Tweak the way you do math homework. You’ll learn more and be less overconfident.
This article was originally published in Psychology Today on Nate Kornell’s blog, Everybody is Stupid Except You
Last night I was tutoring a 7th grader in algebra. The first problem was “Calculate the percent change from 13 to 20.” She thought for a moment about whether or not to divide the difference (i.e. 7) by the original number (i.e. 13) or by the new number (i.e. 20). She divided 7 by 13, multiplied by one hundred, and copied the answer from the calculator onto her page. Correct!
The next 25 problems were identical. They just used different numbers. She had to thinkto figure out the first problem. She never paused to think again. She was basically getting calculator practice. She wasn’t doing math. She started rolling her eyes just a few problems in.
She finished the next 15 or so at lightning speed. So I stopped her and asked “Do you think you’ll be able to get problems like these right on the test tomorrow?” Her teacher’s policy is that students can stop doing homework problems when they think they understand it.
She said something like “Of course, these are so easy!”
I was suspicious that doing the same thing over and over was making it TOO easy. So I told her to stop working on the problems. Twenty minutes later we came back to them.
Sure enough, her lightning speed, and confidence, was gone. In a good way. Like with the first problem, she wasn’t sure whether or not to divide the change by the original number or the new number. Even though the first 15 problems seemed simple, when she came back to them just 20 minutes later, she still didn’t have a better understanding of percent change than she had before starting her homework. But she got another chance to figure it out—and to learn some math.
Her dad came home and asked how math was going. She complained about how boring it was to do 26 identical problems. He asked her how many problems she thought it took her to really understand how to do them. She told him three or four.
But then she surprised me (and her dad) when she explained it to him.
“Dad, just because homework gets really easy after a few problems doesn’t mean you’ll get that stuff right on the test. It’s good to go back after a little while and try again to make sure you actually get it.”
I was delighted that she had listened to me—and learned an important lesson about doing homework (whether it’ll stick I don’t know). Her dad, though, wasn’t focussed on her, he was focussed on the message. His response was, basically, “Wow, I guess you’re right!”
So, just to summarize, here’s the message: When you do your first math problem of a certain type you have to figure it out. When you do the second, third, etc., sometimes you just copy your last procedure with new numbers. This is basically calculator practice. You don’t learn much. You feel like you’re learning a lot, because it’s easy. Feeling confident without learning much, that’s a dangerous combination.
So take a break and come back. That way you’ll get to actually solve the problem again. You’ll learn more. And you’ll make sure you actually get it.
This is a guest post by Hannah Hausman, Williams College Class of 2012.
Follow Nate Kornell on Twitter.
Around The Yard: Life As A Harvard Student-Athlete
- Around The Yard: Duncan Rheingans-Yoo
February22,2018Last year as a freshman, I wasn’t sure how I was going to fit in with the fencing team. I was a quieter type, and it seemed like many of my teammates were louder and more boisterous than me. Add that I was a walk-on, and while the team didn’t treat me any differently than the recruits, I still felt a little out of place, like I didn’t quite belong.
- Around The Yard: Richard Martinez
February17,2018September 4, 2017 marked my first official day as a Harvard Wrestler. The first day of my first preseason will forever be a landmark in my life.
- Around The Yard: Lindey Kneib
February07,2018To be the most successful athlete that I am capable of being, I must play for more than just myself. To be the most successful athlete that I am capable of being, I must play for more than just my teammates. To reach my highest potential, I play for my community.
- Around The Yard: Peter Blynn
January31,2018Lacrosse preseason is one of the most unique, exciting times of the year for the Harvard men’s lacrosse team.
- Around The Yard: Chelsea Ziadie
January24,2018As my senior spring semester starts, I find myself reflecting on all of my experiences at Harvard over the years. While many of my greatest memories were made on the ice with my teammates, many more were made away from the ice, gym, and locker room.
- Around The Yard: Nani Redford
December06,2017The thought of me going to Harvard never amazed me as much as it amazes others until the summer after my freshman year. When I first committed, I was excited not because its Harvard, but instead because of the people I would have the opportunity to spend time with. After meeting the other three girls in my recruiting class, I could not wait to be with them for four years and I had high hopes of befriending many other remarkable people.
- Around The Yard: Jack Connolly
November29,2017Ultimately, my time with NextEra proved to be an invaluable experience; one that essentially convinced me to declare Computer Science at the beginning of this month. Without the opportunities provided by this great school, I may never have discovered my passion for programming.
- Around The Yard: Belinda Hu
November22,2017Beginning my first semester of college proved both challenging and exhilarating. It was a time of firsts: first night away from my parents, first meal in Annenberg, first midterm, first college golf tournament, and more. It was a whirlwind of problem sets, practices, and meeting new people. Everything was up in the air, susceptible to change.
- Around The Yard: Reed Farley
November01,2017I don’t think I’ll forget move-in day. So many suitcases and so much sweat on that 85-degree day. I remember lugging my bags up the three flights of stairs, and then, after several trips, still remembering that I had to grab packages from the mail room as well. That whole day, and, frankly, that whole week was overwhelming and I often found myself asking out loud and internally, “what’s next?”
- Around the Yard: Natasha Gonzalez
October25,2017On a crisp wet Saturday, my teammates and I boarded our van for a very special home match. Instead of playing on our usual home courts, we would be competing at the Sportsmen’s Tennis & Enrichment Center in the Dorchester section of Boston. Sportsmen’s is a club dedicated to helping the community through lessons learned on court.
- Around The Yard: Kevin Dai
October18,2017The typical image of a student-athlete is a tall, strong-looking person, donning jackets or shirts representing his or her respective sport. Student-athletes may have graceful movements, outstanding social lives, and indeterminate physical resolve. One may gaze upon student-athletes and wonder how they can maintain such straight postures and have so much energy outside of their practices.
- Around The Yard: Libby Manela
October11,2017There are many core qualities that are bred into the ethos of a Harvard student-athlete. For one, we are taught balance—how to make each side of the river compatible with the other. We are also taught commitment—how to dedicate yourself fully to a goal with a viable chance of failure.
- Around the Yard: Tim O'Brien
October04,2017The most popular advice I hear from graduating seniors, alumni, professors, and elders in general is to take advantage of the opportunities presented in front of you. It can be overwhelming at times with the constant feed of new emails and event flyers, but you never know what you can find after taking that first step in exploring a new opportunity.
- Around the Yard: Jocelyn Meyer
September27,2017WHO ARE WE? HVB!! This is how we start every match. We come together, excited to represent the Crimson with passion for the game. It gives me the chills every time. The fact that I get to be a part of this team and a student at this college never fails to amaze me. Every time I step on the court, I remember how blessed I am to be at Harvard, a place where opportunities are seemingly endless.
- Around The Yard: Ian Miller
September20,2017As move-in day approached nearly a month ago, I had a moment of realization. This is it, the last beginning of my Harvard career. So as my family and I loaded up our ’05 Ford, bungee cording the trunk closed, I started to reminisce. Past senior teammates had always told me that the years would fly by and that I’d be a senior before I knew it.
- Around The Yard: Madeline Raster
September13,2017Call me a nerd, but sometimes I really relate to Luke Skywalker. If you’re unfamiliar with the Star Wars story, he’s a kid stuck on the desert planet, Tatooine (sorry Hoosiers), who goes on an epic journey through the galaxy. Along the way, he meets some of his best friends who help him realize his Jedi powers. Now, obviously I’m not a Jedi because I’m not that cool, but there is something notable about Luke’s journey.
- Around The Yard: Gregory Royston
April26,2017Yet to return to a normal state after our Ivy Championship title defense this past weekend, I have found myself decidedly unproductive the last few days. It’s okay though – that feeling of satisfaction after a successful outcome of a semester of hard work and sacrifice is worth being enjoyed. If anything, it leaves me more motivated than ever to push hard through my busy reading period and finals week.
- Around The Yard: Anna Zhou
April18,2017“The days are long, but the years are short.” It’s still hard for me to fully register in my head that I’ll be wrapping up my sophomore year at Harvard in less than a month. It doesn’t feel all that long ago since I first stepped foot on campus, a starry-eyed high school golf recruit gaping in awe and marveling at the unfamiliar magnificence the architecture and statues seemed to exude.
- Around The Yard: Julia Baumel
April10,2017I’m privileged to spend about twenty hours each week rowing for the Radcliffe Varsity Lightweight rowing team (RVL). When I’m not on the water or in class, I am likely to be eating, studying, or socializing with my teammates. Given the amount of time I spend with these people, I’m lucky that they are some of the most ambitious, well-rounded, and inspirational individuals I have ever met.
- Around The Yard: Kevin Coakley
April03,2017“We have a sailing team?” That is probably the most common response when I tell someone that I’m on the Harvard sailing team. Frankly, it makes sense. College sailing is a niche sport and not many people know what we do. However, for the thirty members of the Harvard sailing team, the sport has made an indelible impact on our college experience.
- Around The Yard: Drew Reid
March23,2017This truly is one of the more incredible places in the world. We hear so frequently how fortunate we are to attend a university like Harvard.
- Around The Yard: Maddy Kaplan
March17,2017I still remember sitting in Wigglesworth with my seven blockmates, waiting for our housing assignment two years ago. We watched crowds of upperclassmen sprint around the yard, excited to welcome freshman to their houses–where they will live for the rest of their time at Harvard.
- Around The Yard: Luke Mendola
March09,2017Earlier in the semester my friends and I had a great Sunday hiking Mount Chocorua in New Hampshire’s White Mountains. As most things that occur while being a busy student-athlete, the trip came together pretty last minute.
- Around The Yard: Angelina Ye
March02,2017A star of Saturday Night Live, Ghostbusters, and her ever popular skit with Drake, the one and only Leslie Jones made an appearance on campus this past weekend. Thanks to the Office of Student Life, all students were offered tickets to her show, completely free of charge. That Friday evening, after a few classes, a quick practice, and a convenient Annenberg dinner, I met up with a few friends and headed to Sanders Theater.
- Around The Yard: Benjamin Cohen
February24,2017People often ask if it's easy to get lost at a big university like Harvard, but in my opinion the size of the university is actually one of its most underrated assets. I’ve experienced this advantage of access through the research project on human capital in startups that I’m working on at the business school.