What is we use powerful tools to elicit student thinking? How might we learn about students to deeply understand them as mathematicians? And then, what actions do we take to ensure mathematical success for all?
This week’s session began with a gallery walk using Amy Lucenta and Grace Kelemanik’s first five Contemplate then Calculate (#CthenC) lessons found on at Fostering Math Practices.
From Ruth Parker and Cathy Humphreys in Making Number Talks Matter:
No matter what grade you teach, even high school, socalled “dot” cards (which may not have dots) are a great way to start your students on the path to mathematical reasoning. We say this because, from experience, we have realized that with dot cards, students only need to describe what they see— and people have many different ways of seeing! Arithmetic problems, on the other hand, tend to be emotionally loaded for many students. Both of us have found that doing several dot talks before we introduce Number Talks (with numbers) helps establish the following norms:
There are many ways to see, or do, any problem.
Everyone is responsible for communicating his or her thinking clearly so that others can understand.
Everyone is responsible for trying to understand other people’s thinking.
To embolden mathematicians and to prepare to elicit and use evidence of student thinking, teaching teams must practice to develop the habits put forth in 5 Practices for Orchestrating Productive Mathematics Discussions.
You can see our teacherlearnerleaders working to deepen their understanding of and commitment to the Making Number Talks Matter: norms, Smith and Stein’s 5 Practices for Orchestrating Productive Mathematics Discussions, and NCTM’s Principles to Actions: Ensuring Mathematical Success for All.
How might we continue to deepen our understanding of NCTM’s teaching practices? What if we team to learn and practice?
From Principles to Actions: Ensuring Mathematical Success for All
Elicit and use evidence of student thinking.
Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.
And, from Taking Action: Implementing Effective Mathematics Teaching Practices in KGrade 5
In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry, and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners. The goal is to ensure that each and every student succeeds in doing meaningful, highquality work, not simply executing procedures with speed and accuracy. (Smith, 4 pag.)
Worth repeating:
The goal is to ensure that each and every student succeeds in doing meaningful, highquality work, not simply executing procedures with speed and accuracy.
We continue to foster creativity, visual and algebraic representation to strengthen our mathematical flexibility as we learn together.
When mathematics classrooms focus on numbers, status differences between students often emerge, to the detriment of classroom culture and learning, with some students stating that work is “easy” or “hard” or announcing they have “finished” after racing through a worksheet. But when the same content is taught visually, it is our experience that the status differences that so often beleaguer mathematics classrooms, disappear. – Jo Boaler
#ChangeTheFuture
#EmbraceAmbitiousTeaching
#EmboldenYourInnerMathematician
“Seeing as Understanding: The Importance of Visual Mathematics for Our Brain and Learning.” Journal of Applied & Computational Mathematics 05.05 (2016): n. pag. Youcubed. Standford University, 12 May. 2016. Web. 18 Mar. 2017.
Humphreys, Cathy; Parker, Ruth. Making Number Talks Matter (Kindle Locations 339346). Stenhouse Publishers. Kindle Edition.
Kelemanik, Grace, and Amy Lucent. “Starting the Year with Contemplate Then Calculate.” Fostering Math Practices.
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K5. The National Council of Teachers of Mathematics, 2017.
Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.
Principles to Actions: Ensuring Mathematical Success for All
7:15  Establishing Intent, Purpose, Norm Setting

8:00  Continuing Talking Points – Elizabeth Statmore (@chessemonkeysf)

8:15  Number Splats – Steve Wyborney (@SteveWyborney) 
8:25  Fraction Splats – Steve Wyborney (@SteveWyborney) 
8:45  Planning for Splats

9:00  Closure and Reflection

9:15  End of session 
Homework:
Kelemanik, Grace, and Amy Lucent. “Starting the Year with Contemplate Then Calculate.” Fostering Math Practices.
Kaplinsky, Robert, and Peter Morris. “Closest to One.” Open Middle.
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K5. The National Council of Teachers of Mathematics, 2017.
Statmore, Elizabeth. “Cheesemonkey Wonders.” #TMC14 GWWG: Talking Points Activity – Cultivating Exploratory Talk through a Growth Mindset Activity, 1 Jan. 1970.
Previous Embolden Your Inner Mathematician agendas:
For our first session of Embolden Your Inner Mathematician, we focus on Subitizing and Number Talks: Elicit and use evidence of student thinking.
From Principles to Actions: Ensuring Mathematical Success for All
Elicit and use evidence of student thinking.
Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.
And, from Taking Action: Implementing Effective Mathematics Teaching Practices in KGrade 5
Meeting the demands of worldclass standards for student learning requires teachers to engage in what as been referred to as “ambitious teaching.” Ambitious teaching stands in sharp contrast to what many teachers experienced themselves as learners of mathematics. (Smith, 3 pag.)
In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry, and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners. The goal is to ensure that each and every student succeeds in doing meaningful, highquality work, not simply executing procedures with speed and accuracy. (Smith, 4 pag.)
Worth repeating:
The goal is to ensure that each and every student succeeds in doing meaningful, highquality work, not simply executing procedures with speed and accuracy.
How might we foster curiosity, creativity, and critical reasoning while deepening understanding? What if we listen to what our students notice and wonder?
My daughter (7th grade) and I were walking through our local Walgreens when I hear her say “Wow, I wonder…” I doubled back to take this photo.
To see how we used this image in our session to subitize (in chunks) and to investigate the questions that arose from our wonderings, look through our slide deck for this session.
From NCTM’s 5 Practices, we know that we should do the math ourselves, predict (anticipate) what students will produce, and brainstorm what will help students most when in productive struggle and when in destructive struggle. What if we build the habit of showing what we know more than one way to add layers of depth to understanding?
When mathematics classrooms focus on numbers, status differences between students often emerge, to the detriment of classroom culture and learning, with some students stating that work is “easy” or “hard” or announcing they have “finished” after racing through a worksheet. But when the same content is taught visually, it is our experience that the status differences that so often beleaguer mathematics classrooms, disappear. – Jo Boaler
What if we ask ourselves what other ways can we add layers of depth so that students make sense of this task? How might we better serve our learners if we elicit and use evidence of student thinking to make next instructional decisions?
#ChangeTheFuture
#EmbraceAmbitiousTeaching
#EmboldenYourInnerMathematician
Boaler, Jo, Lang Chen, Cathy Williams, and Montserrat Cordero. “Seeing as Understanding: The Importance of Visual Mathematics for Our Brain and Learning.” Journal of Applied & Computational Mathematics 05.05 (2016): n. pag. Youcubed. Standford University, 12 May. 2016. Web. 18 Mar. 2017.
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K5. The National Council of Teachers of Mathematics, 2017.
For our first session of Embolden Your Inner Mathematician, we focus on Subitizing and Number Talks: Elicit and use evidence of student thinking.
From Principles to Actions: Ensuring Mathematical Success for All
Elicit and use evidence of student thinking.
Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.
And, from Taking Action: Implementing Effective Mathematics Teaching Practices in KGrade 5
Meeting the demands of worldclass standards for student learning requires teachers to engage in what as been referred to as “ambitious teaching.” Ambitious teaching stands in sharp contrast to what many teachers experienced themselves as learners of mathematics. (Smith, 3 pag.)
In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry, and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners. The goal is to ensure that each and every student succeeds in doing meaningful, highquality work, not simply executing procedures with speed and accuracy. (Smith, 4 pag.)
Worth repeating:
The goal is to ensure that each and every student succeeds in doing meaningful, highquality work, not simply executing procedures with speed and accuracy.
Let’s pay attention to the whole child. Content is mission critical, but so are disposition and efficacy. What if we learn more about our students disposition to support the social/emotional wellbeing of our mathematicians? How might we elicit and use evidence of student thinking to understand assumptions/beliefs about learning math?
We used the following exploratory talking points from Elizabeth Statmore:
To learn more about cultivating exploratory talk, read #TMC14 GWWG: Talking Points Activity – Cultivating Exploratory Talk through a Growth Mindset Activity.
What is we use powerful tools to elicit student thinking? How might we learn about students to deeply understand them as mathematicians?
And then, what actions do we take to ensure mathematical success for all?
#ChangeTheFuture
#EmbraceAmbitiousTeaching
#EmboldenYourInnerMathematician
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K5. The National Council of Teachers of Mathematics, 2017.
Statmore, Elizabeth. “Cheesemonkey Wonders.” #TMC14 GWWG: Talking Points Activity – Cultivating Exploratory Talk through a Growth Mindset Activity, 1 Jan. 1970.
Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.
Principles to Actions: Ensuring Mathematical Success for All
7:15  Welcome, Materials, Q&A

7:30  Establishing Intent, Purpose, Norm Setting

7:45  Break for Birthday Breakfast 
7:55  Talking Points from Elizabeth Statmore (@chessemonkeysf) 
8:10  Subitizing (a.k.a. Dot Talks) 
8:30  Number Talk 
8:55  Planning

9:05  Closure 
9:15  End of session 
Homework:
Additional challenges
Kaplinsky, Robert, and Peter Morris. “Closest to One.” Open Middle.
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K5. The National Council of Teachers of Mathematics, 2017.
Statmore, Elizabeth. “Cheesemonkey Wonders.” #TMC14 GWWG: Talking Points Activity – Cultivating Exploratory Talk through a Growth Mindset Activity, 1 Jan. 1970.
We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.
Goals:
At the end of the semester, teacherlearners should be able to say:
Facilitators:
Weekly schedule of topics:
Sep. 6  Subitizing and Number Talks: Elicit and use evidence of student thinking 
Sep. 13  Numeracy and Visual Learning: Elicit and use evidence of student thinking 
Sep. 20  Make sense of tasks and persevere in solving them: Facilitate meaningful mathematical discourse 
Sep. 27  Attend to Precision and Construct a Viable Argument: Facilitate meaningful mathematical discourse 
Oct. 4  Strengthen Mathematical Flexibility: Use and connect mathematical representations 
Oct. 11  Visual Patterns – Strength Mathematical Flexibility: Use and connect mathematical representations 
Oct. 18  Mathematizing Children’s Literature (part 1): Implement tasks that promote reasoning and problem solving 
Oct. 25  Mathematizing Children’s Literature (part 2): Implement tasks that promote reasoning and problem solving 
Nov. 1  Designing Intentional Number Strings: Building Procedural Fluency from Conceptual Understanding 
Nov. 8  Using Appropriate Tools Strategically: Building Procedural Fluency from Conceptual Understanding 
Nov. 15  Empowering Learners: Establish mathematical goals to focus learning 
Nov. 22  Thanksgiving 
Nov. 29  Deep Practice – challenged and learning Support productive struggle in learning mathematics 
Dec. 6  The Art of Questioning or Making Sense of Tasks part 2 Support productive struggle in learning mathematics 
Dec. 13  14 Review and Reflection: Pose purposeful questions 
Anchor Resources:
Norms:
Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K. The National Council of Teachers of Mathematics, 2017.
Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 68. The National Council of Teachers of Mathematics, 2017.
Stein, Mary Kay., and Margaret Smith. 5 Practices for Orchestrating Productive Mathematics Discussions. N.p.: n.p., n.d. Print.
Here are my notes from the session.
The agenda, shared ahead of the meeting, looked like this:
The slide deck that accompanies this plan looks like this:
We watched 4:05 minutes of Practice is Everything to renew and review our norms around teaming.
How we practice, how we team, makes a difference. The words we choose and use when offering feedback contribute to how our learners author their identity. As we work to calibrate our expectations, we can also hone and enhance our ability to offer highquality, positive, actionable feedback that empower learners to reach for their next independent level.
As seen in the slides, I used video timers to pace the teamwork time. What I learned is that the timers held me accountable for the work time promised to teachers. I was forced to wait, to be patient, and to not rush. So helpful to hold the time for our teachers.
When we focus on learning,
we hold time for learners.
And, just as we carefully plan and hold time for learning, we carefully choose what we notice and note. Words matter; the story you tell impacts how a learner is thought of and seen.
Amanda Thomas (@TrinityMrsT) found and shared the video below. I used it in our session to illustrate the power of story.
As we begin a new school year with new learners, how will we seek a balanced story, describe what we want to see next, and balance our feedback to highlight success?
What story will we notice and note?
What feedback will we offer?
What will we contribute to how learners author their identity?
How will we show we C.A.R.E.?
My team, the Academic Leadership Team, includes the Head of School, both Division Heads, the Director of Curriculum, the Director of Technology, and me. We strategically plan using our agreed upon essential learnings.
Today, I had the honor and privilege of observing members of my team launch learning based on our goals and plans. Can you see our connectedness, themes, and common language?
All School Meeting
with Joe Marshall, Head of School
Early Elementary Division Meeting
with Rhonda Mitchell, Division Head
Upper Elementary Division Meeting
with Maryellen Berry, Division Head
How might we team to meet the needs of our diverse learners? What if teaching teams plan common lessons based on guaranteed and viable curriculum? And, what can we learn when we observe each other?
#BeTogetherNotTheSame
#GrowAndLearnTogether
This conference is by teachers, for teachers. The structure of TMC contains the following lengths of presentations:
To honor Carl Oliver‘s (@carloliwitter) #PushSend request/challenge, here are my sketch notes from the sessions I attended.
Differentiating CCSS Algebra 1
— from drab to fab using Exeter Math 1 & Exploratory Talk
Elizabeth Statmore (@cheesemonkeysf)
The Politics(?) of Mathematics Teaching
Grace Chen (@graceachen)
What does it mean to say that mathematics teaching is political, and what does that mean for our moral and ethical responsibility as mathematics teachers?
Bridging elementary skills & concepts to high school & beyond
Glenn Waddell, Jr. (@gwaddellnvhs)
Microdecisions in Questioning
David Petersen (@calcdave)
All I Really Need To Know I Learned From The MTBoS
…Not Really, But Close
Graham Fletcher (@gfletchy)
Hitting The Darn ‘Send’ Button
Carl Oliver (@carloliwitter)
Practical Ideas on the Kind of Coaching
We Need to Provide and Demand
Steve Leinwand (@steve_leinwand)
What is not captured in my notes is play: game night, trivia, crocheting, and tons of fun.
How might we grow, learn, and play in community when together and when apart?
Below are my sketch notes from the session I attended.
Desmos and Assessment
Julie Reulbach (@jreulbach)
Principles for Building Activities
Michael Fenton (@mjfenton)
Keynote:
Annie Fetter (@MFAnnie)
Calculus for All
Chase Orton (mathgeek76)