A Lumber Expert's Word Problem Expedition

As a result of pulling my head slightly above water and of many discussions with the 8th grade math teacher at my school, I've decided to adjust the way I teach my math class. She is a 2008 TFA member who successfully taught two full grades in her first year of teaching and is the department chair in her second. She is encouraging and understanding, but relentless and unwilling to compromise expectations. In short, she's a very good teacher.

So far this year I've been fighting to reteach skills that my students have been building for the last several years. Adding and subtracting decimals, converting fractions, comparing positive and negative integers, and on and on... I've slightly empowered some who had already mastered these things, slightly improved some who hadn't, and slightly annoyed the rest. The never-ending battle with differentiation.

But where was I? Oh yes, new direction. The knowledge and skills that my students must leave 7th grade with haven't changed, but I am now going to approach them through the mysterious and dangerous jungle of word problems. I still need to spend plenty of time teaching how to do things like dividing decimals, but I am going to start spending much more time teaching recognition of when and why to do what.

My students DO NOT know how to solve problems. The extent of their problem solving skills are to pull each number out of the problem and then choose an operation at random - like spinning some sort of Wheel of Arithmetic. Here are three reasons why I think this is important:

1. Being unable to think critically about two sentences sets a dangerous precedent for thinking critically about any number of scenarios that my students may be faced with in the future, academically or otherwise.
2. Seeing these skills used in as many contexts as possible will give the most students the greatest chance of internalizing the big mathematical picture. Being able to visualize these numbers and operations is something I take for granted. But a 7th grader has a hard time seeing that a 20% tip is the same as 1/5 of the bill, which is the same as $0.20 for every $1. Once they can visualize it and connect it to the real world, they're golden.
   
3. For better or worse, the one measuring stick that anyone in Texas can easily use to judge these children is by standardized test scores. The TAKS (Texas Assessment of Knowledge and Skills) Test is full of word problems, so knowing how to convert or subtract simply isn't useful unless you know when to. These test scores determine which students get put in which classes, which students pass, which teachers get stipends, which schools get money, and on and on. An imperfect situation? Of course. But it is what it is.
   

I feel a little sheepish for just now landing on these obvious and basic conclusions, but hey - better late then never, right?

On Friday, each student entered my classroom and followed a protocol that will occur at least 3 times a week from now until the end of the year. They each took a half-sheet of paper from the back table and spent 5 minutes beginning the word problem that you will see below while I took attendance. Then we spent 10-15 minutes discussing the problem, where they got stuck, the different strategies they used, and why some did or didn't work.

We've been learning how to multiply, divide, add, and subtract fractions, so my students would all know how to solve this problem once they decided what to do, but no one did.

A piece of lumber is 4 1/4 feet long. If you need a piece of lumber that is 2/3 this size, how long of a piece do you need?

In addition to the above problem, each half-sheet contained a problem solving grid that I adopted with spaces for:

• Question - What are you looking for?
• Data - What do you know?
• Devise a Plan - How will you know you're right?
  
• Answer - Show your work
• Write a complete sentence
• Expression - How did you get there?

On Monday, I'll share the answer and some humorous results of our class discussions. But take a stab at it... are you smarter than a 7th grader?

Sencerly

I just found a few letters that some of my summer school students wrote at the end of this summer.

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July 9, 2009

Dear Mr. Camann

Thank you for being a great MATH Teacher. I learned a lot. Even stuff I didn't understand. What I liked about this class is that you put the math problems different. You showed the whole class different ways to solve a problem.

What would make this class better is if you make it really fun. Nothing else needs to change.

Class helped me by being a better person. In regular school I talked a lot & kinda didn't do my work. But, now that I'm in Summer School, I talk but I do my work. I had good grades in regular school, but then I started flunking. But now I am trying to do my best in Summer School.

Good luck in another school. Good Bye!?

Sincerly,
GR :)

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Dear, All My Summer School Teachers

It was fun spending my summer with yall. Thanks for teaching us. I know some teachers were kinda boring but I still had fun with all of yall. I wish for yall to stay but I know yall have to go. Well theres kids out there who are waiting for these new teachers. I hope they like yall. Well I know I will never forget the teacher who help me reach one goal of mine. Class for me was boring but still fun. Well yall were great for teaching me. Well good luck with your next students and hope yall have a great time of yall lifes. :)

Sencerly
NV

P.S. I KNOW I AM THE BEST! :P

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Dear, Mr. Camann

Your class is awesome. I liked everything you teached. Your class really helped me alot with everything. Thanks for everything. Your awesome

Sincerly,
YT

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EO July 9, 09

To: Me, Myself & I

Well I think I learned more science this summer rather than the whole school year! Math was pretty much easy but that really stupid i failed only by 1 question but I guess! I really hope I pass & I know I did because I know am smart I just like playing around in class especially when is very boring! Reading is boring but not the class ok! Social studies thats a fun learning there I actually really learned something there but what sucks about me is that sometimes I forget stuff that I learned & then I have to think hard to get it back but oh well at lease is worth it!

Cucaracha Count: 1

As students were lining up at the door near the end of first period, I heard "Meester, meeester - cockroach." There, perched proudly on the top of one of the desks, was a huge cockroach, antennae waving.

As if they we concerned, I told the students I'd handle it and filed them out of the room so they wouldn't be late. By the time I turned around, my tiny nemesis was gone.

All of second period passed without another sighting, but once I was alone in the room for my planning period, there he was again - somehow even larger. I realized I probably did have to do something about it, but wasn't quite sure what. I contemplated pounding the little bastard into the carpet with my shoe, but wasn't really psyched about any part of that situation.

I grabbed a pencil cup and notepad from my desk. After a brief period of mumbling to myself and chasing the cockroach around the room, I was finally able to trap it between the cup and notepad. I rushed outside and flung it into the grass. I spent the rest of my planning period randomly shivering as I recounted the grossness of it all.

I should probably figure out a better plan of attack for next time - any requests?

Cucaracha Count: 1
Method of Destruction: none, possible heat stroke outside of trailer 511.

Pre-AP Non-Sequiter

"So, when we're trying to add fractions and we run into a mixed number or a whole number, let's make it easier on ourselves by rewriting those numbers as improper fractions. Any number divided by 1 is the same, and since fractions show division, we can write any whole number as a fraction with 1 in the denominator. For example, we can rewrite the number 6 as 6/1. It's a little different for mixed numbers. Take a look at 5 1/3. We've got 5 whole pizzas, and one piece left over. If each pizza is cut into thirds, how many pieces do we have total? Right, 16. All we're doing is multiplying the whole number by the denominator and then adding the numerator. There's our new numerator. But the pieces are still the same size so the denominator stays the same... Yes, MG - do you have a question?"

"Mister, are you from Irish descent?"

5:00 - 7:40 AM

The alarm springs to life at 5, and I frantically jump out of bed, confused, disoriented, or maybe just plain annoyed. What day is it? What state am I in? Didn't I just go to sleep a couple hours ago? Why do I have a strange feeling that I should be reprimanding a teenager right now? Slam the snooze and back to bed until my cell phone alarm finishes the job a few minutes later. After a long, absentminded shower, I pour myself some Cocoa Pebbles, which I enjoy thoroughly as I check my e-mail, update my fantasy teams, and frantically finish planning for the day.

I throw a sandwich, an apple, and some yogurt in my lunch bag and hit the streets at 6:05. There's something sublime about driving with the windows down at such a comfortably dim hour, aside 10 to 15 cars on the same highway that will be gridlocked in an hour. Air that is unconditioned yet comfortable is hard to come by these days, and 6 AM is about the only shot you'll get. No NPR today; just me and the dawn. I fly over the “road humps” (apparently the Texan equivalent of speed bumps) on Skyline, roll into the empty parking lot, and take a deep breath. Today is a new day - Go Cougars.

After signing in at the front office, I head through the pristine hallways and out the back door toward the middle school trailers. It looks like the custodial staff hasn't come around to unlock the doors yet, because the back door is propped open by a yellow “Wet Floor” sign. Ahh good, this means my early-morning partner in crime has already arrived - the 6^th grade reading and writing teacher in the classroom next to mine. I pop into her room and see that she's about as awake as I am. Still, from her desk she smiles and musters a cheery “good morning!” We talk about Jerry Spinelli for a while as I grab my first cup of coffee from the pot behind her desk.

I unlock the door of room T-511 and head immediately to the thermostat to set the air conditioner at a cool 77. While I wait for my computer to load, I erase yesterday’s homework and objectives on the whiteboard and update them with today's information. “Multiplying Decimals” for periods 1 through 6 and “Unit 1 Test” in big block letters for period 7, my Pre-AP class.

On Monday, I had stolen 3 worksheets that the 8^th grade math teacher used last year with the 7^th graders as homework for adding and subtracting, dividing, and multiplying decimals. That morning I had submitted requests to the copy staff for copies of all 3 along with the Pre-AP test I was giving today. So this morning, I’m spared a trip to the copy room to frantically make copies myself. It only took 3 weeks to get a half day ahead!

First things first, I print off the lesson plans that I finalized the night before and put them in the binder on my desk. Next, I turn on my LCD projector and start putting together a PowerPoint about multiplying decimals. I breathe another sigh of relief as I remember that my Pre-AP class will only be taking a test today. So far my sweetest revelation has been how amazing test or quiz days are, and let me give you three reasons. One – tests gently remind my students of the fact that there is a day of reckoning for any unfinished homework, off-task behavior, or unasked questions. Two – I’m excited to see, after all the work that the students and I have done, how well they can succeed in putting their knowledge to paper. Three - and I can't stress this enough - I get to sit down in a silent room and not say a word.

I finish my PowerPoint and my coffee so I head next door for a refill. Back in my room, I enter some of the addition and subtraction worksheets that my students graded in class yesterday into GradeSpeed, the online grading system that my district uses. The first bell rings. 7:30. By now the students are being herded from the cafeteria to the multi-purpose room, it’s current purpose being to hold several hundred 5 to 15 year olds.

I head back to my desk and read through some of the e-mails that I didn’t get a chance to look at yesterday. I check my calendar one last time to make sure that I’m not, in fact, supposed to be at some professional development training all day or something. I maximize the GradeSpeed window and set it to the attendance page for my first period class, so I’ll be ready to submit their attendance during class.

I sit back in my chair and survey the room for a second. Mr. Camann’s math room, who would have ever thought?

The second bell rings and I head toward the door to greet my students. In the next minute, the serenity of the morning will be broken by prepubescent feet pounding up the metal ramps leading to our rooms. My first class will file past me, intent on doing anything but the simple directions my fresh PowerPoint proudly displays on the SmartBoard. By now my coffee has cooled, but I pound the rest as I reach the door. It's go time.

Shalom

I realize that making 2 posts in a 24-hour span has the chance of knocking the planet off it's orbit, but I decided to chance it to share a quick glimpse into part of my day.

I had a new student come in partway through my second period today. I found him a seat and stumbled back into my lesson. When the class began practicing comparing fractions or whatever we were talking about today, I went over and tried introducing myself and asking his name. He wrote it down for me so I could enter it into my attendance. He was brought into a class of 12 that has a strong contingent of LEP (Limited English Proficiency) students - so I thought he might be in the same boat. I asked him if he spoke English, which he most certainly does not. Then I asked him if he spoke Spanish, and that turned out to be a no as well.

When I found out that my newest student only speaks Arabic, I didn't know what to say to him. I came up with something that I'm sure would have been comforting had he been able to understand it, but instead he looked at me helplessly and I returned to my patrol of the class.

What do you do in this situation? I shot a quick e-mail to the assistance principal to see about switching this student into my 4th period class, which has a student who speaks Arabic and a decent amount of English. I hope this happens... because otherwise, what do you do?

In Spanish, I could convey some meaning if I absolutely had to. I had another new LEP student today that I was able to help with comparing positive and negative integers by pointing at numbers and asking "menor o mejor?" The Spanish-English barrier is one thing - there are other students in the room who speak both languages... but what about Arabic?

I found out after school that some of the other teachers had used an online Arabic-English translator with him to type out some instructions or find out some more about him - BRILLIANT! That's just veteran teachership, I tell ya.

I've only known this kid for half of a day, so I don't know anything about him or where his math strengths are, but I can't help but feel for him. Of course my initial response was to worry about myself and how I would be able to teach him anything this year - but when I got home, all I could think about was what it would be like to get plopped into a room where no one else understands me and I can't understand anyone else... including the goofy dude with the beard and the tie waving his hands at the number line up in front.