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

A Jammed Rational-Irrational War, Stacking Cups Week

Some cool stuff happened this week. Well at least I think it was cool.

Monday: 

One of my math fellows was observed by other math teachers from our district. He was starting a new unit with rational and irrational numbers, focusing on 8.NS.1 and 2. I might be wrong, but pretty dry stuff… here’s how we spiced it up a little.

We did a pre-assessment using the Post-It Plus app. Yes, my obsession with Post-It notes has gone to a new level: digital. We created a file within the app, posted it on his Haiku calendar, and had the students download the file into their app on their iPad. 

Students first worked individually to sort the terms from least to greatest for a few minutes. Since his students are grouped in fours, they then narrowed it down to one iPad screen they thought was most accurate. (Quick demo)

*Reflection: we should have had students paired up first, discuss, and narrow it down to two screens for the entire group. Next, the whole group of four students would discuss and narrow the two iPad screens down to one screen for the group.

Once each group settled on a screen they felt most confident with, they took a screenshot and uploaded their group’s screenshot to the Padlet page my fellow created for them.

My fellow used this Padlet page to assess the overall climate of the class (without teaching them a single thing). He used this real-time data to have some really rich conversations and share-out of ideas from students.

Remember to tell students:

• It’s okay if you’re wrong. 
• Make your best guess.
• I just want to see what you already might know.

Flash forward to Friday:

The previous weekend I asked the same fellow what he thought about playing War with rational and irrational terms. Side note: I play a few card games with my young son and one of them is War. My fellow thought the idea was epic. He ran with it. Here how he made it awesome:

• He made these awesome cards.
• Some values had multiple representations
• Printed them out on card stock.
• Made a graphic organizer for students.
• Each group of four was broken down like this:
• 2 people played War while the other 2 people recorded and were the judges.
• The next round, the roles were switched.
• There were 3 rounds.
• Each round was 6-10 minutes
• He stopped class and made a spectacle whenever two students were at war.
• The third and final round was between the winners of the first two rounds.

I asked if I had his permission to share the cards and he said, “Sure.”

Tuesday:

Another fellow asked me to model Stacking Cups in their first period class, which ran less than 45 minutes. My fellow requested I complete the task with students in one period. I explained that I’ve never “finished” the task in one period because there is so much to explore and learn in the task. I respected the request and  tried to cram it into one period. I spent too much time launching the task. 

Act 2 (the best part) felt rushed and we still didn't finish. My fellow and I debriefed and made some adjustments so she could finish it with her next period. She stuck to the adjustments and did a fantastic job facilitating the task. The students were doing awesome and amazing math during Act 2… and what do you know? The class was over. I love that my fellow was going to revisit the task the next day. Could we have spent another day on the task? Yes. It’s a starting point and I’m very proud of my fellow for trying out something new and doing a great job. I’d say the sweet spot would be one-and-a-half days for this task...
*Side note: I encourage you do styrofoam cups earlier in the year, and use Stacking Cups throughout the entire linear systems unit.

Thursday:

Another teacher wanted me to model Stacking Cups as well. When we sat down to plan, she was totally cool with spending one-and-a-half days on the task. Great news!

I launched the task, used a Padlet page to capture what they noticed. I asked the question, "Where will they tie?" and used a Google form to collect their guesses (see my post on using Google forms to collect student thinking). 

We gave each group only 4 white styrofoam cups. Students were making tables, or writing equations, or some were even wanting to graph their equations. Interesting note: some students started their table with zero cups having a height of 9.2 centimeters. The teacher had only taught graphing systems, so students were already thinking ahead to substitution. It was awesome. She did a wonderful job facilitating her first 3-Act task. We didn’t finish the task in one period, but it felt right knowing we had another half-day to wrap up the task. 

Back to Friday:

After work, I started putting the meat in my upcoming session, Math Mistakes and Error Analysis: Diamonds in the Rough. Although I will be showcasing a couple ways I’ve had success with error analysis with students, I love that I’ll be showcasing some awesome work and contributions from:

• my fellows
• Michael Pershan’s mathmistakes.org,
• Fawn’s Visual Patterns with Michael Fenton’s latest mod
• Open Middle by Robert Kaplinsky and Nanette Johnson

Hope to see you in my upcoming session as we explore why error analysis is important to:

• help drive instruction
• curb student misconceptions and
• strengthen formative assessment. 

Hope your week went well too. If not, hope this week is better.

Rational/Irrational,
516

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?

Jams,
306

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