Saturday, December 20, 2014

Photocopier Survey RESULTS

In preparing for 2015, I asked for your help the other day. Thanks for entertaining my hunch.
Here are the questions and results (from 65 people):

Question: What are the joys of a photocopier?
You had many great things to share about the efficiency of providing your students with copies and some of the detailed functions of the machine. An interesting number of you find joy in the warmth of the copies (I'll admit, me too). Some of you veteran teachers shared how you appreciate the evolution of photocopy machines. Here are a few of my favorite "joys" quotes:
  • The smell of ozone, the warmth of fresh copies, and the feeling that I'm ready.
  • I usually bounce/jam to the rhythm as I wait for my copies...
  • Solving a paper jam. 

Question: What are the frustrations of a photocopier?
Overwhelmingly, paper jams are the most frustrating part of a photocopier according to you. I would say low toner and long lines are on the heels of paper jams. Here are a few of my favorite "frustrations" quotes:
  • Remembering my code
  • When it thinks it knows BETTER than you what size paper you want.
  • Time lost from my life that I will never get back.
First-world problems, right? The next set of questions asked about your feelings, using a Likert scale from one to five.

Question: When the photocopier is functioning, what's your level of satisfaction?
1 = Not satisfied
5 = Extremely Satisfied
Close to 60 people felt satisfied to extremely satisfied.

Question: When the photocopier is malfunctioning, what's your level of satisfaction?
Over 50 people felt little to no satisfaction.

Question: What's your alert level when the photocopier is functioning?
1 = Ho-Hum
5 = High Alert
Varied data, but most seemed to lean toward Ho-Hum.

Question: What's your alert level when the photocopier is malfunctioning?
I'd say close to 50 people felt some alert to high alert. 

Select any feeling(s) you associate with the photocopier malfunctioning.

Select an initial step you typically take if a photocopier malfunctions on your watch.
Let me translate. Most answered that they "Try and fix it (replace ink, clear paper jam, etc.)

Select any feeling(s) you associate with YOU fixing the photocopier.
Look at that! Accomplished! Happy!
We have to respect that there are times we still feel frustrated, maybe even excited.

Here's where I'm headed. 

  • Can any of these feelings or photocopier experiences be similar to learning math?
  • Is fixing a photocopier error analysis?
  • Are there times students just go through the typical process at a ho-hum alert level?
  • Are students given opportunities to be problem-solvers?
  • Are students frustrated with math?
  • Are students frustrated when problem-solving, but persevere and feel accomplished, happy, and excited at the point of resolution?
I have many more thoughts and questions. My goal for 2015 is to provide teachers with a conference workshop/session where we use error analysis as one way to help students better learn and understand math. I've blogged about this a couple of times (Exponents and Linear Systems), but want to continue exploring this arena.

What are your thoughts?


*Google Forms to create the form
*Google Sheets to organize the data and create charts
*Wordle to create the word clusters.

Tuesday, December 16, 2014

Photocopier survey

I'm preparing a new math-conference-speaker-session for 2015 and would love your input.

This survey (found here) will take about 3-4 minutes and your input will prove extremely valuable with the direction I take in preparing my session. Thanks in advance for your participation.

Saturday, December 13, 2014


CueThink is an application (iPad) I would love to see get some serious math love in schools and the online math community. I had the good fortune of being introduced to CueThink by the wonderful people at The Math Forum (thank you Suzanne). I simply want to give you a glimpse in hopes you'll take a tour of the app and teacher dashboard.

*Look over CueThink and keep potential in the back of your mind. The app already has fantastic features, but think how it could potentially support students in being better problem solvers.

Download the app. Take the tour:

What do you Notice? What do you Wonder?
  • Highlight text and see where it goes.
  • Make an ESTIMATE (so cool).
Choose your strategies:

Show and record your solution:
  • Cool tools on the right
  • Record the audio explanation of your solution
Review everything before you submit:

I was giddy exploring this app for the first time; seeing how well it could support students through the problem-solving process, seeing the functionality for feedback, and having a teacher dashboard. I know there's more to come to make this app even better, but think of the potential.

Teacher side: give students feedback at specific points of their recorded solution:

Hungry for more? Check out the CueThink teacher dashboard!


Wednesday, December 3, 2014

LARGE Whiteboards: GET 'EM!

This post is simply a way for me to quickly document/share a few ideas on large whiteboards.

I went to Home Depot and did the following:
  • Found the large whiteboard sheets: 
  • Had someone make two cuts:
  • I get one large whiteboard and two smaller boards:
  • Took home and sanded the corners to get rounded edges:

My classroom desks are in groups of three or four, depending on my furniture, space and mood. Besides using these boards for 3-Act Tasks, here are my favorite everyday activities:
  • Placemat:
Students are given a question to work on. Each student carves out a section on their whiteboard to solve on their own first. As you can see, there's an open space in the middle.
Once students are done with their individual work, they discuss what their group answer should be and write it in the middle section. This really allows students to compare their work with their peers and give each other support, especially for those who might be stuck or need a nudge. Great everyday use and for review activities like Race Car Math. 
  • Brain Dump
Brain dump: Project something and have the students write down everything they know about it in their section. Then they compare and contrast as a group before sharing whole group. You could also do a Notice/Wonder (a la The Math Forum).

Put the timer on and ask students to write as many ways as possible to get to -100 or whatever you fancy. GO!

The Home Depot boards can be a little weighty. If you have the budget, I’d recommend you first look into the large whiteboards from They weigh less, have a slightly better writing surface, have rounded corners, and have a carrying handle for kids to easily carry around the classroom. You can get a set of 10 for a little over $100. Top-notch whiteboards. 

I use cut-up dark t-shirts and socks as erasers. There are plenty more things you can do with whiteboards and I've documented some of them in a few blog posts. Probably the best investment I've made as a teacher. At teacher trainings, workshops, and conferences, I'm practically begging teachers to get these whiteboards in their classrooms.  

Now, I have a blog post in which teachers can refer to. But, here are more awesome additional uses of whiteboards. Nathan Kraft outfitted his entire room with whiteboards, inspired by Alex Overwijk. Don't miss Frank Noschese pioneering all this whiteboard magic. You can see Fawn Nguyen using these on a regular basis too.
Huge style points for them all!


Friday, November 28, 2014

Video Error Analysis (Anti-Khan style)

Something I tweeted this week:
Crystal (colleague) and Lynda (fellow) wanted to know more about this. So here's the story:

The previous week, I met with one of my high school fellows who teaches Algebra to freshman. As with all my fellows, it's been an extreme pleasure to work with her because she's hungry for ideas and will take suggestions and run with them. It was so cool to walk into her class this past week and see her running with an idea, again.

She had already taught her students ways to solve linear systems; graphically, substitution, elimination, etc. On this day, she prepared six short videos of her solving linear systems and linear inequalities using Educreations on her iPad. Students were to watch the videos and do error analysis, reporting the following on their handout:
  1. Identify the mistake(s) for each question.
  2. Explain what should have been done.
  3. Fix the mistake and complete the question correctly.
Each video was between 60 and 90 seconds in length. We both discussed what we thought would be most effective for her students and short videos was a must. Have you ever noticed how the majority of Khan videos can be extremely lengthy? Sal Khan usually talks (and repeats himself) while writing things on his digital blackboard. To me, that's a waste of someone's time. It's like you watching me type this blog post while I reread every sentence two or three times, stalling so I can finish typing. Another thing I can't stomach in Khan videos is when he fumbles around searching for colors to write with. Lastly, I find it unfortunate that the videos rarely suggest the viewer to pause and consider what's happening. Here's an example. Sorry, here's a 9+ minute example:

I suggested my fellow pause the recordings often and write the equations "offscreen" when not recording. Then, press record again when she's ready to talk and/or write something important on her screen. She also took advantage of this offscreen time to select different colors in order to emphasize different equations, steps, lines, or shading (linear inequalities).
*See the video structure below with suggested notes and style points.

It took my fellow one prep period on a minimum day to create six videos, a supplemental handout, upload the videos to Educreations, and create hyperlinks on her Haiku page for students to access all the videos. That's super impressive. Talk about an activity with meaningful and HUGE return from an efficient investment in her prep time.

When debriefing with my fellow after class, she was completely ecstatic.
I asked her, "What elements made this awesome?"
She replied:
  • it was video and new
  • they liked figuring out someone else's mistake
  • the videos were short
  • students could pause, rewind, and start the video over
  • using Desmos to show a graph of the original equations at the end (comparison)
  • gave students the idea to use Desmos to check their work/answer
  • self-pacing
  • very little hand-raising or students drowning
  • the videos were easy to make
  • she passed out the handout and said "go" instead of modeling
  • the handout had a simple structure 
  • the students did most of work, not the teacher
I love this last element the most. The two of us talked about this specific element the previous week. Now she experienced it first-hand and it's an amazing feeling. As an observer, it was awesome to see the students working hard on a meaningful task and helping each other out so it allows her, the teacher, opportunities to calmly circulate and provide support where necessary.

Student engagement and interest were high. Discussions were plenty and authentic. Students were thriving using thinking skills in the "Analyzing" category of Bloom's Taxonomy or Strategic Thinking category of Webb's Depth of Knowledge. Here's a tip I suggested when I noticed some kids plowing through a video and hadn't caught the mistake: pause and make predictions. The video structure will explain pausing and predicting more.

Video Structure:
Part 1: She takes about 8 seconds to explain her plan
*All of this was written on the screen prior to her pressing record. Style points.

Part 2: Multiply the top equation by (-5) in order to eliminate the x-terms

*Here's where we need to ask students to pause and predict what the top equation will look like after being multiplied by (-5).
  • Model this for students.
  • Build "pause and predict" prompts into the video. 
  • Circulate the room and ask students to pause and predict.
SO valuable. Don't skip "pause and predict".

Part 3: Write the new equations "offscreen". Don't record yourself writing these equations.
*Notice the new equation is written in red inkStyle points!
**Pause and predict what it will look like when combining the equations
***Catch the mistake?

Part 4: Combine the two equations.
*Another great use of "offscreen" writing.

Part 5: Find the value of y.

Part 6: Substitute the value of y into one of the original equations.
*Yet, another use of "offscreen" writing here.

Part 7: Solve for x this time.
*Ask your students to check for reasonableness.
**Find an alternate way to validate (or invalidate) their conclusion.

Part 8: Insert a screenshot of the system graphed in Desmos.
*Mind grenade: the graph doesn't match the algebraic procedure.
**HUGE style points by inserting a visual representation of the correct answer.

For those of you who don't have 1:1 devices in your schools, no sweat. I still recommend you make a video of some sort. Borrow an iPad from someone. Create an Educreations video for error analysis. Use the tips and techniques mentioned here. Your videos should be less than 90 seconds. Play it to your class. Pause the video to have students make predictions and/or discuss possible errors. I guarantee you, good things will happen.

Style points,

Tuesday, November 11, 2014

#PuzzleMath ideas

Tonight, my son wanted me to work with him on his new puzzle.

I don't know your strategy for doing puzzles, but I find all the corners first and then start putting the border together before I start working on the inside. Look at that box again. Would you be able to determine the dimensions (in puzzle pieces) of this puzzle by knowing the total number of pieces?

That was my first question:
A) If you know the total number of puzzle pieces, could you think of the all the possible dimensions (in puzzle pieces) of the puzzle?

This puzzle will either be a 1x35 or 5x7.

Then came the next question:
B) Estimate the actual dimensions (in puzzle pieces) given the picture on the box?

I'm going to go with 5x7 because five and seven are the only factors of 35 that would reasonably make the rectangular picture on the front of the box. The puzzle should be 5 pieces high and 7 pieces across from left to right.

With a box of 35 pieces, these questions aren't too ridiculously challenging. However, I know there are crazier puzzles out there in the world; puzzle with 500, 750, 1000 pieces, etc. That's where I called on Twitter to help out. Like a champ, the #MTBoS came through and hopefully will continue to come through with #puzzlemath.

Below are some of the tweets I received followed by additional math questions I'm curious about.

Additional Questions:
C) If you think you know the dimensions, could you determine:
  • The number of corner pieces
  • The number of border (non-corner) pieces
  • The number of inside pieces
If so, could you write a rule for any of these?

D) Knowing these quantities, say you randomly choose a puzzle piece, what are the chances it's:
  • A corner piece
  • A border (non-corner piece)
  • An inside piece
  • The exact center (if possible) piece
Please add to the collection of puzzles and questions by tweeting with the hashtag #puzzlemath.


Roofs Are Expensive!

Today is Veteran's Day. If you personally know a veteran, say "thank you" to them somehow: call, email, text, or in person. If you don't know a veteran, then ask a friend if they know a veteran and if they do, ask them to say "thank you" on your behalf.

Because today is Veteran's day, my district isn't in service today. Therefore, I was able to sleep in a few minutes longer today. I woke up to the sound of this pitter-pattering on the roof of our house. Not five minutes later, my 4.5 year-old son walks into the room and says he hears something that woke him up. I wonder what? Ha.

He climbs in bed with me and I ask him if he knows what the sound is. I proceed to tell him the sounds he hears are birds walking around on the roof hitting the roof with their beaks. When we moved into our house, there was a fake owl tied to our roof. Supposedly it keeps birds away. Not too sure it's all that effective, but we keep it up to have an occasional laugh.

My son thinks that the birds might start to ruin the roof and that we'll have to replace it.
Son: That will probably cost more than $100 to fix.
Me: How much more?
Son: Probably like one-hundred, one thousand dollars.
If you read my Pumpkin Seeds post, you know that his vocabulary includes a thousand now which is the biggest number he currently "knows". I use "knows" very loosely.
Me: Oh, I see. Well, which number is bigger? One hundred or one thousand?
Son: One thousand!
Me: Right. So we say the bigger number first, like this, "One thousand, one hundred."
Son (whispering to himself): One thousand. One hundred.
Me: That's a lot of money.
Son: Maybe one hundred twenty?
Me: Oh, so that's smaller than one thousand, one hundred.
Me: How do you know?
Son: Well, we have a big roof. We would need a lot of wood. We'd have to go to Home Depot and get all the things. 
Me: So we can buy all the things from Home Depot?
Son: Yes.
Me: And then would we put the roof on by ourselves or have some worker-men do it for us.
Son: You and I can do it Dad.
It dawns on me. Geez, I hope it's not $10,000. That's a lot of money. At the same time, I'm glad my son doesn't know the concept/magnitude of "A million" yet. Regardless, I have no idea what a new roof might cost, let alone how to put a new roof on. But maybe I'll save a lot of money on the labor because I have a 4.5 year-old son extremely willing to climb on top of our house and help install a new roof.


P.S. I'm enjoying these conversations and posting about them.
Today felt like Mathematical Practice 4 with my son.

Monday, November 10, 2014

An Amusing Context for Zero

From the mouths of babes:

Tonight, my 4.5 year old son was getting ready for bed. Getting ready for bed means he needs to shower. And as any parent can relate, there's the usual banter of "get your jammies out" to "let's brush your teeth." Tonight went in this direction:
Me: C'mon. Let's get ready for your shower. I have three clothes on still.
He comes around the corner.
Son: Dad, I have zero clothes on still. 
Yes. Yes, he did. He was, indeed, ready for shower. Bahahahaha.

Like I said, from the mouths of babes: an amusing context for zero.


Saturday, November 1, 2014

Pumpkin Seeds

For Halloween, we gutted the larger pumpkin from Day 197 for two reasons:
1) To carve it and
2) To roast the seeds
*Little did I know this pumpkin would produce many number sense opportunities beyond Day 197's weight estimate.

My 4.5 year-old son helped gut the pumpkin with me. We gathered as many seeds as possible and set them aside for the roasting process. The recipe I use can be found here. Before mixing the seeds in olive oil and seasonings, I lowered the pan down to my son and asked how many seeds he thought there were. [How many do you think there are?]
Me: How many seeds do you think there are?
Son: Well, ...[thinking for a few seconds]... there's definitely more than a hundred.
Me: How do you know it's more than a hundred?
Son: It just looks like more than a hundred.
Me: Make me a pile of seeds that would be about 100. 
He takes his hands and makes a pile toward the bottom of the pan. I can't contain my excitement to see what he has done.

His pile actually makes sense to me and definitely looks close to 100, give or take. Now that we've made a pile of his "one hundred" seeds. I ask:
Me: How many piles of 100 seeds do you think we can get?
I see he's a little confused by my question, so I ask it differently.
Me: How many piles do you think we could make where each pile has 100 seeds?
He starts to think, but by this time, my almost two year-old daughter sees the pan of seeds is now at her level, so she comes running over and wants in on the action of moving seeds. I thought our conversation was derailed as I brought the pan back up to counter height. But my son keeps it going. He didn't necessarily attempt to answer my question (which is fine by me). He took it in a different, pleasantly unexpected direction:
Son: What if we could get 10 piles?
Me: Do you mean ten piles of one hundred?
Son: Yes!
Me: Are you asking me how many seeds we would have if we had ten piles of 100?
Son: Yes.
This blew me away. Where'd this come from?
Me: Well, ten piles of one hundred seeds would mean we have a thousand seeds.
Son: A thousand??!!
Me: Yes.
Son: What if we had twenty?
Me: Twenty piles of 100 seeds?
Son: Yes.
Me: Well, what two numbers make twenty? Ten and...
Son: Ten!
Me: Right. So if ten piles make a thousand and another ten piles make a thousand, we would now have two th...
Son: ...ousand! 
Me: Right.
Son: What's 100 piles? 
Me: You mean, what's one hundred piles of one hundred? 
Son: Yea.
Me: That would be ten thousand.
My wife chimes in.
Wife: No. 
Me: One hundred piles of one hundred? Ten thousand.
Wife: Wait. You're right.
And our kids are now off in the other room playing and getting ready for going outside and looking at Halloween decorations before trick or treating. So many cool things happened:
  1. I love how we pursued my son's questions and not mine. 
  2. I love that he was fascinated by the word "thousand" even if it didn't make sense.
    1. Because he thinks a "hundred" is big.
  3. I love how we started with actual seeds (concrete) and went way more abstract.
  4. I love how my wife had the best estimate in the house [375 seeds].
  5. I love how the "pumpkin seeds" estimation challenge is just large enough so you can't accurately eyeball the amount and it's just small enough where it wouldn't take me an absurd amount of time to accurately count.
My wife and son watched the video answer this morning. My wife's response:
This is perfect for my [1st grade] students!

We paused the video when we saw ten groups of ten and paused it again when I made a larger pile of one hundred seeds. He struggled with making sense of final amount. 
Me: How would you say that number?
Son: Forty-eight eight? 
Me: How many piles of one hundred are there? 
Son: Four.
Me: So we say "four hundred" and let's count the piles of ten together. Ten, twenty,..
Together: thirty, forty, fifty, sixty, seventy, eighty,  
Me: And. Wait. There are only eight in this last group. So we say eighty-eight. Four hundred eighty eight. Say that.
Son: Four hundred eighty eight.
Me: Great. Let's go make breakfast.
Here's the recipe again and some pictures of the process.
Ready for the oven.
Roasted and ready to eat!

P.S. Thanks to Christopher Danielson and all he does at #tmwyk!

Thursday, October 23, 2014

Learning-Centered Classrooms

What are elements of our classrooms that are student-centered?
What are elements of our classrooms that are teacher-centered?

  • Instruction
  • Environment
  • Activities
  • Assessments
  • Collaboration
  • Error analysis
  • Summaries
  • Creation
  • Other

Pick any one of the above elements or create your own and go through the images below.
*Note how the size of the circles change.

  • Which would best describe your current status?
  • Would you want that to shift? If so, why? How?
  • What would that look like when making a shift?
  • Can student-centered elements coexist with teacher-centered?
  • What would coexistence look like?

Please share. I will share soon.


Tuesday, October 21, 2014

CMC 2014 Pregame

This weekend is CMC South. I'm looking forward to filling up my schedule book with sessions from your local SoCal MathTwitterBlogSphere agents. My schedule.

In addition, I'll be presenting two sessions at both CMC South and North:

CMC South:
  • Friday at 1:30 p.m., Primrose B
    • Modeling Mathematics Using Problem-Solving Tasks
      • I'll debut a new 3-Act task
  • Saturday at 8:30 a.m., Catalina (Renaissance Hotel) 
    • Get Students Arguing in Math Class with Number Sense Activities
      • Audience arguing (participation) is a must here. 

CMC North (Saturday 12/6/2014):
  • 8:00 a.m. Get Students to Argue Through Number Sense Activities
  • 3:30 p.m. Modeling Mathematics Using Problem-Solving Tasks


Monday, October 6, 2014

New Glasses

I have a new set of glasses. With my new role as a Math and Digital Learning Coach in my district, I get to spend a lot of time in the classroom with teachers and students. Let me explain the set of glasses.

When my son was born, I received a new set of glasses. When my daughter was born, I received an additional new set of glasses. As a new parent, I saw the world in a completely different way than I had before being a parent. The oversimplification for me was the stuff that I used to think was important before being a parent, instantly (and gladly) received a huge shift the second I started caring for and loving another human being that I called my son and daughter. The perspective from behind my parent glasses continues to change and update with time as my children mature. It's AMAZING! If you're a parent, regardless if your child is adopted or biological, you know what I mean. If you're not a parent, you simply have no idea. No offense. Trust me, I had no idea either. And if you're a parent and don't know what I mean, then please check yourself. But chances are good that if you fall into this latter category, you probably aren't reading this blog to begin with.  I'd imagine anyone who does read this blog is in education, and why would you be in education if you don't care about children, yours or someone else's? This could possibly be the harshest thing I've ever said on this blog. However, I feel that if you're in education, it's your duty and responsibility to care about children. I digress. Back to the new set of glasses.

We obtain new sets of glasses throughout our life. By the way, if you haven't figured out by now, anytime I refer to glasses, it's in the figurative sense: how you perceive the world around you through the lens created by your position, role, and/or relation in life. My new set of glasses as a Math and Digital Learning Coach allow me to be a student again. Some might think I should see the role of a teacher differently. This is true, but I think that's putting the cart before the horse here. I get to be a student again. And by being a student again, it helps me refocus as a teacher.

With my new set of glasses, I get to feel like a student again. Which is humbling and powerful at the same time. It has allowed me to focus on the student perspective of learning, exploring, and receiving knowledge as opposed to the teacher perspective of preparing activities, assessing, and delivering knowledge. Think how one role greatly affects the other.

I remember when I first started subbing and was helping students with math questions. At the time, I hadn't done math in a few years, so I was rusty since it wasn't fresh in my mind. Therefore, I was literally working alongside the students trying to figure out how to solve these questions. I was trying to tap into anything I could remember, which usually meant I had to derive some solution or maybe even take the long route to the correct answer. It was exhausting, thrilling, honest, raw, and exhilarating all at the same time. That moment in time flooded my head tonight on my drive home. That was such an awesome feeling, because I felt like a student of math, exploring and persevering. It made me want to pursue teaching. But then I got my teacher glasses and my student glasses went out of focus at times. It wasn't the glasses' fault. It was me. And I'll be the first to apologize for some lousy teaching moments because I lost focus. I wish I had a mulligan for one year in particular: 2012-2013. I tried a lot of new instructional/grading/facilitation/pedagogical strategies and shifts that were not necessarily well received. But let me tell you, I not only learned what to do that year. I learned what NOT to do and I am eternally grateful for the students and parents who (indirectly) made me strive to improve and refocus on the student perspective.

The point of this post was for me to reflect on the power of having these new (or rediscovered) glasses. I'm seeing that students need less and less from the teacher so that they are given the time and room for more ownership of their learning. That's an awfully general statement so I will explain. I believe that students benefit more when the teacher keeps the lesson introduction, question, or objective simple and succinct. The students respond better when the teacher is actively listening to them, not for the correct answer as Max Ray would say. I noticed that teachers are able to better listen to students when they ask interested questions like, "Can you tell me more about what you did here?" or "I didn't get all of that, can you explain it to me again?" or give simple commands like, "Walk me through what you did here." or "I noticed you did ____, please explain that."

As the student, I'd want you to ask me questions that show me you care about what I think and not judge me because I'm wrong and you feel you need to fix me (or my math work). With my glasses, I see students are drawn toward visual representations of mathematical situations: rectangles, patterns, estimations, soda, water bottles, etc. instead of just pure numbers (pure math). With my glasses, I noticed that students appreciate someone interested in their work. I noticed that students like to share with each other, especially when they know how to do something correctly. I noticed that students like to hear a voice other than the teacher.

I was able to notice many of these while maturing as a teacher, but for some reason they are more profound now. I hope these are some examples of how I see the teacher doing less and the students doing more. When I had my teacher glasses on and lost focus of the students' glasses, there were times when I (mistakenly) thought that I had to put on a show for my students or needed to run around like a crazy guy checking every paper or student whiteboard. Have you ever caught yourself saying something like, "My hair could be on fire, and they wouldn't care." or "I'm up there doing a song and dance, and it doesn't matter."? I know I've said something like that. That's exactly my point. I was doing too much, and the students were doing too little. That's exhausting.

If you've made it this far, thanks. I don't plan on rambling/ranting like this in the future. I'm simply happy to have rediscovered those student glasses. Throughout the year, I'm sure I'll continue to sharpen the focus on both my student and teacher glasses. My takeaway is this: by regaining focus on the student perspective of education, I'm able to improve my focus on the teacher perspective so the teacher is doing less in order to create more opportunities for the students in the classroom.


Monday, September 22, 2014

Number Sense Conversations

I've put the elevator speeches to rest. Today's two minute speech went well... I think. As one event concludes, I'm excited to resume my ongoing thoughts about number sense and students.

Working with teachers and students, I can't help but be inundated with thoughts about things I miss, look forward to, and will be challenged with this year in and out of the classroom. However, there's one thing I crave more than anything else, and that's working with students, which usually entails having number sense conversations with students.

Today, I had rich number sense conversations with students in Math 7, Math 8, and high school Algebra classes. As I sit here and put the finishing touches on the slides for my upcoming conference workshop, Get Students to Argue in Class With Number Sense Activities, I can't put to words how valuable it is to allow students to talk about math in math class. That's an oversimplification, but we seriously need to provide our students with opportunities to talk to each other, even argue with each other. Mathematical Practice 3:
Construct viable arguments and critique the reasoning of others.
Steve Leinwand sums it up best:
These nine words may be the most important words in the entire Common Core effort. 
Last December at CMC North, I was honored to give an Ignite talk about something I'm passionate about: number sense and student conversations. It's titled: Number Sense: I Don't Like This Game Anymore.

Students are hungry for number sense conversations in math class. I really do believe. If you don't believe me, just put up this picture in your class and ask your students, "How long would it take to use all of that?" Then ask them to convince you of their conclusion.

As October quickly approaches, I look forward to seeing you at an upcoming conference this school year. In the meantime, I hope to post more about number sense.

Number Sense,

Sunday, September 21, 2014

Common Core Elevator Speech - Day 7

Day 1
Day 2
Day 3
Day 4
Day 5
Day 6

This is my final elevator speech in this series. My 120-second elevator speech for tomorrow is to focus on rigor. Yes, that's difficult to capture in 120 seconds. However, this is what I'll be going with.

I love how teachers are hungry for modeling with mathematics. That in itself, can be one of the most vital elements to rigor in mathematics.


Saturday, September 20, 2014

Common Core Elevator Speech - Day 6

Day 1
Day 2
Day 3
Day 4
Day 5

Did you check out Steve's elevator speech on Day 5? Pretty awesome, right? Here is the second one he emailed me.

"Appealing to an audience that recognizes school math isn't working well enough."
Regardless of what you may think of the Common Core, you must recognize that school mathematics hasn’t been working for far too many students.  You’ve probably heard that the K–12 mathematics program in the United States has been aptly characterized in many rather uncomplimentary ways: underperforming, incoherent, fragmented, poorly aligned, unteachable, unfair, narrow in focus, skill-based, and, of course, “a mile wide and an inch deep.”  Most teachers are well aware that there have been far too many objectives for each grade or course, few of them rigorous or conceptually oriented, and too many of them misplaced as we prematurely ram far too much computation down too many throats. It’s not a pretty picture and helps to explain why so many teachers and students have been set up to fail and why we’ve created the need for much of the intervention that test results seem to require.
These are realities that the Common Core has been designed to fix. How? First, the new standards are common. No longer will publishers cater to a few large states and stuff their books with the union of fifty sets of demands. No longer will our assessments be developed by the lowest bidder and overwhelmingly comprised of low-level, multiple-choice items.
Instead, the prospects of a Common Core set of standards are for shorter, more web-based, better-focused instructional materials and for computer-adaptive, computer-delivered, and instantaneously-scorable constructed response-item assessments.  Second, ignore the misrepresentations and take heart in the fact that the Common Core standards are coherent. These standards replace the vagueness of strands (number, measurement, geometry, statistics, and algebra) with domains, clusters, and well-conceived grade-to-grade progressions of standards. Moreover, they are fair. Many procedures that we have come to teach at grade x, have been moved to grade x + 1, giving us all a chance to build prerequisite knowledge and slow down what has become a drag race through the curriculum. And, lastly, they are teachable. There are only about thirty standards—of varying sizes and depth—at each grade level, resulting in a far more manageable teaching load than the forty to fifty objectives per year that many of us now face.  If you care about your children, if you care about readiness for citizenship and the workplace, and if you care about our future leaders making informed decisions, you should be fighting for, not against, the Common Core.
~ Steve Leinwand

Again, I want to thank Steve for taking the time to prepare two awesome elevator speeches. Hopefully, they've inspired you as much as they've inspired me. Maybe you can use parts in your own elevator speech when the time presents itself. It's not too late to add your own in the comments. Tomorrow, I'll post the last and final elevator speech, which happens to be my two minute speech for my district. 

Common Care,

Friday, September 19, 2014

Common Core Elevator Speech - Day 5

Day 1
Day 2
Day 3
Day 4

I have three more days of elevator speeches to share. Now would be a good time to say why I initiated this whole elevator speech series. I was asked by my district to give a 90 second presentation on rigorous mathematics standards. I will be giving this 90 second presentation on Monday at our district's State of the Schools breakfast where many community members, parents, board members, teachers, and administrators will be present. You know, all the stakeholders. In preparing those 90 seconds, I needed to push myself to come up with elevator speeches related to Common Core math standards and rigor. So Day 7 will be my 90 second elevator speech from the State of the Schools.

For Day 5 and Day 6, I'm honored to share two elevator speeches from Steve Leinwand. It was so cool to see an email from Steve in my Inbox, with him saying, "OK - challenge accepted!"

If you've followed my blog, you know I have great admiration for Steve and have been inspired by him numerous times. It won't surprise you that I thoroughly enjoy (and support) his first speech.

"Appealing to an audience that wants more for their children."
It’s only one of eight Common Core Standards for Mathematical Practice, but we can change schools and change lives if we truly implement Mathematical Practice 3:  “Construct viable arguments and critique the reasoning of others.”  In many ways, these nine words may be the most important words in the entire Common Core effort.  We can’t expect students to construct viable arguments unless we ask them “why?” and “how do you know?” and “can you convince us?”  When we ask such questions we are laying the foundation for the reasoning and justifying that represent the thinking that schools need to develop in all students.  Similarly, we can’t expect students to critique the reasoning of others unless we create classrooms where student thinking is valued and students contribute to their own learning within communities of learners.  Moreover, this isn’t just mathematics, but what needs to happen in English language arts, social studies and science as well. So when one cuts through all of the misrepresentations and politics that surround the Common Core, these powerful nine words transcend our differences and capture what every parent and every citizen should be demanding from their schools and for their children.
~Steve Leinwand 

Thank you Steve for sharing your wisdom and fervor. I look forward to sharing your next elevator speech on Day 6.


[UPDATE]: Check out the audio/visual of Steve's elevator speech.

Thursday, September 11, 2014

Common Core Elevator Speech - Day 4

Day 1
Day 2
Day 3

When I started this idea of preparing an elevator speech about the Common Core, I figured I'd get as far as I can on my own. I wanted to stretch myself and avoid tapping into resources or my Jedi masters. It's day 4 and I find myself at that point where I need a pick-me-up. Who better to do that than Steve Leinwand and his super math gang of leaders at NCSM? All 2014 NCSM attendees received the following framework:
It's TIME: Themes and Imperatives for Mathematics Education. 

I figured I would snag a few lines from the section titled Support an Understanding of the Breadth and Depth of Mathematics Content Knowledge (found on pages 20-21). Today's elevator speech is is from the pros (all 15 writers):
The CCSSM promotes teaching few concepts, but teaching them in more depth, with deeper understanding as the goal. However, teachers must have a deep understanding of the content themselves to teach for deeper understanding.
Mathematics involves more than just recalling facts and performing routine procedures. Mathematics needs to be understood as an integrated collection of knowledge and skills, not as a series of discrete procedures. Mathematics must also be understood as connected to other disciplines and to the world in which we live. A technology- and information-based society requires citizens to be able to think, reason, and analyze. Knowing mathematics means being able to adapt and apply mathematical ideas to new situations and to a variety of problems.
You can find this on page 21. The framework is a quick read at 58 pages and appendices full of strategies and resources. Get your own copy, you can't have mine.

It's TIME,

Wednesday, September 10, 2014

Common Core Elevator Speech - Day 3

Day 1
Day 2

I had a break between events this afternoon, so I stopped at In-N-Out for an iced tea and a chance to hang out for a few minutes. If you've been to a recent training or presentation of mine, I briefly share my admiration for the In-N-Out business model. Although Barry Schwartz doesn't talk about In-N-Out in his TED talk, The Paradox of Choice, he tells a parallel story extremely well.

A few notes from this afternoon:

Today's elevator speech isn't one I'd consider using, but something to chew on:
I enjoy In-N-Out Burger because of the experience, convenience, service, affordability, and great taste. When I think of the experience at a deeper level, every detail is important: the ingredients are fresh, the service is friendly and efficient, and the menu is simple yet customizable. Common Core and the 8 Math practices can be a rich experience that encapsulates critical thinking, conceptual understanding, and applied math. When you decompose Common Core, every part is important because both standards and practices demand our teachers and students to explore concepts in depth, obtain procedural fluency, and apply said skills to real-world situations using mathematical modeling.

Animal style,

Tuesday, September 9, 2014

Common Core Elevator Speech - Day 2

Common Core Elevator from Day 1.

Today, I'm going to take a different direction. Enter the elevator and press your floor number. Here we go:

I believe the Common Core standards are a tool for both students and teachers to explore problem-solving and increase mathematical conceptual understanding. Picture the first cell phone you saw or owned as a tool used to communicate. Compare it to any of today's cell (smart) phones and how the tool has evolved and improved. As a tool, the Common Core standards will help students evolve to be better, more robust math students in order to think critically and communicate.

Next floor,

Monday, September 8, 2014

Common Core Elevator Speech - Day 1

For the next week, I will challenge myself (and you) to work on an elevator speech each day about Common Core Math. I will try to be as fluid as possible in my thinking as if I were describing Common Core to a complete stranger as we rode an elevator together. And with that, here's today's elevator speech:
For me, Common Core is a tool to help students see how the world around us can be explained using critical thinking and mathematical properties. My favorite part of Common Core are the 8 Standards for Mathematical Practice. No matter what grade level, the practices emphasize that both teachers and students are problem solvers and how important it is to understand why mathematical properties and procedures exist, and not just the answer. I get to see my students thinking and focusing on finding solutions through hard work and collaboration instead of me just standing up at the front of the room, telling them a procedure they will most likely forget in a day or two. I get to see students be creative in their mathematical thinking and I help guide them when they need teacher support.
Come along for the ride and share your elevator speech in the comments. Take a minute or two to compose an elevator speech. It's a work in progress...

Going up,

[Update] More days:
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7

Monday, September 1, 2014


The first day of school is this coming Wednesday. I've never been two days away from the start of school and done so little preparation. It's weird. It's really weird. Here's why:

I won't be:
  • greeting students at my door
  • having students estimate my height
  • having students estimate the total class' height
  • passing out papers with school/class procedures
  • setting up grade books
  • making seating charts
  • hanging up stuff in my room
  • preparing for back to school night
  • preparing homework, notes, photocopies, etc.
  • sharing with my students the math I saw during the summer
Admittedly, I won't terribly miss items four through nine. However, the first three and the last always hold a special place in my math heart.

I'll be one of about fifteen Digital Learning Coaches (DLC) in my district this year. I'll be supporting 8-10 middle school math teachers who volunteered to be a DLC Fellow. Together, we'll be finding ways to integrate technology in their classrooms to meet the needs of their students while providing powerful learning experiences. Every time I look at technology or think about implementing some program, application, or digital tool, I look to ask myself (and the teacher), "will this [digital tool] be a more effective and efficient way for student and teacher to learn mathematics, gather data, assess understanding, or communicate?"

I will be:
  • frequently in the classroom with students and teachers (thank goodness!)
  • listening to teacher needs, desires, and goals
  • building relationships with students and teachers
  • building number sense with students and teachers
  • having (mathematical or non-mathematical) conversations with students and teachers
  • developing/designing lessons
  • teaching (co-teaching or modeling), if necessary
  • sharing many of the wonderful resources from you (the MTBOS)

I know I will miss the classroom and having my own students. However, I look forward to designing lessons and testing them out on different students throughout the district.  I look forward to learning so many things from both the teachers and students. It'll be an extreme pleasure, honor, and learning experience for me to be working alongside so many different teachers and students.


Wednesday, August 6, 2014

People Circles

I'm lucky to flesh out some ideas with some great people at Encompass this week. Due to my recent fascination with circles, I had the chance to share an idea I've been wondering about for a few weeks now. I'm extremely curious where you would go with this idea and how you'd weigh in.

Say you have a room full of students or teachers (for a training).
You ask them to stand up and form a circle in the room.

You know how everyone immediately gets that awkward look on their face? The look where people are mentally calculating (or estimating) if there's enough room? Can we actually form something that looks like a circle? What if we can't form a circle, what do we do now? AGHHHHH!
Here's my idea: I'd want to know what size room you'd need to form a near-perfect circle with your students or teachers?

  • How would you facilitate this with students?
  • What questions would you ask?
  • What different question might you ask instead of the one I asked?
  • Can you even form a perfect circle?

I'll share some ideas next Monday or Tuesday, but I'm curious what you think first and appreciate any insight. GO!

People circles,