Being the Answer Key (or not)

After reading through the Pimm Quotes that Dan selected, some type of bittersweet emotion about teachers being the answer key was rekindled within me. I left a few comments/questions and I appreciate Dan's timely and thoughtful responses.

For the following questions, I'll define "yourself" to include you, your students, and your classroom culture.

• Where would you place yourself today?
• Where would you place yourself at the beginning of this year?
• Where would you place yourself last year? 
• Where would you place yourself during your first year?
• Where would you like to be placed at the end of this year? 
• Where would you like to be next year?

*I'll share mine at the end.

There's way more to talk about here. I did not fully capture the essence of Pimm's quote, Dan's response, nor my own thoughts. I just wanted to toss this around as is.

I challenge you to blog about this too.

• Reflect. 
• Label your axes how you want. 
• Should it just be two axes? 
• Either way, create/add some type of visual.

Stadel this school year:

Stadel last school year (I went overboard and it was not enjoyable for anyone.):

AVOID quadrant IV

Stadel in the past (pre #MTBoS):

Stadel as a rookie:

Answer key,

609

Collaboration: Virtual vs. Face-to-Face

First, I don't like the "vs." in the title, but decided to leave it. Don't think of it as a competition or that one form of collaboration is superior to the other. After reading this post, you can interpret the "vs." however you like.  I'm going to do my best to keep this post short even though I thought I could fill it with many links.

One thing I know is this:

My face-to-face collaboration has improved as a result of my virtual collaboration.

Monday, I met up with Fawn (@fawnpnguyen) in Los Angeles to prepare our CMC session for when we present both in November (CMC-South) and December (CMC-North).

Tuesday, I met with the other math teachers at my school to plan out our year as we transition to Common Core State Standards. I wish I could share their twitter handles and/or blog addresses, but those don't exist. Hopefully, they one day will.

Tuesday evening, I presented at Global Math Department. I was grateful to test out a Back to School Night presentation a la Ignite style with Jessica (@algebrainiac) and Amy (@zimmerdiamonds).

Wednesday (today), I have a chance to reflect.

Meeting with Fawn is always a blast. It's both fun, productive, and interlaced with our typical banter and joke-slinging at each other. We usually collaborate via email. However, we both know there are so many virtual ways to communicate and collaborate on anything math-related. We both cherish the online math community as a professional learning network and have greatly benefited from it. But in person. Let me repeat that, IN PERSON! (face-to-face), I feel so much more can be accomplished because of the immediacy and tangible elements a virtual collaboration can lack.

Meeting up with my colleagues at school on Tuesday was great too. Our 7th grade teacher and I went off on a tangent during the afternoon as we talked about the Estimating Celebrity Age activity. We had a blast as we tried to decide a winner if you made this activity an in-class competition. We came up with about four different ways by hashing things out, giving counterexamples, and coming up with strong arguments. Two math teachers totally in the thick of Mathematical Practice 3: Construct Viable Arguments and Critique the Reasoning of Others. It left me thinking that teachers need to take these 8 Math Practices to heart, not just in the classroom, not just with students, but when collaborating with other teachers, virtually or face-to-face.

Global Math Department could not have been anymore beneficial. The online math community showered us presenters with constructive feedback and suggestions, even some jokes. This virtual collaboration was exciting too. We did our presentations and people were honest about the appearance, content, delivery, layout, format, timing, etc. With such a large group of people attending, the Global Math Department has a solid format and structure to allow the presenters to say their piece and receive viable feedback from a respectful community.

Again, this is not a competition. These two types of collaboration are so important and can truly benefit each other. I can safely say that collaborating with others virtually, through this online math community, has helped me improve my face-to-face (in person) collaboration. I'm excited for the school year to start so I can utilize both, once again. Summer has been great, but I miss that face-to-face interaction.

What lies ahead?

• This year, collaborate like crazy with my school colleagues. Go beyond anything I've done in the past. 
• Invite others at my school to practice our BtSN presentations to each other ahead of time. We could help each other by providing constructive feedback.
• Continue collaborating formally/informally with all of you in this digital-virtual medium known as The Internet, and our online math community.

Collaborate,
357

[Makeover] Low Arching Bridge: The Makeover

Once again, the task:

What I like:
I like the placement of the x-axis along the ground to represent zero height.

I like how this task reminded me of the low arching bridges along George Washington Memorial Parkway in Alexandria, Virginia.

What I dislike:
I dislike that the x-axis and the y-axis were already placed for us. The students have no say in this.
I dislike how the arch is already "modeled" by the given function. There isn't any chance for students to explore this on their own, especially if they had no say in the placement of the y-axis.
I dislike the answer to this question. It's hilarious. Get this:
The truck has to be dead center so that it will allow 0.23 feet of clearance on each side of the truck. Regarding number sense, what is twenty-three hundredths of a foot? No one talks like that, do they? After converting this answer, I could see myself telling the driver, “You have less than 3 inches to spare on each side. And that’s ONLY if you center the truck with the middle of the bridge." Let's look for an alternate route or someone might have to get out of the truck [not it] to guide the driver.

Things I'm intrigued by:
What was the reasoning behind the placement of the y-axis? Why isn't it dead center or along the right wall?
Why isn't there any sign on this bridge that says the maximum height and/or width of trucks allowed?
Is this a "one way" road?

Here's what I did:
*Disclaimer: I'm not pretending to nail this Makeover: I think it can be better. That's your job: so let's get it on and help me in the comments. I'll admit, the Makeover was more work than I anticipated and I'm tapped, but I'm happy to do it now during the summer. Thanks Dan for the Makeover challenge!

I found an accident report for a coach bus that crashed into this exact bridge (below) in 2004. There are many of these low arched bridges located along George Washington Memorial Parkway in Alexandria, Virginia. I've seen a few of them when we've taken our 8th graders to visit Mt. Vernon. I remember our bus driver telling us about this specific collision.

1) Show your students this picture, but don't tell them about the collision:

Allow students to make observations and ask questions (maybe Notice and Wonder). Tell them where this bridge is located if they ask. Don't tell them what the signs say. Have a discussion.

2) Now show your students this picture and ask:

Which of these (six) vehicles would safely pass under the arched bridge?

3) Have students make guesses and write it down. You're taking a chance, but at least one student should notice that some vehicles might pass safely using the left lane, but not when the same vehicle is traveling in the right lane.

4) Ask your students what information or tools they might need to help determine which vehicles can safely pass through this arched bridge.

• Bridge height(s)
• Vehicle height(s)
• Width of road
• Width of lanes

5) Find the vehicle heights we'll be working with. Depending on the time you have, students can use the internet for finding the average height of each vehicle. I did the grunt work for you with this slide:

6) Show students three heights of the bridge and street dimensions. They probably want to know what those yellow signs on the bridge say. Too bad! The picture is low quality and very pixelated. I'll admit, this might feel like we're now stringing the kids along, but let's offer them measurable dimensions, not some arbitrary equation that "models" the arch. Share the following:
Height of the bridge on the left side
Height of the bridge in the center
Height of the bridge on the right side

Width of the entire road (including space for lane lines and shoulder) and width of two lanes.

7) Offer your students Desmos or Geogebra. Plot the three heights. Use sliders to find an equation that models this low arching bridge. Here are three four scenarios I came up with in Desmos. I'm still not sure which I like best. You decide. I've linked the Desmos files for you to mess around with.
Where do you fancy the y-axis?

y-axis justified RIGHT:

y-axis justified CENTER of bridge:

y-axis justified LEFT:

Just for fun (the actual bridge):

Okay, I like both the center and the justified right. Placing the y-axis in the center of the bridge made it a lot easier to find an equation that modeled the bridge. Placing the y-axis on the right side of the bridge might produce negative x-values, but since distance is never negative, the absolute value of the domain will tell me how many feet away from the right side of the road the vehicle must be.

8) Give students time to explore the functions, quadratics, sliders, domain, range, and so on. There's more. This task requires students to apply the heights of the vehicles in a specific manner. Sure, students can click and drag on the graphs in Desmos to find the heights of vehicles and determine if it safely passes, but what part of the car "safely passes"? The top left? Top center? Top right? Therefore, students have to now take into account the width of the vehicle. Let's go back to the original question:

Which of these (six) vehicles would safely pass under the arched bridge? And in what lane?

• Which vehicle(s) will pass safely in both lanes? 
• Which vehicle(s) will only pass safely in the left lane?
• Which vehicles(s) would have to go into the oncoming traffic lanes?
• Which vehicle(s) need to stop and turn around?
• Ask how far the vehicles will be from the right side curb when "passing safely"?

9) Tell students to look for a little more clearance than 0.23 feet (2.76 inches). You can read the accident report for all the details about the street and bridge. You'll find the clearance heights posted on the bridge and about 1,500 feet before the bridge.

Unfortunately, the accident report will also show the bus that collided with the bridge while the driver was talking on his cell phone. The bus ran into the bridge without even applying the brakes.

What you did or suggested:
Amy Zimmer emailed:
"Is it the new Daniel Craig James Bond that has the train scene where he has to duck just before he is about to run into the bridge when the good guy and the bad guy are fighting on a speeding train?" followed by "I would give lots of trucks and see which ones fit."

Everyone else's input can be found here:


If you've made it this far. I appreciate your determination and perseverance. Thanks for tuning in. I know this task can be better, so let's get it on in the comments.

Up next, Global Math Department presentation on August 13, 2013: Back to School Night: Ignite. Join the fun.

Under the bridge,
1230

CCSS Workshop 2013

I did my first workshop this past week (5-30-2013), discussing the transition to Common Core State Standards, with a focus on the 8 Standards for Mathematical Practice. I'm working with K-5 elementary teachers, a couple of middle school math teachers, some support teachers, and a couple of administrators in the room. I'll admit, I'm not as eloquent a speaker as Steve Leinwand, but there might be a few times where I actually make sense. I'm throwing this video out there for some feedback. I don't expect you to watch the whole thing so I've provided some chapter markers you might be interested in. At the end of the notes for each chapter, I reflect by creating a wish-list of moves I would've done differently. They come across as rhetorical questions, but feel free to chime in. However, here are a few angles I'd appreciate you considering:
What did I forget to talk about?
Where could I have been more explicitly clear?
Where coud I have used a better strategy? ...and so on.

Opener: 0:00-10:10
I use an estimation task (Day 127) to kick things off, providing teachers with the handout Michael Fenton created for estimation180.com and my students. The handout has been through many revisions and I think we have a final version that's a winner.

I use the whiteboard to write the "Too Low", "Too High", and "My Estimate" of a few teachers, asking for reasoning along the way. We watch the answer and discuss.
8:15 is a precious moment where a teacher asks, "Wait a minute! What was it (the song length answer) really?" I love how a teacher is demanding more information. I wish I spent more time expressing the importance of her question. I feel rushed because of all the workshop content I have prepared. I wish I had allowed the other teachers to address her question more. I do with my students, why didn't I do this here?

Active Notebook Part 1: 10:15-12:55
Teachers glue their Estimation 180 handout to the inside cover of their workshop Blue Book and the Table of Contents to the first sheet while listening to Can't Buy Me Love.

Preview of Workshop: 12:55-20:50
I attempt at working on the following question throughout the workshop,

What's our role as we reshape the classroom with the Common Core State Standards?

I share with teachers what today will not be and what today will be. On a parallel universe I share with teachers what I perceive the CCSS to not be and what I perceive the CCSS to be. Then I share a few personal items from this past school year. Seeing that I'm doing a workshop with multiple grade level and content teachers, I'm expressing the focus of the day to be the 8 Mathematical Practices and what we do in the classroom. How do we help facilitate the learning?

Estimation Task #2: 20:50-26:45
We use Day 129 where teachers see that the song length is also the track length. Listen to their reasoning. I love this! Hearing this reasoning from teachers and students is one of the many joys I get from doing these daily estimation tasks. However, I wish I did a better job (23:50) of getting the teachers to justify their reasoning and "argue" a little more than I did. I wish I created a little more tension. Check out (25:00) the excitement of the teachers as they watch the answer.

I introduce the language of creating a task that has a low-entry point and could see that many teachers had no idea what I was referring to. Not their fault. However, I like their reaction when I translate "lower-entry point" to being easier. I wish I explained "low-entry point" better. I wish I had explained it as creating a task where most, if not all students have an equal opportunity to engage with the task, regardless of their mathematical proficiency. I wish I expressed the importance of providing students with a task where math vocabulary and thinking come as a natural result of solving the task.

Math Tools & Two Uses: 26:45-33:55
I ask teachers to glue a picture of a math tool to the front of their Blue Book and write down at least two uses for each tool. They have two minutes to complete this task. After We Will Rock You, I ask the teachers for their uses instead of telling them. This serves two purposes. Yes, I have a list of uses that I anticipate them to come up with, but I want to hear from them first, selfishly providing me with additional uses that I didn't anticipate. Secondly, I'm using this activity to illustrate how students need to provide the answers in the classroom. I wish I could have given this more time in the workshop where the teachers actually used the tools in the manners they suggested. I also should have had the teachers write down all the uses we came up with.

Introduction of 8 Mathematical Practices 33:55-1:04:00
Again, I'm feeling rushed for time! Yes, I said it, "Let me talk about these 8 Math Practices real quick." Real quick? How silly of me. These practices are not something to gloss over. Don't worry, we spend ample time doing a Jigsaw activity so teachers are out finding information about them. I provided the teachers with the handouts found at Jordan School District's site. The practices are presented in a manner representative of the grade level you might teach. Thanks Fawn for this link.  I could have explained and facilitated this a lot better, but the redeeming value is hearing teachers that were appreciative of this specific activity because they were "forced" to explore the practices instead of just receiving a handout with the information embedded. If I were you, I'd skip the section (39:30-52:00) unless you want to hear some of the teachers talking in their groups as they rotate around the room to their four different stations. I'm proud of the rotation table I provided and how teachers travel together according to their "math tool." DON'T miss the "perfect high-five" at 38:10. I love that a teacher commented that "perfect" is subjective. I say this all the time to my students.
At 52:30 I give teachers time to regroup and complete the practices by receiving information from the other teachers in their group. I recap (1:00:00) and then show teachers how to create a pocket (1:01:00) inside their Blue Book so they can store a Quick Reference "teacher" version (I referred to as "adult") of the 8 Mathematical Practices.
I wish I gave more time for reflection. I wish I reviewed each practice with the whole group by having them share out loud something they learned. During the Jigsaw activity, I was told that my time with the teachers was cut short by about ten minutes so I had to hurry things along. Arghh!

Find My Mistake: 1:04:20-1:13:00
I made an executive decision to skip the model lesson I had prepared for the worksop. I'm glad I didn't skip the Find My Mistake segment of the workshop. I'm very adamant about teachers finding the mistake quietly here. I encourage them to share with each other before we review with the whole group. I give props to Michael Pershan for mathmistakes.org. You can hear kids in the hallway, alerting me that our workshop is coming to an end very soon. We listen to each other make corrections or talk about the misconception and why us teachers are good at knowing the content we teach. We're constantly telling students what their mistakes are and telling them how to fix it. Let's switch that role. Make the students find, correct, and tell each other what the mistakes are, especially items that use algorithms. Remember, most of the teachers here are elementary teachers. I also point out that I haven't been jumping for joy every time a teacher gets an answer correct. Instead, I try my best to throw it back on the class for what they think, allowing them to critique the reasoning of others. I love how estimation and number sense is addressed with teachers on how to help encourage students to avoid these mistakes.
I hit a nerve (1:10:45) when I was asked, "What about simplifying?"
I could very well be wrong here, but my current understanding is we (as teachers) are to allow for multiple representations of the correct answer, unless explicitly instructed otherwise. In other words, ten-eighths is just as acceptable as five-fourths.
I wish I reviewed with the teachers the importance of doing an activity like this quietly and individually first, before group discussion. I wish I expressed how much I love group work and collaboration, but need to remember both teachers and students need that quiet time FIRST. The worst is being in a group where one person dominates the conversation and you don't have time to think or worse, problem-solve. I wish I had covered this with the teachers.

Summary: 1:14:15-1:19:00
I provide teachers with a fill-in-the-blank handout to glue to the inside of the back cover. Again, watch their reaction when we get to "low-entry" point. I hope I drive it home when referencing the "Cent-ed Whiffle Ball" task I recently did in Geometry. I remind myself and the teachers to listen to the students. I'm constantly working on allowing students to finish their thoughts. Don't cut students off or finish their sentences for them. I ask teachers to create a couple of goals. I provide the teachers with a list of resources found here. I like how they (at least some of them) want another in-service/workshop.
I wish I emphasized the importance of knowing the 8 Mathematical Practices better and to use the summer to better prepare for next year. I wish I had more time to pump up these points in the summary. I wish I had more time!

Unleash yourself in the comments if you will.

Thanks!
729

We don't need no stinkin' homework!

What are our students saying when they don't do practice exercises outside of school? This isn't a revolutionary thought. I'm just a slow learner. Last week I finally had enough of seeing too many empty desks when they're supposed to get out their Home Jams (homework) after our daily warm-up. I assign about 3-4 questions nightly Monday through Thursday. They're not worth any points because of the Standards Based Grading model I've adopted this year. I use Dropbox to sync all my home jams so students have access at home and I don't need to make photocopies or rely on students using a workbook or textbook. I don't collect them. I don't keep track of complete or incomplete home jams. Furthermore, chances are pretty good I will spend the first 5-8 minutes of class having students review the previous night's home jams as a group on their giant whiteboards. My school is in an affluent area and every family has internet access so why do I still see a strong majority of empty desks? I'm not the only one who is absorbing this pain and bafflement. Chris Robinson, Hedge, and Fawn Nguyen (my trusty cohorts) jumped in on this conversation/quest.

Let's find some scapegoats: laziness, apathy, age, adolescence, immaturity, puberty, hormones, SBG, points (or lack thereof), Gangnam style, etc.

Are these really worth my blame and energy? Should I be looking to point fingers, because I'll run out of fingers if that's the attitude I take. There seems to be a more productive use of my time and energy. I like Chris' idea of designing meaningful tasks for students outside of class, but right now I battle the clock with trying to design meaningful tasks for students inside of class. Therefore, should I be associating my home jams with incentives? Let's ask our kids what they think first before we rack our brains out. Here are the two questions we asked our kids today:
1. Briefly explain what reasons cause you to regularly complete or regularly NOT complete the homework assignments.
2.What incentives would motivate you to complete more homework assignments?
The results.

Reasons for NOT doing home jams:
I forget: 17
Online hassle: 12
Not worth points: 10
I don't need the practice: 1
I have other homework: 9

Reasons for doing home jams:
Master/practice skills: 18
I don't understand: 3
Prepare for assessments: 10
My parent makes me: 3

I didn't enjoy homework as a student and still don't (BTSA). I don't think students should be doing hours of homework. When my children get older, I hope they don't have hours of homework because I believe it would rob them from family time or time simply being a kid.

As for incentives, students suggested the following:
Make them worth points [that's not happening].
Make them fun [curious what that means].
Give candy [yup, all I need to do is encourage tooth decay, obesity, or diabetes].
Extra Credit [really? Again, that's not happening].
Put them on paper [I'm listening].
Bring in food [that co$ts money, y'know].
Play music [yes, I considered that and I like].
Redeem points for class prizes [who's paying for the prizes?].
Work it into Math B-ball [I considered that too and I like].

So now what? Enter my thought process and your input here. I'm open to the incentive idea. Could there be something for the group (since my students sit in groups) who completes their home jams all week? Their group DJ's music. They get comfy chairs to sit in during class. They get extra points when we play Math B-ball. They wash my car. Oh wait, that last one seems out of place. I'm going to sleep on this.

My parting thoughts go like this. It eats at me that learning just isn't more intrinsic, valued, and supported at home as much as I'd like it to be. Could that be another job for some caped homework crusader we all dream about? Incentives are cool, but is that just trickery? Am I tricking kids into practicing math? Once again, I think I'm asking more questions than necessarily providing answers. I'm not going to rack my brain out here. I'm not looking for a permanent and magical solution. It would be great to see students participate more and value their learning by practicing math. Is this asking too much of my 8th graders?

Jam,
1101

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

Rock, Paper, Scissors

A few weeks ago I was out with my family and caught a glimpse of two kids playing Rock, Paper, Scissors. I immediately made a note of it on my phone for a 3 Act lesson. Here's what I came up with for Act 1:

Rock Paper Scissors - Act 1 [Scoreboard] from Mr.Stadel on Vimeo.

In my mind, Rock, Paper, Scissors (RPS from here on out), is such a powerful way to decide something between two people. I think of all the times it decided who got to ride shotgun, who got the last piece of pizza, who got to go first, etc. We're talking a huge playground staple (at least I think it still is). I have no idea if the two kids were deciding something or just playing RPS for fun. It doesn't matter! I wanted to know who would win? Were they playing straight up to one? Were they playing the best 2 out of three? Who has the advantage: rock, paper, or scissors? What are the chances of a tie? A lesson was born... I have to get it down on paper or make a digital note of it somewhere. Imagine the class activity that could result from this... that will be a future post.
I'll admit, I was proud of this Act 1. I thought I had a slam dunk. Feedback from some tweeps said they preferred the scoreboard (thank you twitter and online colleagues). As you can see only 7 people have viewed it on 101qs.com so far and 3 of them skipped it. Usually those first 7 people are the regular 101qs users who post first. I admire them. I dig their attentiveness. I could list them, but I won't. They're awesome!

I'm over the initial bewilderment that it barely passes 50% perplexity. There's a bigger, more important element here besides my state of mind: comments. That said, I'm excited with Dan Meyer's most recent update to 101qs.com, specifically the option to leave Comments. I would love to hear from those 3 people and what prompted them to skip it? How could I improve it? What about RPS did not perplex them? Bottom lime: I look forward to receiving constructive feedback on 101qs.com just as much as giving it. Our students, classrooms, and craft of teaching all benefit from it. I think Vimeo sums it up nicely when leaving comments, "Be cool and play nice."
What do you think?

RPS,
756

Rolling Tires

It started a little over a month ago when I had to get my car tires aligned. As my car was being worked on, I killed 30 minutes worth of time walking around the industrial park with my son and came across this goldmine:

a dumpster full of used and abandoned tires 

Mentally, I started mapping out some math application(s) for the tires and figured Spring Break would be a prime opportunity to record a 3Act lesson for my geometry class. I'm proudly addicted to Dan Meyer's 3 Act lesson format. I can only hope I'm doing it justice. After trial and error, self reflection, and feedback from both students and online colleagues I'm starting to see the strength in 3 Act lessons, if done correctly. It requires planning, objectives, patience, and of course... time.

Have an objective, a lesson in mind, a real-world example, (maybe use a word problem from a textbook to jumpstart your direction), start training your eye to always look for lessons you can bring to your students...

Make sure it's measurable: Yes, it's fun to throw a picture at students and ask them, "What's the first question that comes to mind?" Both you and your students might agree on the same perplexing question, but if there isn't measurable data or a realistic solution, your media might simply reduce to a fun picture you both were perplexed by, predicted an answer to, and discussed a path to the solution. That fact alone might be valuable enough without the actual construction and implementation of a class activity/lesson.
This Lego pic I snapped is a great example of something difficult to measure: it might open up a discussion, students might make a prediction, but measuring it would be very difficult because of the numerous variables. However, something like my JUMBO and mini stop sign staging is very measurable and a lesson can be constructed beyond the discussion and prediction arena. Therefore, with Rolling Tires, I made sure everything was measurable before pressing record.

Act 1: A video of me rolling a tire (a friend was disappointed it wasn't a supermodel in a bikini). What's the first question that comes to mind? Hitting the initial mark during Act 1 is imperative to the overall success of the lesson.


Act 2: A keynote and/or video to reveal information my students might find necessary to solve the question agreed upon.

Act 3: The video payoff to see how the calculated (theoretical) answers compare to the actual (practical) results.

Please feel free to download and use all three videos. Give me some feedback. Ask me some questions. The necessary information is included in Act 2. I thought, great an actual way to apply circumference. I will try to post any handouts or graphic organizers used. Lastly, if time permits I might make a sequel to include a couple different scenarios.

Possible Sequel: I heard a long time ago that some taxi drivers put smaller wheels on their cabs so the car tires would produce more revolutions, yielding a higher cab fare. Check the tires of that cab before you get in it.

Best,
930

Survey your students

Spring Break Questionnaire 2012:

I believe in the importance of feedback, whether it's:

1. Customer feedback regarding a product
2. Feedback about a restaurant, their food, service, cleanliness, etc.
3. Feedback from colleagues, administrators, students in your class or 
4. The feedback Jimi Hendrix produced wailing on guitar (that's definitely a topic for another day).

I gave my students this questionnaire last week, right before we went to Spring Break:

The feedback I received from my students is invaluable. My favorites were:

1. A student that responded to question 5 and a difficult concept: "I need more space, there were too many."
2. A high percentage of students used the same verbiage for question 6 regarding the warm-up: "It helps get my brain ready for math and I like the second question because it's fun."

So here's the how, why, and when I do questionnaires.

How: 
Keep it simple. Type up a one page questionnaire your students can finish in about 5-8 minutes. Give it to them on the first day of school or at the end of a short test or quiz. Give your students the premise, don't just throw it at them. Tell them their feedback is important to you (because it is). Explain that their honesty and constructive feedback helps you (the teacher) help them (the students). Again, tell them again that their input is important to you (because it is).

Why:
I don't feel much explanation is necessary here as we could come up with a million reasons, but hopefully the reasons are instinctive, logical, genuine, and simple.

Questionnaires allow student's to take the initial step in the ownership of their learning. They see that you are open and willing to make their learning experience rich, rewarding, and reflective of their interests.  They see that you care. Students can possibly gain a better sense of appreciation for your hard work, but this shouldn't be your main objective. If they see you working hard to meet their expectations, then maybe it will rub off on their work habits in your class and pay dividends towards your expectations of them.

The students (your customer) can give you a perspective that you might miss. They might remember something they enjoy in another teacher's class and want to share it with you. Don't take it as a slight. Take it as a Professional Development opportunity. I'm not saying the students dictate the curriculum, daily agenda, or always know best about their learning behaviors, but their input and perspective keeps you connected and in tune to what they are thinking. Simply put, how does your customer feel about the product you are selling? What can you do to enhance your product and better appeal to your customer base?

This a great opportunity to teach your students that constructive feedback is a life skill that benefits from some etiquette. The questionnaire is not a 'comments' section they can anonymously fill out online, bashing the subject or person while they sit in front of a computer screen. Students are given the opportunity to provide words, explanations, and reasons that are constructive, diplomatic, and appropriate. It's a great opportunity for a teacher to teach a life skill... embrace it.

Don't wait until the end of the school year. IT'S TOO LATE. I always found the rating forms at the end of a college course or graduate class pointless. Why ask me after the fact, especially if the instructor was terrible? How do my classmates and I benefit from taking the survey at the end? How come we didn't benefit from a survey given to this instructor's last class? I digress... However, it's important to me that I survey my students frequently. So when do I poll them for their feedback?

When:

Don't abuse questionnaires. Students will see them more as a task instead of an opportunity to provide meaningful feedback. Don't overuse: 4 times max.

Beginning of the year

It allows you an opportunity to find out information, fun facts, learning styles, and their attitude towards your subject area. What a great way to immediately make connections with your students. Use questions that encourage detailed answers. Avoid 'yes' or 'no' questions. Hey, you're gonna spend the next 180 school days together, don't you want to make a connection with your students immediately that will catapult you together into the subject area you teach? Lastly, ask them what is something they would like to know about you...

Before Winter Break

By this time you have been using various techniques, strategies, learning activities, and have gotten to know the make up of your classes. The newness of the school year has definitely worn off and it's time you get some feedback from your students. Use Winter Break to evaluate their responses and give yourself some New Year's resolutions and an action plan upon your return in January. Your response is pivotal. Return in January reminding them what they did, some common threads, and your action plan. It's imperative you follow through with your plan, or you subject yourself to losing your customers...

Before Spring Break

Spring cleaning, right? It might be time for you to utilize some fresh ideas/activities or maybe trash some that are just ineffective. Maybe there's some concepts you need to reteach before those lovely standardized tests arrive. Use Spring Break to prepare some improved ways of reaching your kids. They're older now. They've seen your best and your worst. Give them something fresh upon their return. Maybe this is where you bring out some 'secret weapons' or some awesome activities you found from a colleague on Twitter, 101qs.com, Teaching Channel, a blog, etc. Do something so both you and your students have something to look forward to as you close the school year. Trust me, by this time, your students will feel comfortable enough to tell you what they like/dislike, and how effective/ineffective activities have been in your class. Plus, if you followed through on your January action plan, they trust you will respond equivalently. 

At the end of the year

This isn't one where you just do it as a formality. You have spent 180 days with your students and hopefully have left a positive impact on their life by now. Hopefully they returned the favor. If you're always looking to improve and be a better teacher, this is your opportunity to take the good with the bad so you can better prepare for next year. I know by this time you are looking forward to summer and the last thing you want to do is think about next year, but it will be here before you know it and guess what? Your current students will help you prepare to have an even better and stronger year next year. Yes, your students might be brutally honest on the final questionnaire because they may never see you again, but take off the rose-colored glasses. It might hurt at first, but it can only make you stronger (sticks and stones..., right?). Take the summer to find ways to better connect with that 'one' student who will be in your class again next year. Decompress over the summer, but keep in mind that your former students have given you a valuable gift. They're feedback, their insight and their words are teaching you now. They have left you with a lesson. Think about it, we expect our students to learn from their mistakes, to take chances, be lifelong learners, and always strive to do their best. Expect that of yourself too. Take their feedback and give back. 

Good luck,
720

A Week off to rethink!

My school had a week off... 'ski week.' No, I didn't spend it snowboarding. However, it was one of the best weeks of my life since I got to spend the entire week with my 21-month old son. Another reason it was so great was because it gave me a chance to rethink some of the things I'm doing in my middle school math classes. I plan on keeping this post short by briefly explaining my blog title, my week of rethinking, and a link I would love some feedback on.

Blog Title:
My favorite divisibility rule is that of three. Although common in the math community, take any number, add its digits and if the sum of its digits is divisible by 3, then the number itself is divisible by 3. For example, 582 is divisible by three since the sum of its digits equals 15. The same rule applies to nine, but I am simply drawn to the rule of 3.

Week of rethinking:
An overwhelming majority my week off was spent rethinking my approach to my math classroom, inspired by Dan Meyer. If you haven't checked out his website, blog, or popular TED video, I highly recommend it. He has given new life to the timeless relevance of learning math in the classroom and how it applies to the world. I am not the most eloquent writer and would not be able to accurately describe his contributions to the math community. Simply, check out his downloadable lessons on his website, subscribe to his blog, or find some videos of him on YouTube and you'll quickly see why he such an inspiring educator. He has willingly shared ideas and resources that both teachers and students need. It has given me a whole new set of glasses for looking at life around me and constantly thinking how I can better incorporate media into my lessons.
I will be attempting to apply some of his philosophies and techniques in my classroom, one being the 3 Acts process. Act 1: present media to grab the attention of your audience in a way that allows room for discussion, asking questions, and making predictions. Keep the presented information limited so you can lead to Act 2: encouraging your students to discuss what relevant information is necessary to solve the question(s). Solve. Act 3: Finish the media and compare the actual/practical results to the theoretical results.
*Of course this is my interpretation and have still yet to test the process out... leading to my next part.

Video Feedback:
Using Vimeo, I posted two videos about linear inequalities. I am starting this section with my Algebra classes next week and I am excited to attempt my own version of 3 Acts. I am looking for some feedback. I am open to all constructive feedback and want to see if you think the videos will help open the floor for discussion of linear inequalities, shading, and possible outcomes given the necessary information.

Best,
78,021 (also divisible by 9)
**Would it be cheesy to sign off leaving a number divisible by three? Ha!