I was a good student in elementary school -- an enthusiast who enjoyed learning all subjects, especially math. I loved how math made sense and followed a consistent and reliable logical structure. That was true until 6th grade when we hit percents. This was the first time I felt the pain of learning by memorizing. The percent word problems we solved were problems such as the following.
A restaurant makes fruit juice from fruits, of which 42 are bananas. If 35% of the fruits are bananas, how many fruits are used to make the juice?
Mrs. Cohen, my math teacher, noticed my struggle and tried her best to help me. She appreciated me as a strong student and didn’t want my self-esteem to be affected. She took me for a one-on-one session and promised, "Everything is going to be alright. All percent word problems boil down to three formulas. If you remember them, you’ll be able to solve any percent word problem.” Sounds promising, I thought.
She continued, “If the whole is missing, we would use this formula:
And if the part is missing, we should use this formula:
And lastly, to find the percent we use this formula:
She assigned me a handful of problems and asked me to match each problem to a formula. I looked at the 3 formulas and thought to myself, I can do that! I reread each problem, identified the missing piece and used the appropriate formula to solve the problem. It worked! I continued with the rest of the problems and felt things finally worked out with percents!
The following week we had a quiz. I was confident and energized. After solving tens of percent word problems on my own, I was ready to beat percent word problems. So for the fruit juice problem, I knew that the "whole" is missing. I tried to retrieve from my memory the appropriate formula. Was it "Part divided by Percent" or "Part multiplied by Percent"? Wait a minutes. Should I multiply by 100 or divide by 100? I had a blackout. I needed to sneak a peek at these formulas to remind me. But my teacher didn't allow us to use a cheat sheet. I felt lost, frustrated and betrayed. Mrs. Cohen, how can you not allow us to use these three formulas? See for yourself, they look so similar you can't tell them apart. Unfortunately I failed the quiz. The hard work and efforts of working with the formula sheet didn't pay off. This experience was draining. I remember how disappointed I was at myself. How could other students do it but I couldn't? Maybe I am not smart enough?
Fortunately, over time, I've come to understand that my struggles with percents and formulas were not a reflection of my intelligence or ability, but rather a result of the way math was taught.
As a math educator for many years, I realized educators hold two main perspectives on why we teach math. One is, well... to teach the math. We want children to be able to add fractions, solve quadratic equations, measure angles, calculate area of rectangles. Students must master this content to pass the SAT, to learn science, be good engineers, etc.
However, there is another perspective to teaching math. The underlying assumption of this perspective is that teaching math is a vehicle to developing our brain. And this is where math becomes more interesting, rewarding, fun, and... healthy! For example, finding a common denominator of two fractions isn't that interesting in and of itself. Following the idea of a common denominator, one can add 1/2 and 1/4 with a minimal brain workout.
But the thinking process involved in the question "Why do we need to find a common denominator to add fractions?" is way more interesting and requires active thinking than just adding them. It involves understanding of the concepts of 1/2 and 1/4. Understanding this concept requires much more than writing the addition problem and its solution. The idea of 1/2+1/4 can involve drawing, cooking, singing, sculpturing and so on. What is your favorite way of representing 1/2+1/4?
When we understand rules or formulas or better off - figure them out on our own, we take part in the creation of the content. By involving children and adults in this type of thinking we challenge their mind and demonstrate how rewarding it is to use our brain power. A challenged brain is a healthy brain.
Fast forward to our fifties and beyond, research points to the importance of keeping our brain sharp for our well being. Research illustrates the importance of building our "cognitive reserve" by maintaining demands on our brain that keep it thinking, strategizing, learning, and solving problems. Animal studies show that cognitive stimulation increases the density of neurons, synapses, and dendrites, and therefore builds a brain more resistant to disease. In his book, Keep Sharp: Build a Better Brain at Any Age (Sanjay, G. 2021), Sanjay Gupta, MD, encourages adults to participate in classes that employ high cognitive complexity, such as visual comprehension, short- and long-term memory, attention to detail, math skills and social elements with fellow classmates. He emphasizes that "you can't come to class and be passive. You need to use your mind in a manner that gets you out of your comfort zone." (ibid, p. 122).
My mission is to provide fun opportunities for children and adults to enjoy mental stimulations in a social setting. Our classes provide ample opportunities to enjoy the process of sense making and reasoning. We play strategy games and use hands-on activities that spark learners' curiosity and light up their eyes. Why don't you join? It is never too early or too late to challenge your brain.
Gupta, Sanjay (2021). Keep Sharp: Build a Better Brain at Any Age. Simon & Schuster. Kindle Edition.