Category Archives: Questions

Embolden Your Inner Mathematician Week 2: Contemplate then Calculate (#CthenC)

For our second session of Embolden Your Inner Mathematician, we focus on Numeracy and Visual Learning: Elicit and use evidence of student thinking.

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, so-called “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 teacher-learner-leaders 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 K-Grade 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, high-quality 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, high-quality 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 339-346). 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 K-5. The National Council of Teachers of Mathematics, 2017.

Embolden Your Inner Mathematician Week 1: Number Talks

How might we deepen our understanding of NCTM’s teaching practices? What if we team to learn and practice?

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 K-Grade 5

Meeting the demands of world-class 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, high-quality 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, high-quality 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 K-5. The National Council of Teachers of Mathematics, 2017.

Embolden Your Inner Mathematician Week 1: Talking Points

How might we deepen our understanding of NCTM’s teaching practices? What if we team to learn and practice?

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 K-Grade 5

Meeting the demands of world-class 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, high-quality 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, high-quality 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 well-being 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 K-5. 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.

Instructional Core practice #WordsMatter How will we show we CARE?

As part of our school’s Pre-Planning, I facilitated a faculty-teams workshop to continue our work and learning in the Instructional Core.

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 high-quality, 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.?

 

 

Lesson Study: different teachers, common lesson plan, guaranteed and viable curriculum

What if we share common mission and vision? How might we express our style, individuality, and personality while holding true to a plan and the essentials to learn?

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 SchoolJoeMarshallAug8-17

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

Sketch notes from #TMC17 (a.k.a. Twitter Math Camp)

Becky Holden (@bholden86) and I attended Twitter Math Camp (#TMC17) at Holy Innocents Episcopal School in Atlanta, GA from Thursday, July 27 to Sunday, July 30.

This conference is by teachers, for teachers. The structure of TMC contains the following lengths of presentations:

  • Morning sessions (One session that meets Thursday, Friday and Saturday mornings for 2 hours each morning)
  • Afternoon sessions (Individual 1/2 hour sessions on Thursday)
  • Afternoon sessions (Individual 1 hour sessions Thursday, Friday and Saturday)

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)

Micro-decisions 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?

The Science of Early Learning and Adversity: Daily Leadership to Promote Development and Buffer Stress Day 2

Rhonda Mitchell (@rgmteach) and I are attending The Science of Early Learning and Adversity: Daily Leadership to Promote Development and Buffer Stress at The Saul Zaentz Professional Learning Academy.

How can early education leaders support the design and implementation of strong early learning environments—those that buffer stress, reduce challenging behaviors, and promote development?

Day 2 Agenda (with my notes)

Classroom Strategies to Decrease
and Respond to Disruptive Behaviors
Amanda Williford
Research Associate Professor, University of Virginia, Curry School of Education, Center for Advanced Study of Teaching and Learning (CASTL)

Reflection and Application
Amanda Williford and the Zaentz Team

Strategic Planning Session
Nonie Lesaux and Robin Kane

Universal Design for Equity and Strong Early Learning
Thomas Hehir
Silvana and Christopher Pascucci Professor of Practice in Learning Differences, Harvard Graduate School of Education

My list to think about, reflect on, and grapple with from today includes:

  • How might we meet the needs of diverse learners?
  • How might we develop and strengthen strong positive bonds and relationships?
  • How can we shift the dialog to “what does this learner need from me?” How can we embrace the power of positivity to make change?
  • Can we grow into a  5:1 ratio to make change and leverage the power of positivity?
  • Can we strength our norm of no labels so that we describe what a learner can do and the next step?
  • Can we embrace the Theory of Change to gain clarity?
    structures vs. processes; outputs vs. outcomes, etc.
  • How might we improve learning for all and deepen our understanding of differentiation?