I Answer 3 Questions I Often Ask Others

During the 2017-18 school year, I've definitely made a a conscientious choice to limit my online interactions. Simply put, my children are receiving my time and energy and that is what's most important to me (and them of course). That said, I feel I have learned a great deal this year in my role as an instructional coach, but haven't taken the time to share with you all. Here is a brief summary framed around three questions I often ask teachers about a lesson or task they did with their students:
• what successes did you have?
• what challenges did you have?
• what advice would you give a teacher new to this [lesson/task]?

Regarding the 2017-18 school year so far, here are answers to my own questions:

(1) What successes have you had?
Listening.
This is my fourth year as an instructional coach and I'm laughing and shaking my head at how green I was during my first three years as an instructional coach (or instructional idiot). One of the skills I have come to realize is most important in education is listening. Take the time to listen. Don't listen with the intention to make a suggestion to fix someone's problem. Listen to them. Learn from them. Find out what's most important to them. Listen to learn. Listening allows you to make connections with that person. Ask open-questions that allow teachers to share. Listen. When you think they're done telling their stories, ask questions that dig deeper, allowing you to learn even more about that person, whether it's their personal story, their educational story, or their aspirational story.

Collect stories.
This comes from the "Art of Coaching" by Elana Aguilar. Our district's coaches group has been reading Elana's book throughout the year and most of her strategies always go back to collecting the stories of the people you support. At least that's my interpretation. And how do you collect stories? By asking questions and listening!

Let me give you specific examples without identifying any of the teachers I work with.
If I didn't take the time to collect stories by asking questions and listening, I might not have learned a teacher's story about getting into education late after being divorced and losing a child. I might not have learned about a teacher's hardship with divorce and living between two places while trying to do right by their child. I might have never learned that a teacher has a farm and rides their horse frequently. I might not have learned about a teacher who loves to go thrift-shopping. I might not have learned about a teacher who is new to teaching and their previous math teacher is a teacher I supported two years ago. I might not have learned about a teacher and their adopted children. I might not have learned about a teacher going through their second battle with breast cancer. I might not have learned about a teacher's love of the outdoors and traveling. Needless to say, these personal stories take the coaching relationship to a level I never would have imagined. The work we do as professionals stems from a better personal understanding of each other.

(2) What challenges have you had?
Vision and Systems
Imagine listening to two bands play live music. The first band sounds great. You might not know why, especially if you're not a musician. Here are some reasons why they might sound great. All the instruments are tuned and their volume seems to compliment each other. The musicians know when to start and stop the song. The singer has a good voice because they are in key. And there are way more reasons why a band might sound good to your ears.
On the other hand, the other band sounds awful. Again, you might not be able to put your finger on why the second band sounds awful, but I'll give you some potential reasons. One or more of the instruments is out of tune. One or more of the instruments' volume is obnoxiously too loud. Maybe the musicians don't have confidence in starting a song, the tempo is off, they miss a transition, play off notes, or the singer is out of key. Again, multiple reasons why a band might sound awful.

You don't have to be a musician to tell a good band apart from a bad band. The point is we recognize when something is off and when something is on. Let me explain why a band might be on or off: vision and systems.

Typically, a band that performs well, started with a vision (or goal). For example, a blues band wants to perform cover songs of their favorite artists. For them to accomplish what they envision (their goal), they need to put into place a system that will accomplish said vision. Their system might include, but not be limited to the following:
• create a set list
• schedule rehearsals
• be on time for rehearsals
• establish norms at rehearsals
• have tuned instruments
• listen to each other when rehearsing their songs
• identify parts of songs that need more refinement
• and the list can go on

If a band who wants to perform well has a vision and a system, they're more likely going to sound great when performing in front of a live audience. Often times, bands that sound exceptional put a ton of time, care, passion, and attention into their system. When bands sounds like garbage, they lack the system (and sometimes talent). During the last four years as an instructional coach, I've been part of both bands. Bands that have a clear vision and system and bands that lack a vision and system.

So what's my challenge? My challenge (moving forward) is getting frustrated when I'm part of an educational "band" that lacks vision and system, especially when the strengths and passions of students and teachers are not being utilized. I don't always know how to constructively voice my concerns or ask questions when the vision is unclear and a system is lacking? How do I use my strengths and passions to create and/or enhance a vision and system I am proud to be a member of? I have more questions than ideas here and will continue to look for guidance in this area because I get frustrated when I see great potential untapped.

However, it has been beneficial that I've been part of both educational "bands". The experiences have allowed me to appreciate the effectiveness of vision and system. My high school director is amazing and has great vision and systemic thinking. Having been part of the systems this person has created, I learned a great deal. I'm not done learning as I still have plenty to learn.

(3) What advice do I have for a teacher new to this?
Listen, collect stories, and be patient.
As I expressed above, the more I listened to the teachers I support with the intention to learn more about them and what's important to them, our work will be more meaningful and productive. For example, as an early instructional coach, I often identified what I thought the teacher needed. Nope, don't do that. With experience, I learned to listen to what was important to the teacher and I often verify it by paraphrasing it back to them to be sure.

Collecting stories simply means learn more about the people you interact with. Whether it's your students, your colleagues, your neighbors, or your mail carrier, everyone has a story that's worth knowing. Imagine how meaningful it is when you share your story with someone and they remember it next time you see them or are mindful of a tough situation you're going through. Listening and collecting stories of those we interact with is a gift we can frequently give them.

Being patient is a general statement that can translate to "it takes time". The longer I'm in education, the more I realize things take time. Just like a good performing band, it takes time. I can't appreciate where I am now if it weren't for the instructional coach (idiot) I was a few years ago. Now, I'm just less of an idiot. I'm grateful for the teachers I've supported because they've had patience with me and allowing me to grow as a coach. How unfair would it be to them if I didn't reciprocate that same token of professionalism? Therefore, anytime you would like to grow as a professional, parent, friend, neighbor, or person, be patient with others and be patient with yourself.

Peace,
957

Where's Andrew Been? I'll Tell You

Hi everyone,

I've been quiet lately, but there's been a lot happening.

Some upcoming opportunities:
I'm excited to be giving a two-day workshop here in California on October 6-7, 2017 through Grassroots Workshops.
This two-day workshop is near and dear to my heart because it's designed with math teachers in mind. The purpose of the workshop is to strengthen the teaching tools of those who attend so they can go back to their classrooms and:
  • help students strengthen their number sense
  • use student thinking to drive their math instruction
  • use problem-solving as a vehicle for conceptual understanding

I share more in the video below. I really hope you can make it. Bring a friend!
You can register by clicking here.

Grassroots Workshop Promo from Mr.Stadel on Vimeo.

Family (math) Fun:
This summer I've had a blast doing mathy things with my kids. Thanks to Christopher Danielson and John Stevens. Danielson shipped us out some really cool math boxes that included really cool books, puzzles, and wooden tiles for us to play with. Learn more about them here. John Stevens wrote an awesome book, Table Talk Math. Recently, my kids and I have had some fun and low-risk math-type conversation over these sweet placemats he recently made available. Check them out!

My new-ish role:
I'm starting my fourth year as an instructional coach in my district. We coaches will be expected to support teachers in all subject areas. Our work with teachers will be to focus on specific teaching goals and objectives of their choice while in conjunction with their site goal. It's a new challenge for me and I've already learned a great deal from my fellow coaches and the teachers I have worked with.

One part of my new role is to support a small cohort of teachers who are working with 9th grade students in an algebra enrichment type course. The purpose of the course is to provide students with the conceptual understanding and number sense necessary to transition successfully to a full year of Algebra in 10th grade. We've already explored Number Talks, Clothesline Math, and Which One Doesn't Belong. Visual Patterns is on the horizon and we are using a Standards-Based-Grading model with reassessments to provide ongoing support for student.

Maybe you have seen my Clothesline Integer Game. Leave it to the awesome math community to make it better. I recently had the pleasure of meeting up with Geoffrey Dean and he shared his adaptation of the game; students could play in small groups and try and get 5 In A Row. I'll ask him if I can share it on the page above. I took his adaptation and made a desmos version of it.
In the algebra enrichment course, we will also be trying out this desmos activity on multiplying integers using a number line.

My Master's:
I'm pursuing my Master's in Educational Technology.
Talk about adding even more to my workload. Ha!

That's maybe a fifth of what I've been up to lately... but who wants to read more? Ha!
Hope you are doing well and your year is off to a great start.

Role,
537

Polygraph Word Bank

Have you ever wanted your math students to get better at using math language?
Have you ever wanted your math students to be able to compare attributes of visual mathematics?
Desmos Polygraph activities supported through word banks is your jam!

Over the past three years as a Digital Learning Coach in my district, I've been able to see Polygraph used in a variety of ways. This post will share a few of the many things I've learned.

My first year, I supported a high school Algebra teacher. We debriefed after she ran the Parabolas Polygraph activity with students. She was a little bummed that students weren't using more of the academic language they had been learning. For example, minimum, maximum, x-intercepts, roots, vertex, etc. I offered the suggestion of providing students with a word bank, possibly carved out on a section of the whiteboard, with the words she wanted her students to use. She one-upped me and put them on a half sheet of paper and printed them out to give to her students next time she played polygraph. I'll revisit this technique in a few paragraphs.

My second year, I supported a Math 8 teacher. She was running the Lines Polygraph activity with her students. I looked at the dashboard while students were playing and many of the students were asking questions about the slope using either "uphill" or "downhill" as their descriptor. I asked the teacher about this. She said this is the way she taught it. I asked her about the mathematical association with uphill and downhill and she replied, positive and negative, respectively. I paused the class (before the pause feature existed, ha!) and drew two lines to represent the "uphill" and "downhill" slopes on the whiteboard. I told the class I noticed they have been using the terms uphill and downhill to describe these slopes. I went on to tell them, this is a great place to start, and now we're going to make your language even stronger by referring to uphill slopes as positive and downhill slopes as negative. For the remaining time, we're inviting you to use positive and negative.

I love this experience, because it validated the work the teacher did while raising the bar for the students to strengthen their mathematical vocabulary. I believe if you set the bar low for students, they'll often meet it with a high success rate. If you set the bar high for students, they'll work toward that high bar, often with a comparatively high success rate.

Back to the word bank.
My third year, I supported an Algebra teacher at our continuation high school. She ran the Parabolas Polygraph with her students and had a word bank up on the whiteboard. We debriefed and talked about making a half sheet of the words she would like students to use. Furthermore, let's make a Taboo list of words we want students to avoid using. She tried the Polygraph again, using the word bank handouts and noticed students were using the academic language a lot more than when the words were up on the whiteboard.

It's not enabling the students by providing them with a half-sheet of math terms you want them to practice and use. It's enabling if you're the one telling them what questions to ask their partner, or worse; you're typing in the questions for them. Providing students with the half-sheet, a physical token, places an emphasis on your invitation to students to practice and use specific math language associated with the concepts at hand.

I've learned a lot over the past 3 years, implementing both Desmos Activities and Polygraphs. I would say the use of a word bank handout is one of the most effective ways to get students practicing and using the math language you want them to use. Here are my current word banks (and Taboo lists) for Parabolas and Lines. You'll notice I intentionally left some blank spaces in the tables so students (and teachers) can add their own. I can't think of everything.

Consider the Low-Tech versions of Desmos Polygraph so students can practice using academic language more frequently without devices.

What words would you add to my word bank (and taboo) lists?

Bank,
948

BONUS feature:
You've heard of a swear jar, right?
When someone is trying to curtail their swearing and/or use of bad words, they'll set out a swear jar, placing an amount of money in the jar every time they use a bad word.
*Consider the idea of a VOCAB jar in your math class. (future blog post coming soon)

Low Tech Polygraph

Imagine classrooms full of math students without devices missing out on opportunities to play wonderful Desmos Polygraph activities. It's a miserable thought, right?

Unfortunately, classrooms like this exist. I've been extremely fortunate the past three years to work in a district where every secondary student is provided with a device and can enjoy playing (and learning from) Desmos Polygraph activities. What can we do for students and teachers who aren't 1:1 yet?

I've also been honored to provide professional development for math teachers in various districts across the country. They LOOOOOOVE playing (and learning about instructional uses of) Polygraph during the workshop. However, I often hear comments from teachers like:

• We're not 1-to-1 yet
• We're BYOD and many students just bring cell phones
• I have to book the computer lab because we're not 1:1

I also get questions like:

• When do you recommend we do Polygraph? We have limited time.
• This [Polygraph] is a great tool, what if students are absent?
• I love the idea of students playing Polygraph on more than one day, but how do I do that?

Here's my idea:

Provide students and teachers with a low-tech version of Polygraph. 

Here's the setup I've tried with teachers and the response has been fantastic.

1. Print out four different versions (A-B-C-D) of the sixteen Polygraph graphs
1. I've already made Lines and Parabolas
2. Make double-sided copies of {A-B} and {C-D}
1. Make enough {A-B} copies for half your class and {C-D} copies for the other half
3. Insert one copy into a plastic sleeve
4. Store in a highly accessible place in your classroom
5. Have some dry-erase markers nearby
6. Provide students with a word bank & taboo bank (follow-up post)

You can have students play Polygraph at anytime!. Imagine the possibilities. Imagine even MORE students being able to play Polygraph. Just remind students they can play any other letter besides their own letter. For example, Page C can play A, B, or D. 

Have a go and let me know!

Low-tech FTW,

1104

2016 #NCTMannual reflection: Purpose

There is a lot to process from NCTM 2016. Being a contributor for the Global Math Department this week, I decided to feature snippets on the blog here in order to kill two birds with one stone.

I found it useful to connect all the NCTM goodness with a theme: PURPOSE.

• Marilyn Burns (@mburnsmath)
Be purposeful about what we want our students to do. I loved this slide, connecting reading and math:

• Christopher Danielson (@Trianglemancsd):
Be purposeful with knowing the ability of students. Christopher said,
"Students can. We should let them."
This idea lends itself to students discovering properties in math. Often, when things get discovered in math, they are named after the discoverer. Why don't we do this more with students?"
Goods here.

• Elham Kazemi (@ekazemi):
Be purposeful with a school/department/grade having a shared vision of quality math instruction. Create a structure at your school to learn together. We went on to explore numberless word problems where the purpose is to help students make better sense of the context before applying the numbers. She shared this post by Brian Bushart.

• Carl Oliver (@carloliwitter):
Be purposeful with the space you provide students to explore mathematical ideas. Be purposeful with selecting the task.
Goods here.

• IGNITE talks:
Max Ray (@maxmathforum):
Be purposeful with the resources, tasks, activities, and ideas you pull from the internet. Be purposeful with the coherency in your teaching. Do the resources, tasks, activities, and ideas you pull from the internet add to the coherency of the mathematics you teach?

Jennifer Wilson (@jwilson828):
Be purposeful with the time you allow students to solve math. It's not like fast food, it's like slow food. Enjoy the math students can do when we make it a purpose to do #slowmath.

• ShadowCon16
Kaneka Turner (@KanekaTurner)
Be purposeful in making math a social experience by inviting others into this awesome experience. Kaneka shared the importance of being invited. Call to action: invite at least one person to be part of the math experience.

Robert Kaplinsky (@robertkaplinsky):
The purpose of empowering others through influence can have huge positive results. Robert shared a couple of personal parts on his life and how influential people throughout his life have helped shape who he is today. Call to action: your your power to influence and empower others.

Graham Fletcher (@gfletchy):
Be purposeful in knowing what/how you teach by understanding the standards. Be a better story-teller in your classroom by accurately knowing the standards. Call to action: find out more about a standard you teach.

• Brian Shay (@MrBrianShay):
Be purposeful with polynomials and probability. Brian had us working on using spinners and coins to add meaning to multiplying polynomials.
Goods here.

• Peg Smith:
Be purposeful in framing the task so it "invites everyone in." Furthermore, ask purposeful questions when working with students during problem-solving tasks. Lastly, it's critical for the teacher to explain the goals because it's hard to have a conversation if it's unclear what you're trying to accomplish.
***Let's invite Peg to the #MTBoS and Twitter.

• Andrew Stadel (@mr_stadel):
Be purposeful in the feedback we give students after they make mistakes. Thanks to Robert Berry and Dylan Wiliam, I shared with teachers the importance of providing feedback that benefits students and at the same time challenging them to take traditional feedback and rework it so it's better at moving the learning forward.

• Christina Tondevold (@BuildMathMinds):
Be purposeful in working toward the terminology in the standards, specifically "fluently" and "using strategies" in the K-5 standards. We looked at examples of subitizing, cardinality, and strategies like making ten, double-plus-one, finding fives. We need to be purposeful in students making sense of math for themselves.

• Jason Zimba
Be purposeful in decluttering what we teach, what we ask of students, and what we give to students. Something he got me thinking about: do we Math 8 teachers need to teach the "elimination" process when solving linear systems. Does the procedure support the conceptual understanding? and can we allow high school teachers to teach it while Math 8 teachers focus on graphing and substitution?

I hope to see you at NCTM 2017 in San Antonio.
Send in a speaker proposal here by May 1, 2016.

San Fransisco,
2016

CUE 2016 Takeaways

This past weekend was CUE 2016 and I only attended one day of the three conference days. Even though it was just one day, I was able to leave with some great takeaways.

Session 1:
Making the Hard Parts Easy: Teaching in 2016 and Beyond
by Matt Vaudrey
Great session. Matt is always a treat to watch in a presentation, and he continues to deliver solid, engaging, practical, and useful sessions. He had us up talking with each other, moving around the room, learning from others in the session. He modeled music cues by giving us a 60 seconds to discuss focused questions with a partner (different every time). The music stopped and we knew to stop our conversation so that Matt could allow two teachers the opportunity to share out their conversation.

The session was focused. I love when a presenter tells the attendees in the beginning what we will be doing and sticks to it. We focused on:

• Focus on what matters
• Mess with Curriculum
• Give students authority 

My biggest takeaways:

• Look into Kaizena to offer students voice feedback inside Google docs. 
• Assign less work to students... just one way to make grading easier.
• Quicken transitions in class with music cues by Matt Vaudrey (found here).
• Matt's slides can be found here.

Session 2:

Approach + Process + Delivery = Better PD

by JR Ginex-Orinion and Gerardo Martinez

Another great session. Both JR and Gerardo encouraged the attendees to focus on the "why" when preparing professional development for your site (teachers and admin). Essentially, define the purpose of your session because time is valuable for everyone. I also loved how they had us take a PD title we recently used and rewrite it so it includes the "why" (purpose). Great idea!

My biggest takeaways:

• Use empathy with teachers and administrators
• Value everyone's time!
• Start with the "why".
• Their goods can be found here.

Session 3:

Strengthen Student Understanding in Math and Science with Desmos Classroom

by Andrew Stadel and JR Ginex-Orinion

It was an extreme pleasure to prepare and present with JR. I love his enthusiasm and excitement for science, good PD, and Desmos. The focus of our session was simple: play, tips, and build. We allowed attendees to play two Desmos activities (one from JR and one from Cathy Yenca). We showcased the teacher dashboard for each activity and then we shared our activities so the attendees could see how the activities were built in order to explore the building part of desmos activities. We reassured the attendees that they don't need to necessarily build their own activities, because they could find one in the Desmos library or the Desmos Bank and adapt it for their needs. Thanks to all the teachers who came to our session. We hope it was helpful and you will let us know how teacher.desmos.com is transforming your classroom.

• Our session goods can be found here.
• Use Command F with the dashboard
• JR made two awesome polygraphs:
• Distance and Time
• Phases and Mixtures

Thanks JR. It was a blast to collaborate. I learned a lot.

Session 4:

More Than Data, Science Is a Story: Infuse Writing in Science

by Dan Bennett and JR Ginex-Orinion

I came in late to this session, but it didn't matter. It was easy to know where they were in their presentation.  Within minutes, we were working on the floor categorizing these cards with different colored shapes as a segue to the importance of the Periodic Table. It was a splendid activity. Both Dan and JR shared their experiences in their science classes. A big part of their class was using media to create mystery so students are asking questions. Similar to a 3 Act task. It was a wonderful way to end the conference.

My biggest takeaways:

• Create mystery with students. Use stories to explain the mystery
• Our brains, chemically, enjoy stories. Use them more often in class.
• Their goods can be found here.

Thank you to all the presenters who worked so hard to prepare great sessions. By reflecting on the highlights, it will allow me to incorporate many of the techniques, resources, and ideas with the teachers I support and the professional development I offer.

CUE,

933

Bonus:

I loved this on display at the Hard Rock Hotel. Sorry, I didn't grab the artist behind this gem. Look close, those are vinyl records. So cool!

Clothesline Cards Hit the Floor

A colleague and I stumbled upon an opportunity to strengthen number sense with students using a double clothesline. The video says it all:

 *For more fun with clothesline math, go to Chris Shore's designated site: clotheslinemath.com

Floor,
831

Clothesline

Dear Chris Shore,

Thanks for introducing Tustin Unified to Clothesline during your awesome professional development workshop!
You, Math Projects Journal, and Clothesline rock (David Lee Roth style)!

With all of my math heart,
Andrew

*Check out Chris' post on Clothesline (link coming soon).
**I highly recommend inviting Chris to your district/school for math workshops.

Where do I begin?
I used to have a number line in my old class. But it was static. All of the benchmark numbers were taped to the wall. I used it often, but not often enough.

Flash forward to Chris' workshop last week. He introduced Clothesline using this great quote from Tim McCaffrey:

"Clothesline is the master number sense maker." says @timsmccaffrey according to @MathProjects. Good call Tim! pic.twitter.com/bVvvJz7CtX

— Andrew Stadel (@mr_stadel) August 19, 2015

You better believe my ears perked up when I heard "master number sense maker". Check it out!

When I worked with teachers in Irvine today, my ice breaker was asking the teachers,

"How long does Dyson think it should take you to dry your hands with their machine?" 

I've never posted this picture online because it's my favorite ice breaker to do with teachers at conferences and workshops. However, I will use the context to illustrate how I introduced Clothesline to about 150 teachers, coaches, administrators today.

As teachers were discussing, I went around and asked

• two teachers for a guess that's too low (3 and 5 seconds)
• two teachers for a guess that's too high (30 and 40 seconds)
• four teachers for a guess that's just right

I used a big black marker to write the numbers on the red papers for the first four teachers with their "wrong" answers. I then had them place the red papers on the 25 feet long clothesline hanging on the side wall. I had the last four teachers write their "just right" guesses on the green slips. 

You'll notice the green slips might be hard to read from a distance. I did this on purpose so that we could get the visual effect (from a distance) of placing their green slips accurately on the clothesline using correct spacing (sorry, no pictures), based on where the red slips were originally placed. I reminded the teachers that this is a dynamic number line. You can move the numbers along the clothesline as you please. Please note that the teachers (in this case) were doing all the work, thinking, critiquing, and adjusting. In other words, students should be doing the same in my class as I help facilitate the conversations.

Throughout the rest of the day, I worked with teachers grades 7-12 during three breakout sessions. Therefore, I made a handful of cards for each breakout session to correspond to numbers or expressions relevant to them and their content area. Here's a sample:

I love when Chris used colored papers to focus on the numbers being placed (or in question). Notice the "benchmark" numbers are on white paper.

THE ROPE
The clothesline is 25 feet long. I think this is plenty long. I went to Home Depot and bought a 100 ft. clothesline. I made three cuts to make four lines of 25 feet. I used a flame to burn the ends of the rope so they stay in tact.

THE CLOTHESPINS
I noticed Chris used these to stack equivalent values together vertically. Brilliant. See above for examples that could stack.

THE NUMBERS (or expressions)
NCTM suggests using 3x5 cards, but then you have to use more clothespins, making the number line more static. Chris suggested using strips of paper. Using strips of paper allows the number line to be way more dynamic, allowing the numbers to slide along the clothesline or making it easy to place the numbers or take them off without the use of clothespins.

VARIABLES
Many teachers loved the idea of using variable expressions. Here's how I determined x for each group. I asked the three teachers in possession of the variable expressions to share how long they had been working in the district. For example, three teachers shared 12, 13, and 15 years. Therefore, 40 was the value of our variable, x.

FUTURE USE
Whenever I give a professional development workshop for teachers from now on, I will be using Clothesline. IT'S AWESOME! It is a master number sense maker. If I happen to be at your district or school doing PD, I'll bring a handful of clotheslines to raffle off (or give away). At the end of my last session today, it was awesome to have two excited calculus teachers be extremely thankful for receiving a clothesline. One walked away saying, "I'm going to use this Wednesday." Their first day of school! Calculus!

Last, but not least, test it out at home if you have the chance. My five-year-old son and I had fun this past weekend. He threw me a few surprises.

Clothesline 1
I just tossed up a few numbers on the clothesline for him to first get acquainted with the idea of numbers on the clothesline. "Move the pieces of paper so they make sense to you."

Clothesline 2
My son caught me off guard when he pursued something he was interested in. 1, 2, 3, 6.
"What?"

Clothesline 3
I wanted to see how my son did with spacing the numbers.
"Show me where four and five go."

I'd love to hear about your Clothesline experiences.
Check out Kristin Gray's great post from the other day. I love how much she anticipates student thinking in preparing for a successful Clothesline activity.

Clothesline,
930

Counting Dots

A teacher asked me about the Counting Dots activity I did in her teacher workshop I facilitated a couple weeks ago. I did the Counting Dots activity as a follow-up to Max Ray's Ignite talk: Why 2 > 4. I believe we teachers need to experience how valuable it is to listen to each other share strategies. If we're going to do it in our classrooms with students and value student thinking by listening to them, then we need to practice ourselves. You know? Build that muscle memory.

I was inspired by Dan Meyer's 2014 NCTM talk titled Video Games & Making Math More Like Things Students Like. You can find his specific reference to Counting Dots at the 30-minute mark. This link includes Dan's NCTM session and references to Ruth Parker's work, who according to Dan popularized Counting Dots.

I also made a video of the exact slides I used with teachers, a few extensions to counting dots, and a behind-the-scenes for anyone interested in making their own.

Questions? Let me know.

Dots,
1200

Featured comments:
Graham Fletcher shares an insightful article on Subitizing.

Dan Kearney shares more goodness from Steve Wyborney.

How Do You Like Your Bacon (Math Modeling)?

During the past few weeks I've had the pleasure to work with and learn from teachers in various places in the country, facilitating district/school workshop trainings as they prepare for their school year. Part of our time together was working on problem-solving tasks and breaking down Mathematical Practice 4: Model with Mathematics. At some point, either before lunch or in the afternoon, I tossed up this Estimation 180 challenge and asked:

How long to cook the bacon, starting with a cold skillet?

I love this estimation challenge because it showcases many parts of the modeling process, especially the two following parts:

• Identifying variables
• Formulating a model

Here's why. Teachers instantly start asking questions like:

• How do you like your bacon?
• Crispy, charcoal, or like beef jerky?
• What type of bacon is it?
• Turkey bacon or real bacon?
• Is it thick cut or the other stuff?
• Is the bacon room temperature, cold, or frozen?
• Is it cooked on a gas or electric stove?
• How hot is the flame?
• What is the percent decrease in size of one strip of bacon?

Teachers are identifying variables and asking for information that matters to them in order to formulate a model. I love it. I have also done this Estimation 180 challenge with students before and they have asked many of these same questions too. I love it.

I had a great conversation with Joe Schwartz and others at TMC15 about state tests lacking what the modeling process demands: asking questions. Why do the SBAC and PARCC tests not have students simply ask questions about scenarios? If we're asking students to identify variables and ask/search for information necessary to formulate a model and solve a problem, why don't tests place more of a focus on this? What if we presented students with scenarios a la the Math Forum and simply have students first submit mathematical questions that could be solved. What if we then followed it up with giving students a list of three to four questions they could solve and they pick one?

Another great conversation I had with Nathan Kraft and others at TMC15 was the idea that direct instruction can have a negative connotation in the MTBoS. A similar notion is that the instructional strategy "I do, we do, you do." also has a negative connotation. With problem-solving and mathematical modeling, direct instruction is not the focus. The focus is conceptual understanding. From my experience, I've learned that timing and placement of direct instruction is what matters. I've been catching up on reading NCTM's Principles to Actions and I highly recommend it to anyone; teachers, coaches, parents, administrators, students, and more. It's about 100 pages. Get on it! I think it paints a pretty clear picture why, how, and when conceptual understanding should take place in relationship to procedural fluency.

Principles to Actions really does a great job driving the point home that procedural fluency is important. However, procedural fluency won't stick nor have significant meaning if the students lack the conceptual understanding first. When I'm done with Principles to Actions and have had a chance to let it simmer in my brain, I plan to blog more about it. I also need to explore the Principles to Actions Professional Learning Toolkit.

Last, and certainly not least is literacy. I'm glad that one teacher at a recent workshop voiced her concern about teaching literacy in math and that the use of multimedia in a 3-Act task or an Estimation 180 challenge really doesn't strengthen literacy. I agree.

Trust me, I'm all about building literacy. However, the more I teach and work with teachers, the more I believe in the importance of making the conceptual understanding accessible first as a means to transitioning to procedural fluency and strengthening literacy by scaffolding. If I don't make the conceptual understanding accessible to my students, than I'm not scaffolding both the mathematical procedural fluency and literacy.

That said, I tried to imagine what Day 185's bacon estimation challenge might look like. I still love the visual and simple question and would still start with the current setup as the introduction to the task. Once students and teachers voice their questions, Act 2 information might be presented in text. Here's what I came up with (I know it could be better):

I have 20 minutes to prepare and eat breakfast before leaving for work. I need to cook 12 pieces of bacon for my family and the skillet only holds 6 pieces at a time. We like our bacon crispy, but not like charcoal. The gas stove will be at a medium to high heat. The first batch of bacon starts to sizzle one and a half minutes after I put the skillet on the lit stove. Five and a half minutes after the bacon starts to sizzle, it is about 65% cooked. Will I have enough time to cook all 12 pieces of bacon?

I'm not sure this blog post brings much closure. However, it has brought a greater focus for me as I prepare for the school year. I am more focused on

• students asking questions
• students building conceptual understanding first
• teachers making conceptual understanding more accessible (as much as possible) 
• teachers scaffolding their classroom activities and direct instruction to strengthen procedural fluency by building upon conceptual understanding

Does this sound reasonable?

How do you like your bacon?

Let me know. I'm on my way to finishing Principles to Actions.

Bacon,

219

CA Teachers Summit Ed Talk

I had the honor and privilege to give an Ed Talk at the California Teachers Summit held on Friday, July 31, 2015. Across the state of California, teachers attended college campuses for breakout sessions, Ed Talks, and keynote speakers. I gave an Ed Talk at the Pasadena Convention Center titled, Estimation: A Gateway To Better Number Sense. Check it out.

I gave an Ed Talk at the California Teachers Summit on July 31, 2015.

I also had the privilege of meeting the other two inspiring Ed Talk presenters, Nicol R. Howard and Thema Bryant-Davis. The highlight of the day for me (and my son) was that I got to meet one of the Keynote speakers, astronaut Leland Melvin!

Nicol, Leland, and me

Ed Talk,
1146

iPad Summit 2015

Last week, I had the extreme pleasure to co-present with my friend and colleague, JR Ginex-Orinion, who tweets at @gochemonline <---Instant follow! Our presentation was at the San Diego iPad Summit put on by EdTechTeacher.

That's a lot of links in those last two sentences, right? Here's one more: our presentation slide deck. Feel free to look through it and contact one of us if you have any questions.

Our session, Quick and Powerful Assessment Tools for the iPad, had the following goals:

• share why it's important to use assessment tools
• present four assessment tools
• give attendees a hands-on experience with each tool
• mention shortcomings and suggested uses for each app
• provide time for Q & A

With about 120 attendees and an hour, we had our work cut out for us. However, I think JR will agree that we effectively met our goals and had fun with all the attendees. My intention is to share a few highlights from the session and not recap the whole thing.

Why?

My good buddy, Robert has encouraged me to address the "why" part of a presentation and I'm really appreciative for this encouragement. As we told the attendees, it's easy for us to show you what the assessment tools are and how to use them, but let's first focus on why we should use them.

We talked about why it's important to use assessment tools because they:

• are a window (not a glass house) into student thinking
• can tell a story about your students
• should be informative (to guide your instruction) and
• should be efficient

The tools we presented were:

• Kahoot
• Socrative
• Classkick
• Pear Deck

I won't deny it. I think we saved the best for last. Pear Deck was definitely a crowd favorite. Ironically, we had to throw it in last minute because our originally planned tool, Infuse Learning, will be stopping their service in April. Pear Deck is such a great tool for capturing student thinking. I highly recommend you check it out and give it a test run in your class. 

All in all, it was a fun conference. I picked up some inspiration from Doug Kiang's keynote and Sabba Quidwai's session. More importantly, I look forward to presenting with JR again in the future sometime!

Summit,

129

Thank You 2014

There are many parts of 2014 for which I'm thankful. Here are some math-related ones.
*Apologies if I missed someone or something. Please remind (badger) me in the comments.

• YOU for reading this blog, giving me feedback, sharing ideas, making suggestions, attending my conference sessions, sharing stories about using tasks or Estimation 180, and being in education to support students (children and adults).
• The MTBoS for helping me continue to grow as an educator.
• TUSD for having confidence in me as a coach to support fellow math teachers.
• TPSF for allowing me to contribute to such an amazing summer learning environment. 
• DLCs and Co. for being a great bunch of tech-junkies in the name of meaningful learning
• Conferences:
• GLAMC for being wonderful people, organizing great mini-conferences, and gathering wonderful Los Angeles teachers.
• OCMC for hosting highly accessible and meaningful PD opportunities in Orange County throughout the year. 
• NCSM for allowing me to nerd out with Chamberlain and Kaplinsky in New Orleans.
• NWMC for a jam-packed conference of sessions in which multiple states and countries can partake in.
• CMC for holding the best conferences in the biz. I was truly honored to be a small part.
• Consulting:
• PYLUSD, Rockwood, and CUSD: thank you all for your confidence and willingness to have me work with your math teachers. I learned a great deal!
• Christopher Danielson for sending me a wonderful estimation book (still reading).
• Tracy Zagar for including some Estimation 180 in her upcoming book.
• Motion Math for making wonderful-amazing-delightful math apps for my son and me to enjoy together.
• Eric Milou, Gwen Zimmerman, Robert Kaplinsky and Dan Meyer for putting up with me during our NCSM 3-Act project and allowing me to learn a great deal from you all. 
• Hannah for being the best colleague last school year.
• My niece for designing the Estimation 180 logo and artwork.
• Johnny and SPEYSYDE for helping me get my Estimation 180 shirts printed.
• Steve Leinwand for the continued inspiration and top-notch CCSS elevator speech about MP3.
• The Math Forum and the Encompass crew for the continued opportunities to connect, collaborate, and create in the name of problem-solving.
• CueThink for creating a digital problem-solving app to support students and teachers.
• Global Math Department for allowing me to frequently write a short blurb in their newsletter.
• Kaplinsky for being a great (math) friend and coercing teachers to ask for sticky note autographs.
• Fawn for still making fun of me.
• My students for teaching me.
• My family for your love and support that encompasses everything.

Thank you,

123

Stretch

I am reluctantly pressing "publish" for this post. However, please know that the rawness and honesty in this post is aimed at making each and every one of us better at what we (both individually and collectively) do to support our students.

Kate wrote a great post the other day about some teachers coming out of TMC14 feeling inadequate. I support Kate's attitude and conclusion:

We are all good at some things and suck at other things. One thing we all share is the recognition that we all have work to do, and that we can all get better, and that focusing on that is worth our time.

I believe we need inadequacies and need to feel them at times because they make us better at what we're striving to be: the best teacher for our students. We don't need inadequacies to feel inferior to other teachers or generate some type of MTBoS worth. Here's how I think we all need inadequacies.

I started learning and exploring how to play the guitar in high school. I stunk. My family probably got tired of me playing Deep Purple's Smoke on the Water and Metallica's Enter Sandman all day. The first two riffs (and eventually songs) I learned. However, I practiced. A LOT. When I wasn't playing basketball, I practiced guitar. When I was supposed to be doing homework, I practiced guitar. There were guys at my high school who played guitar and were better. It made me practice more. It made me want to be better at something I loved doing.

When I got into college, my focus on guitar playing was similar. I was a lot better by this time, but still practiced a lot. When I wasn't working or going to class, I practiced guitar. When I was supposed to be studying, I practiced guitar. Then I joined a few bands and we practiced a lot. Not only did I continue practicing by myself, but now I practiced with others. That's awesome. We got better together! I would also jam with other guitarists who were better than me. Sometimes they were better so I learned a lot. Sometimes, I was better so I got to share some things and could relate. Every time I jammed with someone, it was a chance for me to improve at something I loved doing.

I loved going to concerts or watching videos of my favorite guitarists like Jimi Hendrix, Eric Clapton, or Warren Haynes. I wanted to cut my hands off many times because there was no way I would ever be as good as them. However, it only made me want to learn from them, steal some of their licks (guitar moves/techniques), and be the best I could be with their help and inspiration. I remember meeting James Hetfield from Metallica and was star struck. I thanked him for his inspiration. That's all I could muster up the intelligence to say. If I could jam with him I'd probably mess up A TON! But I'd never turn that opportunity down, because I'd learn a lot and he'd push me to get better.

Once during college, I was in Chicago at Kingston Mines blues bar hanging with my cousin. This blues/funk band, Charlie Love, was up there laying down some great songs. I went up at their break to compliment them and they invited me up to do a funk jam with them. I was completely honored and humbled at the same time. Here is this tall white guy trying to play funk with the Chicago blues/funk band and I did not play as well as I could have. However, I was grateful to meet them, I learned a lot from watching them, and it again made me want to go home and practice until my hands fell off.

For me, this connects so well with where I am as a math teacher. I am grateful for many other math teachers who have inspired me. There are many times I feel inadequate. Maybe I've met some of these math teachers and I feel like my brain shuts down. The best I can utter is some number and ignorantly nod my head in agreement. However, meeting inspiration and hanging out with inspiration has made me want to become a better teacher for my students.

Imagine there was an opening at your school and you could hire your teaching colleague. Would you turn down the chance to work alongside:

• Dan Meyer because of his 3-Act creativity? 
• Steve Leinwand because he's the Tasmanian Math-devil challenging you to be your best? 
• Fawn Nguyen because she cusses and can't afford to not help her students do amazing things. 
• Karim Ani because he looks at the world in interesting ways to tell stories and use math to serve them? 
• Kate Nowak because she's pioneered blogging and has crazy-cool math stuff?
• Matt Vaudrey because he's willing to grow (or wear) a mullet for a ratios lesson? 
• Cathy Yenca or John Stevens because they're integrating 21st century skills in their classrooms? 
• Robert Kaplinsky because he writes detailed and amazingly cool PBLs?
• insert name because they inspire you and make you want to be a better teacher? 

This is a snapshot of the many teachers who have inspired me and continue to raise the bar for me. I wouldn't turn them down because I might have some inadequacies. They would make me a better teacher for my students. Imagine if you were the teacher after receiving students from any teacher who inspires you? Imagine if you're the teacher before sending your students to a teacher who inspires you? Wouldn't you want to be the best teacher for your students? Isn't that healthy? Who wins? I would hope your students. 

I recently offered a keep-your-head-up comment somewhere saying,

"Think of the skills you will acquire when making changes."

My challenge to you (and myself), if you're feeling inadequate or inferior at any time is to:

• take risks
• be brave
• tap into your influences and inspirations to stretch yourself
• be the best teacher for YOUR students, not the MTBoS.

Stretch,
210

Get Students to Argue in Math Class

I recently submitted my speaker proposals for both 2014 CMC conferences. One of my proposals is for the following session:
Title: "Get Students Arguing in Math Class with Number Sense Activities."
Description: Get students to productively argue about math situations. Participate in number sense activities requiring students to construct viable arguments, critique the reasoning of others, and use sense-making. Get ready to throw down.

I also had to answer a few questions justifying the session and connecting it to the CCSS and 8 Mathematical Practices. I provided the following connection:
The presenter will use number sense activities to get participants to construct viable arguments and share their reasoning like students. Using presenter-made tasks (Estimation 180) and other online resources appropriate for grades 3-8, attendees will be able to see the importance of student reasoning and creating productive discourse in the classroom. Teachers will also be provided with sentence frames and stems for all students, especially English language learners.

I'm really excited at the thought of this session getting accepted so I figured I would jot down a few ideas here and see what you all have to contribute. Even if I'm not accepted, I think every math class has to have students productively arguing at times. Doing estimation challenges with my students has been so beneficial for them to get better at the art of arguing. However, I know it could be better. I'm not sure if you've ever experienced it before, but it's a treat to stand off to the side or in back of a group of students arguing about a question in math. They have no idea you're nearby because they are so caught up in the argument. Don't get me wrong, it's not like they're swearing at each other and calling each other names. They are having a rich discussion, sharing conjectures, examples, counterexamples, etc. and I have the pleasure of spectating. I usually turn to an innocent bystander (nearby student) and whisper, "Awesome, look at them arguing. Isn't it great?" The student usually looks shocked that I'm happy their classmates are arguing. I love it!

I'd like this session to place a big emphasis on two mathematical practices:
MP 3: Construct viable arguments and critique the reasoning of others.
MP 1: Make sense of problems and persevere in solving them.

I plan to break these two practices down more in my session. For now, I feel I need to focus on three major parts to arguments: having excellent content, capturing the arguments, and indirect facilitation.

Content: There's a wealth of content available, but I think the more controversial the point of contention, the better. One of my favorite moments in math class was when we did Mathalicious' Datelines lesson. Students were arguing about which celebrity shouldn't date another celebrity because of the age discrepancy. Some students disagreed about the rule of (n/2) + 7, especially since I was teaching 14 year-olds at the time. It was awesome.
Here's my current list of resources that have given my students great things to argue about:

• Estimation 180
• Mathalicious
• Would You Rather 
• by John Stevens

My kids went nuts arguing about a similar question to this "Would You Rather" found here.

These don't have to be full-on lessons. They can be warm-ups, math talks, used during classroom transitions or to break up your direct instruction, etc. I'm really looking forward to using @MathCurmudgeon's site MathArguments180.com
Imagine your students arguing about which student should pack your parachute based on this data.

Another up and coming resource is Open Middle by Robert Kaplinsky and Nanette Johnson.

What resources would you add to my content list?

Capture: I need to capture these arguments for a few reasons. Students need to listen to other students argue, especially from different classes. My memory is very porous, and I can't remember what students say verbatim. Students can listen to the recordings and pick a side, or provide their own agreement or dissent. I'd also love to share student arguments with other teachers, especially at this session. How do I capture this?

I just downloaded Voice Memos for iPad onto my school iPad. I will test it out next week with students. Wish me luck. Here are the features I'm optimistic about:

• It will record in the background while another app is running.
• It was $1.
• I can pause the recording.
• I can trim audio clips.
• I can sync with Dropbox.

Have any tips for capturing student arguments?

Facilitation: Here's where I need to do a better job. For many of my students, English can get in the way of them articulating their point. I'd like for students to listen better to each other and respond accordingly. I want to hear what they have to say. I want them to be a contender in their disagreement, but I don't want them to be held back because of language deficiencies. Therefore, I need to provide them with sentence starters and stems. Fortunately, these can be used with any student. Here's a few:

• My opinion about this is _____________.
• I could argue that _____________.
• I disagree with your statement that _____________ because _____________.

Have any stems or sentence frames you're already using with students to help them articulate their thoughts?

Argue,
339

NCSM 2014 Day 1

Day 1 of NCSM was yesterday and here’s something I found interesting. Robert Kaplinsky, Dave Chamberlain, and I were walking back to our hotel room from the conference and I saw this clearance sign to the entrance of our hotel. I have been known to do estimation challenges before with clearance heights, not once, but twice.

I thought to myself, "There's NO WAY that thing is 6 foot 4 inches!"

I walked up to it and thought I should hit my head. Nope.

Okay, I’ll stand on my toes. Nope.

Okay, what’s going on here?

Why is this mislabeled? What’s your theory?

I’ll admit, this made me a little suspicious of the other clearance height challenges I’ve captured. Is this worthy of Estimation 180?

Photo bomb!

Suspect,

852

Presentations & Workshops

Last month I added the Lessons page to Estimation 180 so you can quickly access lessons I've made. I will continue to add lessons as I make them and host them in that space.

This month, I'm adding a Presentations & Workshops page to the site. Since last November, I've been fortunate to work with some amazing math teachers at conferences and workshops. I've learned a lot and have truly enjoyed doing math with teachers as we share instructional strategies and lessons. My goal is to help support math teachers in strengthening their instructional tool belt for the Common Core classroom. 

I'm excited about this new chapter. Drop me a line if you're interested.

PD,
945

Why I Blog (maybe)

Kate Nowak challenged us to share a few thoughts on blogging as she prepares to be a featured speaker at NCTM. I have a few minutes to share so here it goes.

1. What hooked you on reading the blogs? Was it a particular post or person? Was it an initiative by the nice MTBoS folks? A colleague in your building got you into it? Desperation?

I was hooked on blogs when I discovered I could use things others had created. I discovered that my teaching could improve by learning from others who were humble and honest about the mistakes they made. A close friend of mine who teaches science sent me Dan Meyer's TED talk and my blog reading increased from zero minutes a day to about 240 minutes a day: time-suck!

2. What keeps you coming back? What's the biggest thing you get out of reading and/or commenting?

I keep coming back because I get the opportunity to observe other teachers (even if it's a snapshot) without being in their classroom. Anytime I've been in another teacher's classroom, I've learned so much. It doesn't matter if the teacher was good or bad, I was either learning what to do or what not to do. Reading other blogs is a similar opportunity for professional growth.

3. If you write, why do you write? What's the biggest thing you get out of it?

I write to document things, reflect on things, and share something I'm proud of. If I had time to blog about everything I do, I would. However, it would become white noise for those who take the time time to check in. Therefore, I write about things that stand out to me: great experiences, cool lessons, or things I'm proud of. It's not intended to be perfect. I hope to keep it raw. I'm not the best writer. Somehow, I happen to write a few things that a few people are interested in. That positive energy keeps me going.

Specifically, I blog at two places now: Divisible by 3 and Estimation 180. Divisible by 3 is reserved for all the things I've mentioned above. I blog at Estimation 180 to keep people updated on new estimation challenges I posted and/or any stories behind the challenges. I enjoy when a story is attached to a mathematical experience. 

4. If you chose to enter a room where I was going to talk about blogging for an hour (or however long you could stand it), what would you hope to be hearing from me? MTBoS cheerleading and/or tourism? How-to's? Stories?

From my experience, I enjoy a keynote speaker who is both inspiring and interactive. I like the sessions where the speaker is well-spoken, engaging, inspiring and challenges me as I leave the session to become a better teacher. However, I don't want the entire 60-90 minutes to be spent by them just showing me pictures, videos, quotes, or other things that are one-directional. I also need to be challenged by actually being forced to do math, tasks, or be given the opportunity to explore what they're presenting on. Make it feel like a classroom where I get a healthy mixture of inspiring talk and engaging tasks. Kate, I'd love for you to share the good, the bad, and the ugly about blogging. Then have me get out my internet device (phone, tablet, or computer) and either explore a list of blogs or even create a blog. Put up a list of blogs that do different things. Have me explore them. Give me some questions/tasks:

1. Compare and contrast the blogs.
2. Which blog would you find yourself using most often, least often, never?
3. What kind of blog would you like to create?
4. What suggestions do you have for these people blogging?
5. ...and so on

Give your attendees a Google Form to fill out so you can document the answers. By this point, you've already shared with me your inspiring thoughts on blogging and you're getting me involved. Get me to experience blogging while we have time together. Don't make blogging a homework assignment for your attendees.

Hope that helps. Good luck Kate!