Some years ago, I taught an evening course at a community college that catered to working adults. The students varied in age from 20 to 60, but they all shared one thing in common. They all had a huge amount of math anxiety. They were all absolutely convinced that they were not “good at math.” This class, with the innocuous name of “General Mathematics for Non-Mathematicians,” was designed to bridge the gap between the skills the students were supposed to have mastered in middle school and high school and where they needed to be. After the mastery of skills in this class and two other prerequisites, the goal was for them to excel in their future mathematics classes and graduate to become clean-room technicians, health workers, machinists, electricians, and dental hygienists.
I remember one woman in particular who came up to me at the beginning of the school year and was literally trembling because she needed the class to graduate and she was so afraid she wouldn’t pass. I promised her that she would do well and would even grow to like math. She looked at me as if I were from Mars.
So what does it take to be “good at Math” and what can we do as educators and parents to foster this mastery in our children? The beginning steps to understanding any subject and to delve into its inner workings further is curiosity. Without intellectual curiosity and a desire to explore there can be no progress into a deeper level of learning. Adults who have had little success with mathematics have already labeled themselves with the “I’m NOT good at math label.” One of the keys is to explain to students that mathematics is challenging for everyone.
“Do not worry about your problems with mathematics, I assure you mine are far greater.” –Albert Einstein
Adopting a spirit of exploration by pulling numbers apart, going down blind alleys with trial and error, playing number games, and teaching students how to self-check their own work can help their fears subside. A student who has been shown varying techniques for skill mastery and concept understanding has a greater chance for success in mastering mathematics at all levels. Our job as teachers, educators, and parents is to help foster this type of high-level engagement and interest.
Everyone makes mistakes. It’s OK to make mistakes. The first time I tried to bake a loaf of bread, I did something wrong with the yeast. My bread turned out to be a lethal weapon instead of something palatable. The next week I tried again. The second loaf of bread was even worse than the first. But my parents and my teachers taught me not to give up so easily. With any new skill, my expectation was, and is, that it may take me some time to master it. The third time, I spent a lot of time focusing on the details of the proper yeast proofing. The resulting loaf was almost as tasty as my Mom’s home-baked bread. Those bites of bread tasted especially flavorful to me because the success was hard won.
The student who is “good at math” doesn’t give up too easily. He or she realizes that there are usually several different ways to solve any mathematics problem. If one pathway doesn’t work or is arduous, there might be a pathway to a clearer process around the corner. There are over 400 proofs of the Pythagorean Theorem. They all achieve the same goal but they vary greatly in length and complexity. The details of each proof matter. Those details are what make that particular proof viable.
I have made this letter longer than usual, only because I have not had the time to make it shorter. –Blaise Pascal
Just like Chinese, Italian, or the acronyms associated with a particular industry, mathematics is a unique language. The use of symbols in mathematics helps to communicate precisely and in a relatively short length. However, just as it takes mastery to be fluent in a language, it takes careful thought, time, and effort to become masterful with mathematical language. But here’s the joy in it…we can write “x + 7 = -25” and it will be understood around the world. Fluency in any language requires practice and the language of mathematics is rich in visual symbols. Once a student understands those symbols, they become second nature and a very complex thought or relationship can be summarized in a very short space.
So, let’s think about how we can represent what it means to be “good at math.”
a = intellectual curiosity
b = a spirit of exploration and play
c = persistence when faced with challenges
d = a toolkit of different techniques to try
e = the ability to pay attention to details
f = fluency in the language of math
g = “good at math”
a + b + c + d + e + f = g
The good news is that these are qualities that we can foster in our children and students. We can also work on these qualities in ourselves as we improve our own mathematical abilities as educators.
My adult student who was trembling at the beginning of our math class went on to become the best student that quarter. She said to me “I wish I had realized how much I could enjoy math. I never would have been afraid to try when I was younger.” That poignant comment stuck with me and influenced my view of the role of mathematics educator ever since.