Learning math (or anything) is easier when you think about it the right way
Article written by a Tutor.id tutor, Diogo
How often have you looked at a math problem, only to get that sinking feeling of “It’s too hard”? It’s easy to see something intimidating and feel unprepared, lost. This is especially common with Math students — they see something unfamiliar and intimidating, and can’t pick a place to start. In math and in life, an unfamiliar problem can be seen as a test, something that will “determine” or “label” your skills, intelligence, or even worth.
My students used to frequently complain to me about facing this hurdle. Being intimidated by the problem can actually prevent bright, passionate mathematicians from trying a difficult problem. Their fear of failure paralyzed them.
By examining any difficult math question you can turn the problem around, making the path towards the solution clear. Math, after all, is fun. I adopted an approach to make the scary, unassailable math problems easier and saw my students perform miracles. For everyone whom I have tutored for any period of time, this approach helped eliminate the sense of dread and confusion ahead of solving a difficult problem.
My trick is a simple realization that came to me when I was trying to map out the source of my students’ confusion. The chart helped me boil down the problem to two possibilities:
- The student is unclear on what the question actually is
- The student is unfamiliar with the problem in front of them
Once I realized this, I started asking another question to my students. This question does not care whether the student already knows how to face a problem or not, or whether they have the relevant math skills or not. In fact, it doesn’t concentrate on your current ability to do anything at all. The question is simple:
“Do you believe that you can learn how to solve this problem?”
If the student’s answer to this question is negative, there is very little a teacher can do. At least, not until they have tackled this belief with the student. I don’t mean that “believing in yourself” is a magical solution to every problem. Rather, what I mean is that believing that you can improve is a core component of learning motivation. I like to think of the difference between the “yes” and “no” answers to the question as a core difference in mindset. By adopting a growth and learning mindset, you open up a path to changing, rather than staying stuck. Your general attitude towards the world and the problems that face you make a huge difference in every aspect of your experience. I witnessed the power of this shift personally in many of my classes.
When leading a class in exercises I try to never actually solve any problem, trying to guide the students to discover the answer themselves. I concentrate especially on the logic of the solution, the reasoning. To me, it’s not about the mechanical task of performing the calculations correctly, but rather understanding the logic. Some of my students tried to perform the calculations in their heads. Naturally, they would make mistakes from time to time. What struck me as interesting, however, was that their answers usually sounded apprehensive and unsure.
I focused my training on getting the students to answer firmly, with confidence. I tried to raise in them the sense that there was nothing to be apprehensive about, and that even arriving at an incorrect answer was valuable in the learning process. Trying to do something and making a mistake was a great way to figure out how to learn more, and where to improve. Instead of being worried about getting it “right”, I showed them the opportunity they had to learn from their mistakes.
I was surprised at the results. I had my class do a simulated college test as part of my teaching program. With the encouragement of my students to practice the “growth mindest” they did not become perfect overnight. But, they did become more thoughtful, engaged with the difficult problems more, and found a way to think through the problem more frequently. Instead of shock, I saw curiosity. Instead of fear of being judged, I saw genuine excitement in them. The students showed genuine interest in the subject and actively asked thoughtful, smart questions that helped them master the topic.
I invite you, dear reader, to try out a perspective that sees wrong answers as opportunities to learn. I’d be very curious to hear your personal experience with a change of mindset.
ou can find Diogo, the math tutor on https://tutor.id/odiogo