Tag Archives: collaboration

Neuron Problems & Classroom Norms in Algebra 2

Day 3, Fri Aug 12, 2016

A vs Don-stepmom-shoulderTarget: Recognize that  Voice = Choice when it comes to having a growth mindset as we solve problems about our amazing brains.

Entrance Ticket
I greeted the students at the door, but today I was checking homework. They only had to do one problem of their choosing from the Neuron Facts last night. If they did not have it, they had to quickly do one outside. Message sent: You are doing your homework in this class.

Growth Mindset
On the growth mindset web site they make a point of the “voice = choice,” meaning that we have a choice whether or not to listen to the fixed mindset thoughts that we all have, They give a 4-step breakdown of how to shift from a fixed to a growth mindset. I had fun soliciting the help of a very ancient visual of a devil and an angel on your shoulder.

Voices choices

Neuron Fact Problems
So then came time to practice recognizing the fixed voice and talking to ourselves in the growth voice, while doing challenging math problems. They already sit in groups of four, so I had them spend the rest of the period working through the Neuron Fact Problems, which I created from the Facts on the front side of the paper.  They were to call out any fixed mindset words or actions demonstrated by their partners. They actually did. I worked the room with Neuron stickers and Nicki. I honored about half the groups. I was pleasantly surprised at how well my crew worked.

During the lesson, as I worked the groups, I asked  one student how she got her answer, and she told me that she had copied from her partner. I praised her for her honesty, then paused the class and brought their attention to our classroom norms.


These were originally shared with us by Dr. Juli Dixon (@thestrokeofluck) in a math training at our district. They became very popular among our teachers. Our new principal has implemented them schoolwide, providing posters for every classroom. I drew the students attention, that we “Share, Don’t Copy.” When we share, one person explains, the other listens, then question follow if we don’t understand or if we disagree. If these three norms are occurring then writing down someone else’s solution is not copying.

After a half hour of solid work, we debriefed where we saw evidence of a fixed mindset and where we saw evidence of a growth mindset. This whole activity was very well received by the students. I gave them advance notice that Monday we will be debriefing their actual solutions to the problems.

Wrinkle Sprinkle

  • Share, Don’t Copy.
  • The equals about 3 lbs.

Introductions & Neuron Facts in Algebra 2

neuron vertical
Day 2, Thurs Aug 11, 2016

The Brain Surgeon
Today, we began my regular routine of designating a daily Brain Surgeon. Since this was our first day of the Brain Surgeon, I introduced the routines of the Drum Roll, Reading of the Dual Target, Music Cues, and the Wrinkle Sprinkle. The students seem to embrace the spirit of of it all.

Student Introductions
As with every new school year, I had each student briefly state their name and something interesting about themselves. When they were all done,  I recited all their names. That always impresses a class. Then I told them things about myself. I state that yesterday we started with math, because that is what we are all about here. But since I teach math to them, they are also important and I need to know who they are.

Growth Mindset
Most of our Course Teams across the district agreed to do some kind of growth mindset activity. Here was mine.

I started by summarizing the plethora of lists of fixed vs growth mind set statements with two pictures. I told the students that research in student learning is showing that self-perception of talent as a limit or as a starting point has a tremendous influence on their learning.

Talent Wall

Then I shared that scans of the brain of someone with a fixed mindset versus a growth mindset, shows something very interesting. When faced with a challenge, the fixed mindset brain “goes cold.” It literally shuts down. However, when faced with the same challenge, the growth mindset brain “fires up.” It knows that more is being asked of it, so it kicks into high gear to meet the challenge, rather than duck it.
Brain MindsetsNow it was time to test out where we see ourselves demonstrating  a fixed or growth mindset.

Neuron Facts
I gave the students the worksheet with the Neuron Facts on the front side. I found these on the internet and thought they would make for a good lesson since they highlight the amazing function of our brains. I added the subheadings of Fast, Crowded ,etc. I started with a common practice of mine Notice & Wonder popularized by Annie Fetter (@MFAnnie) of Math Forum.  My Gradual Reel-In process looked something like this:

  1. You Do: Independent response.
  2. Ya’ll Do: Each member of the group shares both their notice and wonder.
  3. We Do: Each group decides on one Notice and one Wonder from those shared. These get shared out by each group as I write them on the board.
  4. I Do: I summarize the major point(s) that I want all students walking out with. Here it was the process of Noticing and Wondering and how we facilitate group discussion in class… And of course how amazing our brains are.

The groups were then tasked with doing one problem together. Homework was to do one more.

Wrinkle Sprinkle
Tying into the concept of the plasticity of the brain, I joke that when we learn we get a new wrinkle on the brain. Each class then concludes with what we learned that day. The brain surgeon leads and records the discussion. The students today stated that they learned…

  • Negative thoughts shut down your brain
  • Speed of the brain cell
  • The amount of oxygen the brain uses

Re-Cap: NCSM 2016


Oakland, CA , April 2016NCSM Logo

I have summarized each session with some simple (•) bulleted notes, red underline quotes to encapsulate my major take-aways, and occasionally a brief italicized commentary.

Game-Based Learning: The Hype is Starting to Give Way to Some Surprising Substance  — Keith Devlin (Stanford)

  • Pic Keith_DevlinBig Take-Away = Start with the thinking (which is the more important), then follow with the notation.
  • The “Symbolic Barrier”: Symbols are a terrific way to use mathematics, but a horrible way to learn them.
  • The vast majority of our population is taught symbolic notation, yet most need mathematical thinking.
  • Students using Dragon Box Algebra learn the Algebraic thinking needed for solving equations in 90 minutes. However, this ability did not transfer to paper/symbolic test, therefore, both are needed.
  • We teach students to play music, before we teach them to read it. The same should be true of mathematics.

Personal note: I’ve had Dr. Devlin’s book, Goodbye Descartes, for almost 20 years; after his talk he signed it for me.

Developing Deeper Student Thinking  and Reflection — Patricia Rogers (Gilroy USD)

  • Big Take-Away = Use “structured” student collaboration to enhance student reflection, and thus student thinking.
  • Good collaboration needs to be: Regular, Brief, Prepared, Open-Minded.
  • 3 Teacher Moves (Phil Daro)
    • Student thinking made visible (to other students, not just the teacher)
    • “Everyone Ready” (ALL students individually prepare themselves to share thinking.)
    • “Make an Expert” (of a students who has viable strategy) then have the rest of the class “Turn and Talk” when productive struggle weakens in order to focus on targeted math topic.
  • Classroom Discussions (Chaplin, O-Connor, Anderson)
    • Wait Time
    • Revoice (The teacher rephrases what the student just said.)
    • Restate (Student(s) rephrase what a student just said.) 
    • Add-on (Student(s) extend or challenge another student’s conjecture.)
    • Apply (Students apply their own reasoning to someone else’s reasoning …” just try it on.”)

I’ve seen the two techniques of revoicing & restating demonstrated a great deal lately and have now been challenged to bring these into my class more often.

SFUSD logoThe San Francisco USD Mathematics Teaching Toolkit: Changing the Practice Along with the Content — Glenn Kenyon & Kathy Bradley (SFUSD)

  • Big Take-Away = Established Vision, Beliefs and Goals before building district curriculum

“All students will make sense of rigorous mathematics in ways that are creative, interactive, and relevant in heterogeneous classrooms.”

1. All students can and should develop a belief that mathematics is sensible, worthwhile, and doable.
2. All students are capable of making sense of mathematics in ways that are creative, interactive, and relevant.
3. All students can and should engage in rigorous mathematics through rich, challenging tasks.
4. Students’ academic success in mathematics must not be predictable on the basis of race, ethnicity, gender, socioeconomic status, language, religion, sexual orientation, cultural affiliation, or special needs.”

3 Goals
1. Help students express, expand and clarify their own thinking. 2. Help students to listen carefully to one another and negotiate meaning.
3. Help students deepen their reasoning.

“The teaching strategies in the SFUSD Math Teaching Toolkit are designed to support an inquiry-based approached to learning mathematics, with an emphasis on classroom discourse. This approach reflects the shifts of pedagogy required to promote the Common Core Standards for Mathematical Practice.”

  • Unit Design Structure to incorporate tasks

SFUSD Unit Design.png

1) Math Talks
(SMP#3. “Math Talks”, instead of Number Talks, so discussion can broaden {e.g. strategies for computing area})

2) Three-Read Protocol
(Model for close reading of complex math text)
First Read (Teacher Read Aloud) = What is the Situation?
Second Read (Choral Read) = What are the Quantities & Units?
Third Read (Individual Read & Think) = What question can be asked?
This only runs 10-12 minutes. Take away the question to create a rich task.

3) Participation (Group) Quiz A technique to give public feedback on group work. Lists ways a student can contribute (“You can help your group if you can…. create a table, draw a diagram, listen to people’s ideas and ask questions, etc) Also publicly list teacher expectations (e.g. How groups … us shared space? ask question? explain thinking? etc)

  • Video Exemplars & PD modules are available on district web site.
  1. SFUSD has a PHENOMENAL math web site chalked full of resources for supporting teachers implement the vision and the curriculum. Check it out!
  2. The description of their Group Quiz speaks to the need to explicitly teach students how to productively collaborate.
  3. This was the first of three sessions that spoke about the importance of vision. It will be the predominant point that I take home with me from this conference.

Beyond Relevance and Real World: Talking with Teachers About Engagement in Mathematics? — Dan MeyerPic Dan M

  • Big Take-Away = ‘Real World’ does not have to be real, just accessible and engaging.
  • 62% of teachers surveyed : Greatest challenge is “unmotivated” students. Interesting that they didn’t say motivating students was the challenge.
  • Question: Why don’t teachers spend more time developing good questions?
    Teacher Response: “Because we don’t have the time.” (True that.)
    Real Issue: “Lack of creativity. Giving the answers does not require creativity.” (True that, also, but ouch!)
  • A stronger option than the typical “engaging images or context” in a textbook: Redefine Real World. A situation is in the process of becoming real to you if you are able to … 

1. Ask a question about it.
2. Guess about it .
3. Argue about it.

High School Coaching Model: Building Bridges Between Coaching and PLC Culture — Kris Cunningham & Jeanette Scott (Phoenix UHSD)

  • Big Take-Away = Roll out PD through PLC teams.
  • New initiatives first unveiled during PLC team meetings.
  • Most powerful change agent was a lesson study. (1st day by 1 teacher, next day by all teachers)
  • Most teachers took 3-4 years to show change; 4 of 5 teachers showed significant change within 5 years.
  • There exists a Common Lesson Plan format for lessons studies and co-planning.
  • Professional Development certificates tied to evaluations. (i.e. Professional Growth affects evaluation outcome.)

The fact that teachers took 3-4 years to show change aligns with Maggie McGatha’s research shared at last year’s NCSM conference

Practicing the Five Practices: Coaching Teachers to Use Student Work in Planning  — Max Ray-Riek (Math Forum)

  • Big Take-Away = Walk teachers through the 5 Practices of Discourse with student work samples.
  • Max shared with us the Teddy Bear’s Banquet pattern problem. He had us determine the Math Goal for the lesson, and then Anticipate the student responses.
  • Max then offered 16 samples of true student responses (Monitor) and then had us Select and Sequence some of the responses for classroom discourse and share why. We were then asked to Connect the responses to the Math Goal.

This is a great training tool that can be brought into any PLC structure.

I also witnessed Max slyly counting on his fingers. This was his way of giving is all wait time on his prompts. 

Smarter Balance – Making Connections: Eliciting to Acting on Evidence —  Judy Hickman (Director of Mathematics, SBAC)

  • Big Take-Away = When the scoring focus is on Reasoning, students can still score full credit with a minor calculation error, if they show understanding.
  • Do NOT put too much emphasis on Interim Assessments. As “snapshots” they will give you good information, but it will be an incomplete assessment.
  • The authors of the exams were shocked that students answered so few questions correctly.

Four Keys to Effective Mathematics Leadership — Mona Toncheff & Bill Barnes  (Activating the Vision )





  • Big Take-Away = Vision needs to be created by ALL stakeholders
  • The Four Keys:

1. Establish a Clear Vision for Mathematics Teaching & Learning
2. Support Visionary Professional Learning for Teachers and Teacher Leaders
3. Develop Systems for Activating the Vision
4. Empower the Vision of Family and Community Engagement

This was the second of three sessions that spoke about the importance of vision. This one stressed the need to have all stakeholders (admin, teachers, classified staff, parents and the business community) in on the creation of the vision. Mona & Bill then asked, “If you were ask 10 people on your campus, ‘What is our vision,’ how many answers would you get?”

The Secret to Leading Sustainable Change: Vision, Focus, Feedback, and Action! — Dr. Tim Kanold (Turning Vision into Action )

  • Big Take-Away = Set the Vision, Help people advance the Vision,  Celebrate Evidence that the people are advancing the Vision, and take Action on the feedback towards the Vision. 
  • Sustainable change requires evidence that the change is bigger than their opinions.
  • Is the work you are doing formative? Meaningful feedback must be followed with results in action by the teacher or teacher team.
  • Meaningful Feedback = F.A.S.T. Action: Fair, Accurate, Specific, Timely. Action from your feedback is required.
  • Mary Beth call. Dr. Kanold told a story of when he was Superintendent of Stevenson HSD. He called a secretary at one of the schools, restated that ‘engagement’ was part their district vision, and asked “What does engagement look like in your job.” That’s keeping the vision in front of the people!
  • The Popeye Moment: Change happens when the moment of moral courage vocalizes what Popeye often said, “That’s all I can stands, cuz I can’t stands n’more!

This was the third of three sessions that spoke about the importance of vision. The story of calling the secretary is tattooed on my brain. Dr. Kanold stressed that the vision should be posted visibly during every PLC meeting, and that any unproductive dialogue can be redirected with the simple statement, “How does this conversation advance this vision?”

A Math Coaching Package — Donna Lione, Rebecca Williams & Chris Shore (Me) (Temecula Valley USD )


My colleagues and I presented the framework for developing a comprehensive math program. The details of each of the 8 components will be posted as separate posts.

  • Vision
  • Relationships
  • Humility
  • Influence
  • Passion
  • Faith
  • Focus
  • A Plan

Recap: NCTM 2016

San Francisco, CA , April 2016
I have summarized each session with some simple (•) bulleted notes, red underline to encapsulate my major take-aways, and occasionally a brief italicized commentary.

The Status Quo Is Unacceptable: A Common Vision for Improving Collegiate Mathematics Diane Briars, & Linda Braddy, Christine D. Thomas & Dr. Uri Treisman

  • Big Take-Away #1 = College failure rates are 55% higher than for more active forms of instruction.
  • Big Take-Away #2 = The math ed reform movement is now reaching the post-secondary level.
  • Big Take-Away #3 = The change must be institutional.

  • The challenge facing the Math Ed Community (the dismal stats)
    1) Only 50% of students earn A, B or C in college algebra.
    2) Women are twice as likely as men to not continue past Calc 1.
    3) While 20% of all Bachelors Degrees are awarded to Blacks & Hispanics, only 12% of Math Degrees are.
    4) Math is the most significant barrier to degree completion in ALL fields.
  • Innovation does not affect normative practice. Out of 81 different projects (2-3 yrs) connected to a grant or leader, NONE replaced normative practice, because they were based on faculty development, not institutional change.  Dr Treisman, “Institutional change is a bitch.”
  • Historically, school system does change when necessary.

The Learning Mindset Movement and Its Implications for Addressing Opportunity Gaps — Dr. Uri Treisman (The Dana Center)

  • Big Take-Away  = Besides Growth Mindset, there is Belonging Mindset and Purpose Mindset.
  • “I find Algebra beautiful, but will it knock the socks off of a 13 year old. Algebra well taught should leave them barefoot in the park.”
  • “Why do kids give up? Most of the work I do is confusing, cause no one gives me problems in the back of the book.”
  • Growth Mindset = “Can I do this?”
    Belonging Mindset = “Is this where I belong?”
    Purpose Mindset = “Does this connect to who I want to be?
  • Dr. Catherine Good:  Building Bridges to Belonging: Mindsets that Increase Participation, Achievement and Learning
  • Build Belonging through effort & engagement, not talent.
  • Positive Belonging Mindset = Assume they belong.
    Negative Belonging Mindset = Need to be invited in.

Paper Cup + Gust of Wind = Yearlong Rich Task — Peg Cagle

  • Big Take-Away = Revisiting the same task through-out the year emphasizes math as reasoning not simply answer-getting.
  • Peg had us roll a paper cup on its side. She then left us to our own devices to answer several questions, each of which addressed a different mathematical topic throughout the school year.
  • Day 35 Question: How can you convince a skeptic of the shape that the cup traces out as it rolls?
  • Day 70 Question: How can you locate the center of the shape that the cup traces out as it rolls?
  • Day 105 Question: How can you use a cup’s dimensions to determine the area of the shape it traces out as it rolls?
  • “Efficiency is overrated: That is a concern after you learn something.”

Coding to Enrich ALL Math Classes — Jason Slowbe

  • Big Take-Away = Coding in Math class helps teach the Math, not just the coding.
  • Coding can be done on the TI-Calculator
  • Can help students understand the meaning and power of mathematics. For example, Archimedes’ method for approximating the area of a circle.

Rich Problem Solving to Support Today’s Standards — Chris Shore (Teacher Created Materials)

I conducted a product promotion for Teacher Created Materials. The session was on Problem Solving and Linda Gojak’s What’s Your Math Problem Anyway? My presentation focused on the following questions about the teaching of problem solving, each of which I will answer in its own post:

  • What is problem solving?
  • Why teach problem solving?
  • Who should learn problem solving?
  • When should we teach problem solving?
  • How should we teach problem solving?
  • Where do we find resources for teaching problem solving?