Estimation vs. guessing Part 1

Estimation vs. guessing and the space between, let's talk about it.

If you've been following my thoughts lately, via Twitter (#estimation180) or this blog, I've really been investigating the relevance of estimation for some time now. However, the past few days have really had a great impact on my approach with students, leaving me even more intrigued with the relevance and application of estimation with students. Over the next few days, I plan to share a few of the interactions: here's part 1.

Today, I visited a fourth grade classroom at my school. It's a personal goal of mine this year to visit as many classrooms as possible during my prep period and learn, learn, learn from other teachers, especially elementary teachers. I love observing elementary classrooms and seeing how so many children are still excited about learning. I'm constantly looking for strategies to bring back to my own classroom that will create a sense of excitement with my middle schoolers. The fourth grade teacher and I will be working on creating and implementing 3 Act lessons this year, so I was getting acquainted with the climate of her classroom. It was destiny: the class was discussing estimation and guessing.

First off, she's a fantastic teacher. Second, she did a wonderful job comparing and contrasting what the students thought estimation and guessing meant in their own words. She created a list for each on a huge giant sheet of paper, like a giant Post-It note. She does this often and sticks them around the class for students to refer to. The fourth graders decided that guessing could be something:

1. you don't know
2. you think could be the answer
3. 50% sure
4. or anything

As for estimation, the fourth graders decided it could be something:

1. you round
2. you think is close to the answer and reasonable
3. you look at and use clues to carefully give an answer

This last definition was very insightful for a fourth grader.  The teacher proceeded to pick up a cup in front of the class and tell the class there were cubes inside. She asked them to make a guess and students were stretching their necks to gather any information about the cup in her hands. She did a great job concealing it, but many students had already mentally logged characteristics of the cup. She had a low-entry point for the students. They all wanted to know how many cubes were in the cup. They wrote down guesses in their journals and she took them to the next level. She showed the students how full the cup was with the cubes and asked them if this would be a good time to keep guessing or make an estimate. Students agreed, they had more information to make an estimate and they jotted this new number down in their journal. Lastly, she passed out cups, requesting students to not touch, but think of a strategy with their small group to get an even better estimate of the cubes in the cup. Students shared their theories:

• I counted the cubes in the top layer and then counted the layers down and multiplied the two numbers.
• I counted the number of cubes around the cup on each layer and made a reasonable guess for the hidden cubes inside.

The teacher asked the class who had similar theories and many of them chose the first. I really enjoyed how the teacher didn't once offer her theory on how to estimate. She let the students take ownership. As the lesson drew to a close, she requested the students work together to quickly count the cubes inside their cup and compare it to both their guess and estimate. The teacher had a low-entry point for all students, she let the students define their own vocabulary, she took them up the ladder of abstraction with gradually revealing information they needed/wanted and going from guessing to estimation. Lastly, the payoff was huge as she allowed students go hands-on with the cup and cubes to validate their learning for the day. I left her class inspired. But before I left, the teacher and I had a valuable brief discussion. A few things came out of that conversation I will touch base on in part 2.

Part 2 will connect estimation with guessing and the space between, sometimes referred to as a guess-timation. I want to create a low-entry point that's even more inviting for students. Lastly, I want to discuss how number sense can be strengthened as we transition from guessing to estimation before the payoff.

Part 1,
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Hey points, meet my new friend SBG

Dear Points,

We've been in school together for such a long time. Remember those book reports in elementary school where I just read enough to complete the book report so I got a good enough grade? or that time in high school where I colored a few extra maps and did some word searches in my geography class to earn points and raise my grade? or how about that senior English class in high school where I racked up massive extra credit points for turning assignments in early? or that one time at band camp? O wait, I wasn't in band. We had some good times, didn't we? Or so I thought.

When we went to college, we hung out way less and I wasn't ready for that. I missed you because my classes and instructors actually wanted me to demonstrate understanding of course content. They didn't really have a relationship with you. Now I know why. I had those math, science, and engineering courses that simply assessed my understanding through tests and labs. You abandoned me many times throughout college. After college, I fell into teaching and you showed your face again because I was confused and thought we could be friends again.

After teaching for 8 years now, our relationship has taken a toll on me. Last year, we definitely butted heads mid-year with a student and their parent who demanded I give them a point-based assignment to raise your grade from an F to a D-. What did they learn? Nothing. What did I learn? YOU SUCK! Our relationship while being a teacher has always been constrained. I'll admit, I was never 100% committed and vested in our relationship. Each year I was trying new ways to convince myself and my students that we needed you on campus or in my class by revising homework procedures, quizzes, tests, etc. I couldn't wait for last school year to end and be free from you during the summer. I ran into someone new over the summer: Standards Based Grading. He goes by SBG.

SBG introduced me to friends (teachers) who keep learning exciting and relavent for their students: Sam Shah, Shawn Cornally, Frank Noschese, Dan Meyer, etc. They have open relationships with SBG and share how their students are benefiting from it. In the short months of summer 2012, I've already learned more with SBG than my entire academic career with you. Points, you suck! Even better, I got to spend my summer getting well acquainted with SBG and discussing with Fawn Nguyen and Nathan Kraft about how flexible SBG is. All three of us had our reservations about committing to SBG, but we have now seen how SBG is the BFF to both students and teachers. SBG doesn't put any clamps on student learning nor hold a carrot in front of them. SBG has a circle of friends that welcomed me. They have unconditional love for my students and their learning. It feels naturally right. Recently, Chris Robinson even devoted an entire website to SBG.

This isn't the first goodbye letter you've received. I read the letter my pal Timon Piccini sent you and I was thoroughly excited to write you one as well. There's been others and I hope you receive more... maybe more letters than Santa receives at Christmas time. Be lucky it's just a letter and I'm not filing a restraining order. I wish I could. However, I know that we will have to coexist at my school. I'm not moving to another school, but if I ever do I know SBG will come with me and can only hope there are SBG friends there too. Since we have to coexist at the same school, I will respect those you hang out with, even if they're in my department. You still have their friendship based on fear of changing. Leaving you intimidates them. Points, you suck! My department wants to see how long and fruitful my relationship with SBG is this year. They're ready and willing to spend next summer getting better acquainted with SBG. I think your days are numbered. However, my greatest joy is that you will no longer bully my students this year. On the flip side, I hope you don't bully kids in other classes too much or let teachers abuse the joy of learning. I wouldn't want them to be the victims of your rebound.

I bid you farewell, points. Feel free to keep anything I've lent you. Keep my worksheets, handouts, CDs, that one t-shirt you borrowed, and even my book report from third grade. I need a fresh start and SBG has given me that. If we see each other on campus, in the hall, or in another teacher's classroom, I won't turn my nose up at you or talk down to you. We can still coexist at school, just know that you're not welcome in my classroom. If I see you bullying any of my students, expect me to stand up for them. SBG has my back, know that!

Sincerely,
Andrew Stadel

Estimation 180

Estimation initiative:

[*UPDATE: www.estimation180.com has gone live]

Last year I willingly started adding an estimation question to my daily warm-up, inspired by Steve Leinwand, Dan Meyer, and a monthly ASB gag we did a few school years back. Everyday, I greet my students at the door and hand them a 3x5 index card for their warm-up. They get the first 2-3 minutes of class to complete the warm-up exercise and estimation question. The first question reviews the previous day's skill. As for the estimation question, last year I was putting questions that were comparable to fun facts and students had no context clues for making logical estimates. It got silly. Here are some examples:

• How many miles is the California coastline?
• How long does an elephant stay pregnant?
• How many In-n-Out Burger restaurants are there?
• How many miles from the Earth to the Sun?
• etc.

Stepping back over the summer and really fine-tuning the goal of estimation (improving number sense), I began using estimation questions that were more relative and provided better context clues. Every chance I get, I use a picture or something inside my classroom that will allow students to make logical estimates. Here's today's (Day 10):

I've had to cover up the bottom half of the screen now because students come in and immediately want to go for the estimation question. They want to come up to the screen and do weird measurements, or ask me factual questions, and they flat out forget about the first question. I don't blame them. It's fun. Once we go over the first question (favorite yes/no), I usually have students give me estimates that are too low or too high and then we "go right at it." "Who thinks they got this?"

Once I get about 8-10 estimates, I reveal the answer and it's so cool to see how the students react. "Ohhhh, I was sooo close." Or "I was way off!" Either way, I ask the student or students who were close to explain their logic. It's fascinating how kids think.

For today's, I snapped a picture of a measuring cup full of almonds (my new favorite snack). Tomorrow, they'll estimate how many are in the jar from CostCo. Estimation should build. The whole first week we talked about height, based off my height. 

Day 1: What is Mr. Stadel's height? They don't need a picture for that.

Day 2: What is Mrs. Stadel's height? They needed a picture for that. 

Day 3: What is my son's height? Another picture.

Day 4: What's the height of a lamppost Mr. Stadel is standing near? etc.

The first four days used my height as a frame of reference. Check out Estimation 180 (Google doc will be replaced with estimation180.com )and you'll see what I mean. My estimation initiative is to begin documenting my 180 days of estimation, simply titled Estimation 180. Seriously, do I need one more thing on my plate right now? No. However, I do this every day and would love to share this stuff and receive feedback. Estimation is important to me. I've already seen student improvement with number sense in just 10 days of school.  

I'm starting small here, but would love to expand this idea: stay tuned. In the meantime, check out the spreadsheet catalog (tab at the top).

[UPDATE: estimation180.com is live. Forget the spreadsheet!]

Number sense,

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