“It’s been my observation that people who understand the to-do list and “two-fers” get the maximum benefit from their time. What is a “two-fer”? Example: I never get in a line at an airport without something to read.” -Zig Ziglar
Traveling has taught me a lot about patience, but it’s also taught me a lot about purpose. I never get in line at an airport without a bag of math manipulatives. My traveling adventures have become the perfect place to optimize the “two-fer” as I wait in airports and on airplanes. I try to make the most of my time by sharing the magic of math manipulatives at the same time as patiently waiting (OK, so I’m not always waiting so patiently, but it really works with the title of this blog post).
When I strike up a conversation with a nearby traveler, some of the first questions they ask are:
“So, where are you headed?”
“Is it a work or pleasure trip?”
When I tell people that I am an educational consultant traveling to another city to work with schools to help them build on their successes and implement additional best practices, they almost always answer,
“What a cool job!”
The next question is,
“So, exactly how do you do that?”
If I’m conducting Tabor Rotation Training, I give them a brief description of what small-group, differentiated instruction looks like in a classroom. I also explain how mathematics, even at the secondary and post-secondary level, can be made into something which is engaging and meaningful.
The next response is usually,
“I wish someone had taught me that way when I was in school. I never really understood math.”
And, that is when I bring out the BIG GUNS (sorry, the Texas in me just came out). I pull a bag of manipulatives out of my briefcase and share a way to understand a mathematical concept through concrete manipulation. Since the first time the TSA agents pulled a bag of manipulatives out of my carry-on suitcase and asked, “What are these things for?” I have carried at least one mixed bag of manipulatives with me throughout every trip.
Here is one instance when the magic of math manipulatives was apparent. Remember the TSA (Transportation Security Administration) agents who pulled my Ziploc bags of manipulatives out of my suitcase while hand searching my bags? The manipulatives which most fascinated that group were the spongy pattern blocks. They initially thought they were used to clean. I asked the three agents, who were standing closest to me, if they ever truly understood why ½ of ½ is ¼.
They all admitted they had no idea why the answer was ¼, but had just memorized the formulas their teacher had given them. I asked them if they’d like to see why ½ of ½ is ¼ if I could show them in less than five minutes. After they nodded I did the following:
- I set two yellow hexagons on the conveyor belt and put them together. I asked them if they could agree that together they made one whole. Everyone shook their head yes.
- I took another hexagon and placed one red trapezoid on top of the hexagon. I asked what fractional part of the hexagon did the trapezoid represent. They all answered ½.
- Next, I pointed to one of the hexagons and asked what fractional part of the whole was it? All answered ½.
- I asked one of the agents to make another whole with two hexagons and place four red trapezoids on top of them to make the second one whole.
- I asked another agent to put one red trapezoid on top of one of the hexagons.
- I asked the next set of questions, “Do you agree that it takes four trapezoids to make one whole and that one of the trapezoids is ¼ of the whole?” If everyone can manipulate the pattern blocks and understand that, then we move to the next step.
- “So one of the hexagons is ½ of the whole and the one trapezoid is ½ of the ½?” If there are nods, all I have to do is give enough wait time and someone always bursts out, “So ½ of the ½ is ¼!
I wish I had a video camera to show the faces of the adults who now truly understand a concept. The light bulbs firing in their eyes makes it worth the minutes it took to show them. If my plane isn’t taking off for a while and the security lines aren’t too bad, I let them use rhombuses and triangles to discover why ½ of 1/3 is 1/6 and why ½ of 1/6 is 1/12. (This sometimes happens in small airports, especially if TSA takes their job very seriously and are determined to hand check all of my bags. If you’re going to search my bags…you’re going to end up learning something about mathematics!)
On my last few trips, I’ve also brought my Algebra manipulatives. This has caused the greatest stir and the most conversation in the seats around me. More on that in the next blog…
“History shows us that the people who end up changing the world – the great political, social, scientific, technological, artistic, even sports revolutionaries – are always nuts, until they are right, and then they are geniuses.” – John Eliot