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Mr. Sierpinski and the Triangle of Doom

5/13/2016

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I couldn't take any more of those damn Face-ing Math worksheets. My students and I were both tired of PowerPoint presentations. There was no way I was about to fill my cabinets with more posters. Pair those feelings with a restless group of 8th graders who know their ticket has been punched to the high school. Testing was over. No finals to give.

Yep, the end of the school year was fast approaching and I needed something that my students and I could get interested in without running the class off the rails of sanity.

​Enter: Mr. Sierpinski and the Triangle of Doom. 
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The instructions were simple:

OK class, your job is to create a Sierpinski Triangle. Using a clean sheet of paper, a pencil, and a ruler, you need to create each iteration with precision. There may not be any folds or holes in your paper when you are finished. You will leave your paper here at the end of class... NO TAKING IT HOME! I must caution you, however, to be very patient with this. It isn't as easy as it looks.

"Yeah, whatever Stevens, that's what you always say," proclaims Amber, ready to take on the challenge.

Sure, Amber. You wait. Here is what you will need:
-- Paper (up in the front of the room)
-- Patience
-- A ruler with a straight edge!
-- PATIENCE
-- A very sharp pencil
​-- PATIENCE!!!


You will be graded on the precision of your triangle along the following guidelines:

-- 8" Equilateral Triangle
-- 4" Equilateral Triangle
-- 2" Equilateral Triangles
-- 1" Equilateral Triangles
-- 1/2" Equilateral Triangles
-- 1/4" Equilateral Triangles

Any questions?


Nope. After all, it's just a silly triangle. Students grabbed a ruler, the one sheet of clean paper, and a handful of confidence. I mean really, how long should it take to draw a triangle?
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The class quickly realized the need for precision and measurement. What was supposed to be an 8" equilateral triangle took a lot more time and patience than initially expected. Especially for the GATE students and high performers, this was humbling. It's just a triangle... How hard can it be?

Sure enough, all students cleared the first hurdle and thought they were onto the next one. Next up was the 4" triangle and, if the measurements are sound from the 8", this shouldn't have been too tough.
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Quickly, the measurements students had made for their 8" triangle were coming into play with the 4" triangle, proving that they were slightly off. Even a 1/64th of an inch difference can make a noticeable slant in the triangle. ARGH!

Oh yeah, you'll need an eraser, too.

Starting over was incredibly common, which was great for students to see. It wasn't "the smart kids" flying through the challenge; it was the low-to-middle students who were persevering.

Once the 8" & 4" were precise, students got into the 2" triangles and mistakes were shining through.
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To be expected, there was a high amount of frustration during this entire process. We had built a culture in our classroom all year where it was OK to get frustrated, OK to be stuck, and OK to ask for help. We really​ needed that culture for this project because kids who have never struggled in math were struggling mightily.

And they were furious that they couldn't take it home. 
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Something pretty amazing started happening as the students were given a safe space to struggle. While many of them would typically plow through a problem set, a project, or a challenge without asking for help until the very end, the overwhelming majority of the class let down their guard and were constantly checking in against the rubric.

Stevens, am I good?
*goes back, draws a line*
How about now?
*goes back, draws a bisector*
...repeat


Better yet, they were checking in with their peers and lifting each other up to get through this common goal: draw a triangle.

By day 3, I had become unnecessary, other than to hand out new sheets of scratch paper. Students walked into class, grabbed their triangle, ruler, pencil, a ton of patience, and got to work, then checked to make sure their table group was looking good. 

For 5 school days, we worked on drawing triangles, but it was so much more than that. Seeing the look of accomplishment on their faces for "conquering" Mr. Sierpinski after all they had been through was rewarding for them and for me. 

If you have some time at the end of the school year, a stack of scratch paper, and a lot of patience, it's worth trying out.
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Happy "Sierpinski Shenanigans" Fishing
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Sometimes, Failure is Final

5/4/2016

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Under the bill of every baseball cap I wore from the time I was 12 until the day I stopped playing, there was a simple inscription:
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REFUSE TO FAIL

It was my gentle reminder to myself that if I was going to have a great day, it meant a game with no flaws; not just errors, but no bad throws, no swing-and-misses, no mistakes. Those three words helped get me through countless struggles on and off the field, up until May 4th of 2005.

"Johnnie, come on in. Have a seat."

It was our annual player/coach meeting, the one where we go through the year and how everything went, where I would need to focus over the summer, and what next year had in store for me and my role on the team.

Earlier in the season, while stretching before a game at Cal Poly Pomona, my shoulder popped. It wasn't the gentle grinding that I'd been feeling since September, the one that warranted a fresh bag of ice after every practice or round of catch. No, this one was different. It didn't hurt. No shooting pain, no throbbing, and no odometer reading of many throws since the time I was four years old. No, it was numb. Due to play catcher in game one of our double header and be the designated hitter during the second game, I quickly rushed to Pomona's trainer and asked for a quick diagnosis. He lifted my arm, but there was nothing; I had no strength.

"That's fine," I said, "I'll just see if I can throw and work through it." 

I went back to the line where the team was warming up, dropped to one knee, held up my glove, and received the first throw from Derrick, the starting pitcher for game one. I reach into my catcher's mitt, grab the ball, and wind back... but can't. The ball barely leaves my hand, as do my hopes and dreams of ever playing professional baseball. I knew at that moment something was terribly wrong.

​Neither pain killers, therapy, ice, nor alcohol would help soothe the pain of not partaking in an activity I had grown to love since Kindergarten. After all, I had refused to fail, yet my body had failed me.

"Look Johnnie, we appreciate what you've brought to the team, but I'm afraid I can't keep you on the roster for next year. I don't know what's going on with your arm, but I can see if another school could use you for next year if you'd like."

I went from being worthy of the Major League Baseball draft to getting cut in the matter of one conversation. One arm circle. One failure. This was final.

​The months that followed were the darkest days of my life. After all, there wouldn't be another chance to refuse failure. As soon as I walked out, I knew that I needed to accept it. But how? I've been telling myself since I was 4 that I loved the game of baseball and since 12 that I refused to fail.
I share this story because it's important on a number of levels. First, that I had been telling myself something unrealistic for so many years. Second, it feels good to get the worst chapter of my life out into the open. Third, I fear that it relates all too well to what we're doing in education. 

The poster above, grabbed from one of many Pinterest boards, touts this acronym that makes me cringe. It's been the tagline for many educators on Twitter lately and gets shared around as a way of encouraging students to persevere. After all, it suggests, it's OK to fail because ultimately you'll succeed. But what if they don't? What if they continue to work, thinking that it's "yet another first attempt" and don't see the gains? What if, after years of working toward a goal, they just... fail?

I get the premise, and I'm all for encouragement. What I fear we are doing here is using a four letter word defined as a negative and desperately attempting to pivot it into a positive. Instead, I would love to see us eradicate the word "fail" from anything that isn't absolute. If you're going to give a test, quiz, project, or assignment that can be made up or re-taken, students can't fail it. 

As I've thought about this idea, I realized that my small shortcomings weren't failures. Hall of Fame sluggers routinely create an out 70% of the time they come to bat. We say that those people are successful, yet our definition says that they fail more than twice as much as they succeed. Realistically, my the underbill of my ballcaps should have all read:

DEMAND SUCCESS

It doesn't ignore my first attempt in learning, and it also doesn't ignore my second, third, fourth, and so on, as long as I reach success. 

Think about the students who struggle the most in our classes. If we tell them that an F is alright because, "even though you failed, it's your first attempt in learning the content," we're lying to them and they know it. Those kids have more than likely struggled through a number of classes and phases of education.
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