of authority, my nervous replies did not disappear once after I was old enough to legally purchase beer throughout Canada and North America.
I should come clean. I said, earlier, that I conducted my subtraction research in 1996 and from 2000–2006, but that is not entirely true. It would be more accurate to say that I laid the ground work for my subtraction research during those years. What I noticed during that time was that the employees who were attempting to determine whether or not I was of age had a tough time with subtraction. Being born in 1977, the difficulties clerks had with borrowing in 1996 and from 2000–2006 was something that I noticed. I could see their mental arithmetic efforts in their faces. However, the context, the nerves, and the long line up of older people standing behind me meant that I would usually only make note of the subtraction troubles of the clerks after our exchange had completed. And, not making much money at the time, I focused my in-the-moment efforts on making sure that the clerk gave the right amount of change back. (Remember using cash to make purchases?!) Then, one day, one exchange changed everything for me.
I’m not sure what made me do what I did on that fateful day. It must have been a cocktail of getting older, being sick and tired of getting IDed, and being more confident with myself in life, in general. In 2006, a 29-year-old Egan J Chernoff was asked, “Can I see your ID?” as he was purchasing some beer. My response, as I was reaching into my wallet for my driver’s license, was, “Yes, you may, but you’re going to have to tell me how old I am…”
At that very moment, it was abundantly clear to me, and the numerous people in the lineup behind me, that I had irreparably upset the balance of power between IDer and IDee. The hunted had become the hunter. The clerk, an elder gentleman, was a bit stunned with the question. I don’t think he knew what to say at that point. He took my ID, looked at it, handed it back and said, “You’re old enough.” Not satisfied with the answer to my question, and channelling the nerves of all those people throughout the years who felt, and still feel nervous about handing over their ID even though they are of legal age, I doubled down: “How can you tell me I’m old enough without telling me how old I am?” His response, “You’re old enough,” was not satisfying. In that moment, I realized that I may have lost this battle. But it did not matter, because I was about to engage in a war with liquor store employees every time I got asked for my identification.
“Sure. Please tell me how old I am,” is now my go-to response when I am asked for identification. The responses that I have been given over the years have been fascinating. Clerks are stunned when I ask this question. So are the other people in line. The most memorable response is also one that still bothers me to this day. At the very moment that I finished asking a nice lady behind the till to tell me how old I am — that is, to do a subtraction problem in front of me in real time — she looked like she had seen a ghost. My question must have taken her back to some dark place in her mathematical past. Perhaps she used to get singled out by her teacher to walk up to the board and do a subtraction problem in front of the rest of the class. Perhaps she had a tough time with her subtraction Mad Minutes. Who knows. I do know, though, that she became so pale that I told her I was just joking. But it didn’t matter — the damage was done.
There are also employees who will indulge me in my request for subtraction. They are wrong much more often than they are right. The most common mistake is that they age me a decade older than I actually am. I contend that this mistake is because, as we all found out at some point, borrowing is difficult to do when engaging in mental arithmetic via the traditional algorithm learned in school. Checking the ID of someone born in 1977 in the year 2005 becomes, in the head of most clerks, 2005–1977. Utilizing the traditional algorithm involves crossing out the 5, then crossing out the 0, then crossing out the other 0, then crossing out the 2, putting a 1 where the 2 was, putting a 10 where the 0 was, crossing that out to put a 9 where the 10 was, then putting a 10 where the other zero was, then crossing that out to put a 9 where the 10 was, so that you change the 5 to 15 so that you can subtract 7. And that’s the easy part. Clerks always get the last digit of my age correct. In this example, of course, that’s 8. But, in this example, I would be incorrectly told that I was 38 years old, and not 28. This stems, I think, from the inability to keep track of the 0 turning to 10 and then turning to 9 in the tens column, which means subtracting 10–7 instead of 9–7. Whether young or old, those who employ the traditional algorithm for subtraction when unexpectedly tasked with mental arithmetic often, in my experience, get the answer wrong.
I’m still waiting for the day when I ask my question and the clerk standing between me and the purchase of my beer says something along the lines of, “Well, it’s 2014 and you were born in 1977, but if it were 2017, then you would be 40, which means I need to account for three years, which makes you around 37, which means I don’t have to worry about the month that you were born in for your stupid request, sir.” Alas, no such exchange has taken place. Actually, I have found that my subtraction requests are being thwarted by a change that embraces the poor numeracy skills of North American citizens.
The days of having to complete a subtraction problem to determine whether or not someone is of legal age, for all intents and purposes, are over. The signs are everywhere. Actual signs. I walked into a bar in Hawaii a few years ago and hanging on the wall was a sign, an electric sign that updated in real time, that read, “We I.D. Must be born on or before this date: [Month Day, Year].” Closer to home, similar signs are now hanging in the back rooms of pubs, bars, cold beer and wine stores, and liquor stores. Developments such as these, I contend, must be taken into consideration the next time you hear somebody utter the phrase, “Damn kids these days, can’t even make change without a calculator.”
Look, I agree: young people, those working behind tills and counters, should be able to make change. But I’m not sure I agree that their inability to make change is a true measuring stick for the rapid decline of the teaching and learning of mathematics in our schools and our society as a whole. The fact that I have consistently encountered relatively older employees who are unable to correctly answer a simple subtraction problem could easily be used to assert that we are, perhaps, looking through rose-coloured glasses when comparing the teaching and learning of mathematics of different generations. However, I would rather use this opportunity to shift the discussion from the change-making ability of young people to what’s happening in the world around young people today.
Society is heading in a different direction — one less dependent on the elementary arithmetic skills of individuals. A society where restaurants calculate potential tips on your restaurant bill, even the 10% tip, for your convenience. A society where electronic signs on the grocery store shelves have already calculated the unit price for the items you want to purchase, for your convenience. A society where electronic signs post a birth date to let clerks and bartenders know if you are of legal age, subverting the need to do a simple subtraction problem. Our society is slowly eliminating the need for elementary arithmetic, one of the last bastions for teaching mathematics in school… whether those damn kids with those damn calculators can make change or not.