For several years, I served as the Coordinator of Pure and Applied Sciences for a school district serving over 50,000 students from K to Pre-University. This enabled me to visit schools and teach at any grade level as an invited guest, providing me with the opportunity to observe young people, as I attempted to dazzle them with mathematical tricks and counter intuitive problems. Days before I was to appear in a teacher’s class, I would ask her to send me a copy of the seating plan. On the drive to the school, I would memorize the students’ names. Then, after the teacher introduced Dr. Kelly as a “mathematical wizard,” the circus would begin.
“Good morning students. I must admit that I’m a mathematical wizard with a giant brain, because I’ve been studying math all my life, and that has made my brain grow supersize! I can read minds.”
“No, you can’t!” responds a skeptical young lad in the middle row.
“Oh yes, Kevin; I know everything.”
Kevin’s face shows alarm, “How did he know my name?” he whispers to a classmate.
“You don’t know my name,” says his classmate, Andrea.
I pause, as if I’m drilling deeply into my psychic powers. The longer I pause, the more certain Andrea becomes that I’m stumped. Then, after sufficient agonizing, I announce, “It’s coming to me Andrea…”
“Wow, he knows my name!”
“Oh, I even know your birthday!”
“No, you don’t!” says Andrea with absolute certainty.
I display the cards below on the overhead projector. “The day of your birth is shown on some of these cards. You tell me which cards contain the day of your birth and I will tell you your birthday,” I assert with appropriate theatrical wizardry.
Andrea chooses the second and fifth cards. I struggle as if I am waiting for my psychic powers to receive signals from cyberspace and then I announce, “Your birthday is on the 9th of the month!”
Andrea’s mouth falls open and she is speechless. Then a flood of student hands are thrust into the air, “Guess my birthday…”, “You can’t guess my birthday.” After a few more correctly identified birthdays, I’ve won them over and I have a chance to teach the children some engaging math.
On one such occasion Debbie, a Grade 6 student, jumped up and said, “I can guess your birthday! Tell me which cards show your birth date.”
I responded, “My birthday is on the first, third, and fifth cards.”
She hesitated. Then she mimicked my theatrics, placing her hand on her forehead, and pronounced, “You were born on the 21st!”
“That’s exactly right!” I said with great excitement. “How did you do that?”
“I just added the numbers in the upper left corners of the cards that you told me contained your birthday. So that was 16 + 4 + 1 or 21,” she responded, exuding the joy of a magician who has just mystified an audience.
Debbie provided what educators call a great teaching moment. I explained the trick to the students, showing them how to write all the numbers up to 31 in base 2. I then explained that the first card showed all the numbers whose first digit is 1 when written in base 2. The second card contained all the numbers whose second digit is 1 when written in base 2, and so on. My birth date, being on the first, third, and fifth cards has binary expansion 10101 which is 1 × 24 + 0 × 23 + 1 × 22 + 0 × 21+ 1 × 20 or 21.
Most students didn’t understand the explanation of why, but they understood how to do the trick and delighted in their ability to dazzle their friends. (A full explanation, is given in https://www.intelligence-and-iq.com/intelligence/)
At the end of the class, I asked Debbie how she had learned the trick. “Oh, the game came in a package of gum.” As she shared in the glory of her discovery, Debbie’s eyes sparkled, her enthusiasm was at a 10 on a 10-point scale. She loved challenges, paradoxes and puzzles. A view of Debbie at that moment would reveal to virtually any educator, a young person of high intelligence. It was no surprise when the teacher told me later that Debbie was her top student. “She goes after new concepts like a dog after a bone,” the teacher said.
During my subsequent travels across schools throughout the United States and Canada, I saw many students like Debbie. Through the sparkle in their eyes and their total engagement, they project the excitement they experience in learning. Such young people are easy to identify as highly intelligent. However, there are also very intelligent young people who are somewhat shy and reluctant to put themselves forward. The intelligence of such students is often difficult to assess without some long-term observation. Sometimes, it’s manifest in their work, sometimes in the questions they ask and in some cases, it’s latent and doesn’t manifest until much later. Intelligence is difficult to define, but we know it when we see it, even though it doesn’t always show itself.
In a later post, I’ll share my observations that help me identify highly intelligent adults and their opposites.
