Dear Dr. Linda,
My grandson called me the other day and asked me if I knew what an 84-sided polygon is called. I didn’t know the answer, so I told him to ask his grandpa, who’s a retired accountant. He didn’t know either. We both got online to find the answer and then called our grandson and asked him how he knew. He told us that his algebra teacher stopped in the middle of class and asked, “Does anyone know what an 84-sided polygon is called?”
Our grandson was “intrigued” and went online like we did, but he dug in deeper, and continued to look up the names of other polygons. “There’s a pattern,” he said. “It sounds hard, but I figured out that each name is simply a combination of prefixes.
I’m sharing this story with you because I’d love you to put it in your column. I want to thank those teachers that incorporate thought-provoking material into their everyday lessons in order to open up their students’ minds. Grandma Claire, retired principal
Dear Grandma Claire,
Thank you for sharing this because it’s a perfect example of how a teacher can motivate children to think and learn at a higher level than just memorizing material. This teacher inspired your grandson and maybe others in the class to think about something they probably wouldn’t have thought about. Plus, it motivated your grandson to do some research and to analyze what he found. Traditional instruction has historically emphasized recall and understanding: Here’s what I want you to know. Memorize it and see if you can recall it on the Friday test.
However, this will not suffice in the 21st century. Students need to be challenged by projects, vocabulary and activities that encourage them to do something new and different with what they have learned. As a principal, you know this is called “higher-order thinking.” That skill, already highly prized in our society, will be essential for future leaders in the global economy.
This all sounds wonderful, but sometimes there just isn’t enough time in the school day for teachers to incorporate all levels of thinking into their lessons. Also, not all lessons or subject areas lend themselves to higher order thinking. Memorizing the multiplication facts is just that…memorizing the multiplication facts!
Hopefully, though, teachers can find time, like your grandson’s teacher, to give their students those little gifts of knowledge that will stimulate some students to do some higher order thinking on their own.
I must admit, after receiving your email, that I didn’t know the answer. I, too, was intrigued and went online to learn what an 84-sided polygon is called for myself. All the definitions began by reminding me that a polygon is any 2-dimensional shape formed by straight lines. A shape with three lines or sides is a triangle or trigon. A four-sided polygon is a quadrilateral (like a square or rectangle) or tetragon. A five-sided polygon, like our five-sided military complex in Washington, is a pentagon. A six-sided shape is a hexagon — like a beehive or snowflake.” A shape with seven sides is a heptagon and one with eight sides is an octagon— most often seen in a “stop sign.” The list goes on and on.
Most kids learn the shapes of polygons with fewer than 10 sides in elementary school, but they usually don’t learn the name for a polygon with 84 sides! So here it is:
Knowing this, ask your grandson if he knows how many sides the following figures have:
See the pattern? (Just as a hint, “kai” is Greek for “and,” and “gon” is always the final suffix.)
Answers: 1) 65, 2) 55, 3) 88