Category Archives: Reflection

Connecting Ideas, Creativity, Professional Development Plans, Questions, Reading, Reflection

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

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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.

#LL2LU, Ask Don't Tell, Connecting Ideas, Learning Progressions, Professional Development Plans, Questions, Reflection

Embolden Your Inner Mathematician Week 1: Number Talks

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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.

Conferences, Connecting Ideas, Learning, Questions, Reflection

The Science of Early Learning and Adversity: Daily Leadership to Promote Development and Buffer Stress Day 1

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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. This professional development features keynote speaker Walter Gilliam (@WalterGilliam).

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?

Agenda (with my notes)

Today’s Early Education Landscape
with Nonie Lesaux and Stephanie Jones

Understanding Stress and Behavior
in the Early Education Environment
with Walter Gilliam
Director of The Edward Zigler Center in Child Development and Social Policy and Associate Professor of Child Psychiatry and Psychology, Yale University Child Study Center

Reflection and Application
with Walter Gilliam and the Zaentz Team
facilitated by Robin Kane

Strategic Planning Session
facilitated by Robin Kane and Emily Bautista

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

  • Micro-stresses pile up.
  • How might we pay attention to and recognize stress?
    (Student stress, teacher stress, family stress, leadership stress.)
  • Empathy: Who is it given to? From whom is it withheld?
  • What are we looking for and who are we looking at?
  • How might we anticipate expected “unexpected” events?
  • What structures can be put in place to support learners, teachers, families, leaders?
  • When sharing information about a learner, check intent. Are we sharing knowledge and understanding to support the learner?
    • Can we offer evidence to show what we know and understand?
    • Can we share information without adding judgement and labels?
  • How do I and who helps me check my bias?
Assessment, Connecting Ideas, Learning, Questions, Reading, Reflection, Sketch Notes

#LessonClose with @TracyZager at #MtHolyokeMath

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I’m taking X.MTHED-404: Effective Practices for Advancing the Teaching and Learning of Mathematics (K-12).

Here are my notes from Session 8, Lesson Close with Tracy Zager.

Tracy’s session connects, for me, to a practitioner’s corner in David Sousa’s How the Brain Learns.  He writes

Closure describes the covert process whereby the learner’s working memory summarizes for itself its perception of what has been learned.  It is during closure that a student often completes the rehearsal process and attaches sense and meaning to the new learning, thereby increasing the probability that it will be retained in long-term storage. (p. 69)

How might we take up Tracy’s challenge to “never skip the close?” What new habits must we gain in order to make sure the close is useful to the learner?

Sousa continues

Closure is different from review. In review, the teacher does most of the work, repeating key concepts made during the lesson and rechecking student understanding.  In closure, the student does most of the work by mentally rehearsing and summarizing those concepts and deciding whether they make sense and have meaning. (p. 69)

What new habits must we gain in order to make sure the close is helps them reflect on learning, make connections, and/or ask new questions? In other words, do we plan intention time for learners to make sense of the task?

Closure is an investment than can pay off dramatically in increased retention of learning. (Sousa, p. 69)

Sousa, David A. How the Brain Learns. Thousand Oaks, CA: Corwin, a Sage, 2006. Print.

Conferences, Connecting Ideas, Creativity, Learning, Reflection, Sketch Notes

#NCSM17 #Sketchnotes Wednesday Summary

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I’m attending the  National Council of Supervisors of Mathematics  2017 conference in San Antonio.  Here are my notes from Wednesday along with the session descriptions from the presenters.

Conferring with Young Mathematicians at Work:
The Process of Teacher Change
Cathy Fosnot

If children are to engage in problem solving with tenacity and confidence, good questioning on the part of teachers during conferrals is critical. Questioning must engender learner excitement and ownership of ideas, while simultaneously be challenging enough to support further development. Video of conferrals in action will be used for analysis, and a Landscape of Learning on the process of teacher change is shared as a lens for coaching.

Leading to Support Procedural Fluency for All Students
Jennifer Bay-Williams

Principles to Actions describes effective teaching practices that best support student learning. In this session we will focus on one of those teaching practices: “build procedural fluency from conceptual understanding.” Ensuring that every child develops procedural fluency requires understanding what fluency means, knowing research related to developing procedural fluency and conceptual understanding, and being able to translate these ideas into effective classroom practices. That is the focus of this session! We will take a look at research, connections to K–12 classroom practice, and implications for us as coaches and teacher leaders.

How to Think Brilliantly and Creatively in Mathematics: Some Guiding Thoughts for Teachers, Coaches, Students—Everyone!
James Tanton

This lecture is a guide for thinking brilliantly and creatively in mathematics designed for K–12 educators and supervisors, students, and all those seeking joyful mathematics doing. How do we model and practice uncluttered thinking and joyous doing in the classroom, pursue deep understanding over rote practice and memorization, and promote the art of successful ailing? Our complex society demands of its next generation not only mastery of quantitative skills, but also the confidence to ask new questions, explore, wonder, fail, persevere, succeed in solving problems and to innovate. Let’s not only send humans to Mars, let’s also foster in our next generation the might to get those humans back if something goes wrong! In this talk, I will explore five natural principles of mathematical thinking. We will all have fun seeing how school mathematics content is a vehicle for masterful ingenuity and joy.

Deep Practice:
Building Conceptual Understanding in the Middle Grades
Jill Gough, Jennifer Wilson

How might we attend to comprehension, accuracy, flexibility, and then efficiency? What if we leverage technology to enhance our learners’ visual literacy and make connections between words, pictures, and numbers? We will look at new ways of using technology to help learners visualize, think about, connect and discuss mathematics. Let’s explore how we might help young learners productively struggle instead of thrashing around blindly.

When Steve Leinwand asked if I was going to sketch our talk, I jokingly said that I needed someone to do it for me. We are honored to have this gift from Sharon Benson. You can see additional details on my previous post.

Conferences, Connecting Ideas, Reflection, Sketch Notes

#NCSM17 #Sketchnotes Tuesday Summary

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I’m attending the  National Council of Supervisors of Mathematics  2017 conference in San Antonio.  Here are my notes from Tuesday along with the session descriptions from the presenters.

Tracking, Equity, and the Many Paradoxes of Algebra II
Jason Zimba

What is Algebra II good for? For whom is it good? Phil Daro raised these and other questions for the Carnegie-Institute for Advanced Study Commission. Fast forward to now, and the debate about ‘what mathematics and why’ has found its way into the pages of the popular press. Is there anything district leaders can learn from this conversation? How might a district leader who prizes equity think about the question of tracking in school mathematics?

Routines for Reasoning:
Ensuring All Students Are Mathematical Thinkers
Amy Lucenta, Grace Kelemanik

Instructional routines embody research-based best practices for struggling learners, especially when they focus on the Standards for Mathematical Practice and include ‘baked in’ supports
for special populations. Participants will explore a universally designed instructional routine, Connecting Representations, and learn how to leverage it to develop teachers’ capacity to ensure development of ALL students’ mathematical practices.

Letting Go: Cultivating Agency and Authority Through Number Talks in the Secondary Mathematics Classroom
Cathy Humphreys

In this session I share my dissertation study of two high school teachers as they learned to enact Number Talks. I wanted to know what the teachers found most challenging and how coaching supported their learning. In examining the videos of classroom lessons, I noticed marked differences in how agency and authority emerged in the two classes. I hope what I learned while searching for “Why?” will be useful for teachers and coaches alike.

Winning the Game in Mathematics Leadership
Matt Owens

Mathematics leadership is multifaceted in nature as we strive to intentionally impact students and educators in classrooms nationwide. Leadership pathways can be different from leader to leader, but ultimately curriculum/ content, instruction, activism, and assessment (CIAA) are all areas of evaluation for “PRIME” leaders in mathematics education. Discover the top seven practical strategies for overcoming the struggles that may arise in your role as a mathematics leader within your school/university, district, state, and national professional learning communities, while building the capacity of teachers’ leadership among mathematics educators in these respective communities.

Approaching Ten Tough Mathematical Ideas
for High School Students
Salmon Usiskin

The main purpose of this talk is to provide insights into mathematical content that many mathematics teachers may not have seen. By covering a broad range of content, from aspects of manipulative algebra through proof in geometry and in general, discussing language, applications, and representations, my remarks are designed for leaders to help in decisions they make in the professional development of their teachers.

Conferences, Connecting Ideas, Reflection, Sketch Notes

#NCSM17 #Sketchnotes Monday Summary

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I’m attending the  National Council of Supervisors of Mathematics  2017 conference in San Antonio.  Here are my notes from Monday along with the session descriptions from the presenters.

Knocking Down Barriers with Technology
Eli Luberoff

One-to-one. Accessibility. Personalization. Internationalization. Low oor. High ceiling. What do these all have in common? Each is targeted to making mathematics work for every student. Not just the con dent students with engaged parents, not just the struggling students, every student. We will explore the technology and techniques that can open doors, challenge the bored, empower the disempowered, and turn every student into a mathematics student.

Gut Instincts: Developing ALL Students’ Mathematical Intuitions
Tracy Zager

We’ve long misunderstood mathematical intuition, assuming it’s innate rather than developed through high-quality learning experiences. As a result, students who haven’t yet had opportunities to foster their intuitions are often denied access to meaningful mathematics. Through analysis of powerful classroom teaching and learning, we’ll explore three instructional strategies you can use to empower ALL students to grasp mathematics intuitively.

Problem Strings to Change Teaching Practice
Pam Harris

A problem string is a purposefully designed sequence of related problems that helps students mentally construct mathematical relationships and nudges them toward a major, efficient strategy, model, or big idea. We show how problem strings can be leveraged for changing teachers’ practice. Because it puts students’ ideas at the center, teachers are forced to listen deeply to kids and structure mathematics conversations around their thinking.

Rethinking Expressions and Equations:
Implications for Teacher Leaders
Michelle Rinehart

How are one- and two-variable expressions, one- and two- variable equations, and the standard form of a line connected in a powerful way? How might this progression support student learning of these “tough-to-teach/tough-to-learn” ideas? Explore the underlying theme that uni es these seemingly disparate topics using a technology-leveraged approach. Consider research and the role of teacher leaders in developing real understanding of these topics.

Talk Less and Listen More
Zachary Champagne

It’s a simple, and very complex, idea that great teachers
do and do well. Genuinely listening to students can yield incredible opportunities for teachers to not only know and connect with their students, but also increase the quality of teaching and learning that happens in the classroom. Join us as we explore the power of listening to students and using that information to inform our instruction. We’ll also explore strategies to help provide the supportive conditions and frameworks to help leaders support teachers in doing this work. We’ll do this through examining video clips of students sharing their mathematical ideas and consider what listening affords and what questions could be asked to further their mathematical thinking.