Many people continue to believe that you are either a math person, destined to be able to do math easily, or you’re not. If you’re not, math classes will always be hard, and you’ll never be comfortable with numbers and calculations. This type of thinking is seriously misguided, and really sends the wrong message to any student that is exposed to this idea.
What is a growth mindset?
“In a fixed mindset, people believe their basic qualities, like their intelligence or talent, are simply fixed traits. They spend their time documenting their intelligence or talent instead of developing them. They also believe that talent alone creates success—without effort. They’re wrong.
In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment. Virtually all great people have had these qualities.”
Carol Dweck, Stanford psychologist and researcher and author of Mindset: The New Psychology of Success – How We Can Learn to Fulfill Our Potential
Psychologist Carol Dweck has completed decades of research and has identified that people tend to adopt one of two mindsets: fixed or growth. You can learn more about a growth mindset by clicking here.
People with a fixed mindset tend to think their abilities, personalities, and intelligence are determined at birth and can’t be changed. They may tend to avoid activities if they fear they’ll fail, since this will expose a lack of ability that they don’t believe they can change. This creates a truly problematic cycle. Students who believe, for example, that they aren’t good at math might avoid situations in which their poor math ability would be exposed. They make the choice to avoid raising their hands, for fear of seeming dumb. Therefore, they don’t ask questions to clarify their understanding in class. They may even avoid doing their homework, since it’s easier mentally for them to do poorly because they didn’t study than to try their best and fail, thus confirming a belief that they may just not be smart enough.
Ultimately, and over time, a student with a fixed mindset starts to try less hard, do less homework, and fall further and further behind in whatever academic (or other) areas they’ve decided they weren’t naturally given the talent to succeed.
This process continues until the evidence seems to confirm that yes, other people “have it” when it comes to math or another academic subject, but they don’t. By the time they get to the “math” portion of the ACT, SAT, GRE, or GMAT, they are in deep trouble. They haven’t practiced or built up their math skills, and they don’t even believe they have the potential to acquire math skills in the first place.
“The ‘I’m-bad-at-math’ has been a common refrain throughout my tutoring years. It seems that many students whip this phrase out as soon as they encounter a little obstacle in a problem. Often, this obstacle happens to be one short step away from the answer. It’s like a marathoner stopping at mile 25, saying he is bad at running. At this point of imminent breakdown, I’ve learned to prod students and give that little nugget of information they need to solve the question. Soon they are able to solve this level of question without much difficulty. Often, the same routine continues until I am having them legitimately solve difficult questions on their own."
- Chris Lele, GRE/SAT Expert from Magoosh
By contrast, people with a growth mindset believe that abilities and talents are built up over time through hard work, persistence, feedback, and ultimately learning. They view their minds and brains like a muscle that grows the more it’s used. They’ll ask a question in class in the honest pursuit of feedback and learning, without being too worried about sounding dumb. They have no fear of being exposed as lacking math skills, because they believe they can and will build up their math skills if they lack them today.
But isn’t there some truth to the idea that you can be naturally good at math?
Let’s pause to explore the idea of having a natural talent for math. Is it possible to have more natural talent? Probably yes, to some degree. But many factors determine whether a person is good at math—their genes yes, but also effort, teachers they have had, paying attention in class, consistently doing or not doing homework, etc. In large part, being good at math is something you can control; it’s a choice you can make.
Do genes matter when it comes to math? Of course, on some level. Some people start out with slightly different hardware (i.e., brain processing power) than others. But it is almost impossible to untangle the web of factors that creates mathematical ability. You may be born with a brain that, when measured for memorization skills and information processing ability at a young age, is average or worse. But, after 15 years of diligent studying, paying close attention in class, developing passion for math, receiving feedback from parents and teachers, you may now have much higher math skills than everyone else around you.
On a biological level, the reason that the “growth mindset” we talked about earlier results in better performance is that the brain is in fact malleable. Biologically speaking, it is somewhat like a muscle. New neural pathways are built when your brain encounters new ideas and concepts, and its actual physical structure changes. This is probably why studies have even shown that performance on IQ tests, which are supposed to measure the “hardware” you are born with—the natural, unchanging intelligence determined by your genetic make-up—changes over time. People who have achieved higher levels of education, who have explicitly engaged their brains for longer periods of time, perform better on IQ tests later in life.
How do you become better at math?
You become better at math by practicing, which means you become good at math by doing your homework until you truly understand it. It’s as simple as that. You find ways to be interested, pay attention, and ensure you have a proper foundation before tackling more advanced topics. You don’t give up on a problem until you understand it, getting expert help (perhaps from math tutor) if necessary.
Cal Newport is an assistant professor of computer science at Georgetown University who specializes in the theory of distributed algorithms. In other words, he works in highly complex mathematics at the PhD level at one of the best universities in the country. Newport graduated from Dartmouth College in 2004 and earned his PhD from the Massachusetts Institute of Technology in 2009.
Outside his academic career, Newport blogs regularly about how to achieve high levels of academic and professional success by following evidence-based strategies to increase your performance. In other words, he blogs about study strategies, time management, professional development, career decisions, etc.
In an April 2011 post entitled “On Becoming a Math Whiz: My Advice to a New MIT Student,” Newport writes to a new MIT student looking for advice on how to excel as a math major:
“Here’s how to become a math whiz:
Keep working on your problem set after you get stuck.
Don’t just sit and stare at it: think hard; until you’re exhausted; then come back the next day and try again. This will be uncomfortable, but that discomfort is the feeling of your brain stretching to accommodate new abilities….
…I explained that I had been studying theoretical computer science and mathematics at a high-level for the past decade, much of it spent right here at MIT. Over these years, one conclusion has become increasingly clear: the more hard focus you dedicate to a technical subject—be it computer science, chemistry, or physics—the better you get.
Junior graduate students think senior graduate students are smarter, but they’re not: they simply have more practice.
Senior graduate students think junior professors are smarter, but they’re not: they simply have more practice.
And so on.”
Now, you might not find that bit of advice all that interesting. It’s easy for someone like Newport, a natural math talent with a PhD from MIT, to write a passage like that, extolling the virtues of hard work because his mind is so sharp that, for him, hard work pays off easily. But read on to learn a surprising fact about Newport’s background:
“When I arrived at Dartmouth, to name another example, I didn’t consider myself good at math. I had taken AB calculus during high school (not BC), and had scored a 4 on the AP exam (not a 5). By my sophomore year of college, however, I had made a name for myself by snagging the highest grade out of 70 students in an advanced discrete mathematics class. What happened in between? A lot of hard focus.
Eventually, this all becomes clear, but for an incoming freshman, it’s not intuitive. When you struggle with a calculus problem set while a classmate knocks it out in an hour, it’s easy to start to thinking that you’re just not a ‘math person.’
But this isn’t about natural aptitude, it’s about practice. That other student has more practice. You can catch-up, but you have to put in the hours, which brings me back to my original advice: keep working even after you get stuck.”
When I first read this passage, I was blown away.
Let me put some context around the passage to illustrate what it means (or, what it doesn’t mean) to be naturally intelligent or “gifted,” particularly at math.
I also graduated from college in 2004, and when I was in high school, I too took AP Calculus AB. I scored a 4 on that exam, just like Newport. I’d argue that most people believe that by the time you’re a senior in high school, whether you’re going to excel in math is relatively clear. In 2001, Newport and I were both sitting there in high school in our AP Calculus AB class. However, dozens of our classmates were performing better than we were by either scoring a 5 on the AP Calculus AB exam or taking AP Calculus BC, a higher level of math altogether.
In fact, at my high school, and I’m sure at Newport’s, there was actually a third group of students. Each year, a small number of students who were a year younger would be brought up a grade level and would join the AP Calculus BC class a year in advance because their math skills were so good. So when Newport was a senior in high school, he was in the worst performing group of students who were studying calculus. Of the three levels—students taking AP Calculus AB at grade level, students taking AP Calculus BC at grade level, and younger students “bought up” to study AP Calculus BC—he was in the least advanced group.