When I was in kindergarten, my mom would sit me down at our dinky kitchen table and teach me how to do long addition on the back of bill envelopes. I remember she would constantly laud me for how smart I was, motivating me to want to learn more and more. Other days, she would bring out the multiplication flashcards that people from church didn’t want anymore, and run me through my twos, then my threes, and so on. By first grade, I knew how to do long multiplication and division while in school we were just beginning multiplication tables. My mom had long stopped teaching me at our kitchen table by the time I hit middle school, but she always emphasized how important it was to build a strong foundation in math early on. Of course she was right — geometry and algebra came much quicker because I knew my arithmetic.
This Sunday, I found myself running through makeshift multiplication flashcards with a sixth-grade student I tutor in West Philly. I’m a senior at UPenn now, and I’ve been tutoring since I was a freshman. Though this student and I had been working recently on more advanced math homework, such as long division and fractions, I discovered. that Sarah still didn’t know off the top of her head what six times seven was.
The truth is, she’s one the best students I’ve had. She’s always focused and engaged during our sessions, and it’s clear that she is really motivated to do better in school. When she told me that her teacher had said students “should stop doing their math homework after 30 minutes because they’re too stressed,” Sarah shook her head in disapproval and said she often spent an hour or more each day on math. I, too, was surprised — 30 minutes? When you’re learning, one problem can take 10 minutes, and three problems is certainly not enough practice. Besides, struggling with a problem builds one’s ability to work through frustration.
Beyond being hardworking and driven, Sarah learns pretty quickly if I give her clear instructions on what to do. I once spent an hour-long session teaching her how to do long division. When I brought it up again the next week, it only took her about 20 minutes to relearn everything, with her constantly saying: “Oh, it’s coming back now.”
What I’ve realized is that knowing how to do basic multiplications is not about your intelligence or ability to learn, nor does it reflect your potential to succeed. At the start, it’s a memorization game, and what it does correspond to is time spent and repetition, often requiring the help of a parent or teacher. While this skill is easily gained, knowing your multiplications up to 12 is also crucial to future success in math. Students forced to move on to fractions and decimals cannot think about abstract relations when they have to use a calculator to figure out six times four. Determining the greatest common factor when you don’t realize that both 64 and 72 are divisible by eight makes simplifying fractions a Sisyphean feat. Having a good grasp of numbers makes life easier too, especially for budgeting money and time.
With parents and teachers already overworked, the problem can be treated, but not cured, with weekly tutoring sessions. That Sarah’s parents are willing and able to drive 20 minutes to and 20 minutes from Penn’s campus each Sunday is already more than what could be asked of many parents who work two or three jobs to keep their family afloat. Perhaps the most straightforward solution would be increasing the Pennsylvania school budget, which has been vastly underfunding low-income school districts for years, falling $4.3 billion short in 2005 of providing enough money to prepare students to meet state standards. The distribution of funds, originally intended to alleviate inequalities, applies only to “new money,” so low-income districts are still left with insufficient funding. Students like Sarah are at the mercy of these school budgets, which affect material needs, such as technology and textbooks, as well as learning conditions, such as student-teacher ratio, extracurricular activities, and the possibility of regular, on-site tutoring.
My goal with Sarah over the next few months is to become my mother at the kitchen table, not simply to get through her math homework, but to really solidify foundational math concepts. While it may seem tedious now, I’m hoping it will be helpful in the long run.
Joyce Xu is a student interested in observing human behavior through the lens of neuroscience and literature, as well as an icebreaker enthusiast.