Monthly Archives: July 2013

Rational Expressions – The Path Not Taken


Lessons Learned in a McDonald’s Play Area

Yesterday, I took my 2-year-old, Rylan, to McDonald’s for breakfast, and of course, he immediately noticed the play area. Who wouldn’t? It’s brightly colored and it has a sense of danger and adventure to it. So after eating half of a hot cake, he headed over to the play area. No one else was there so he just crawled in.

He climbed upward through the play area until he was about 8 feet up. He felt a little nervous being so high up so he asked me for help – well, “cried for help” is a more accurate phrase. However, the structure he climbed was inside of a tube that was not designed to handle someone of my age or weight. So I told him I was just too big. His cries got louder, indicating that he really didn’t care how big I was, it was my fatherly duty to help him. (I’m translating, of course.)

So I made my way as far as I could and offered to help him down, but that’s not what he wanted. He wanted me to follow him through the colorful maze and see him through to the other side.

Before I weighed the pros and cons of giving in and climbing up, he had already moved on. He was all the way to the top and starting to move through the tunnel. Relieved, I wormed my way out of this contraption and watched from a safe distance. At one point, his foot got caught and he was unable to move forward or backward, and he could not wiggle his foot free. At that point, I reached up and pushed on his foot until he was able to continue. He made it the rest of the way, and slid down the long tube slide at the other end of the play area, emerging at the bottom with a huge smile, a mix of joy and pride in himself.

After that, he repeated the same path over and over again, each time getting faster with an increase in confidence. Once he felt he had mastered it, he started to explore other ways to get to the slide, and he even went to other destinations within this activity maze. When it was time to leave, the cries came back, but only because he wasn’t finished exhausting all of the possibilities of this wonderful colorful world of adventure.

I think the educational analogies are pretty obvious in this tale, but let me just summarize. Ultimately, even though students want teachers or classmates to hold their hand through new learning experiences, they get much more of a sense of accomplishment if we let them struggle, and only help them when they are genuinely stuck (a conclusion that is reached by us, not them). And our focus should not be on accomplishing a task predetermined by us, but rather on exploration of a concept so that they can experience the joy of making a seemingly new discovery on their own. And once they’ve done that, they can seek to make new discoveries, some that will pan out and others that won’t, all the while feeling like they are not wasting their time, but enjoying the process to the point where they don’t want to quit when the bell rings.

Learners should not be asking us each day, “What are we learning today?” – or, at least, not expecting a direct answer. Yes, they need to learn a long list of required skills, but does it really matter on what day a specific skill is learned? As long as they are given a general framework and tools to use, let’s let them figure out things like properties, general formulas, and even theorems – and their applications – by themselves. But always be there to give them a little nudge when they get stuck.

Rational Expressions – Elementary


Rational Expressions – Exponential Decay


Rational Expressions – That About Summers It Up


Rational Expressions – Branching Out

Happy Canada Day!! I want all my Canadian friends and family to know that I miss them dearly, and I will be celebrating with them today.



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