Fall PD Opportunity: Embolden Your Inner Mathematician

How do we effectively lead mathematics education in the era of the digital age?  We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.  

To build confidence as well as a more visual approach to elementary mathematics learning and teaching, we have designed ongoing, early morning, job-embedded professional learning around teaching practices and current research. 


At the end of the semester, teacher-learners should be able to say:

  • I can exercise mathematical flexibility to show what I know in more than one way.
  • I can make sense of tasks and persevere in solving them.
  • I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.


The weekly schedule of topics are as follows:

If you are  interested in emboldening your inner mathematician and would like to join us, please contact us for additional details.

Jill Gough | Director of Teaching & Learning
jgough@trinitatl.org | @jgough
Trinity School | www.trinityatl.org
4301 Northside Parkway | Atlanta, GA 30327
Phone 404.240.6220 | Fax 404.231.8111
Blog: Experiments in Learning by Doing
Blog: Jill Gough notes

Summer Learning 2017 – Choices and VTR – here’s the data

In a previous post, Summer Learning 2017 – Flyer and Choices, I describe our summer learning plans and choices.  We make a commitment to read and learn every summer.  This year, in addition to books and a stream of TED talks, Voices of Diversity, we offer the opportunity to read children’s literature and design learning intentions around character and values.

Here’s the data on what we selected to learn:

Another way to consider the data:

Throughout the year, the Academic Leadership Team has been working with teacher-teams in many ways in support of our team goal shown below.

We can design and implement a differentiated action plan across our  divisions to meet all learners where they are.

Tier 1 Differentiation: Learner Choice and Voice

Our plan involves using the Visible Thinking Routine Sentence-Phrase-Word across all selections to notice and note important, thought-provoking ideas.

Tier 2 Differentiation: Level Up Pathway to Success

To meet our expectations, learners should read, view, or plan closely using the Visible Thinking Routine Sentence-Phrase-Word when engaging with their selection.  To exceed our expectations, learners again have choice.  They can use both Sentence-Phrase-Word and Connect-Extend-Challenge for deeper, connected thinking. Or, learners can learn and share publicly using #TrinityLearns, #TrinityReads or posting comments on the connected blog pages for reading a book, viewing the TED talks, or using children’s literature to build character foundation.

Be together, not the same. Learn and share. Level up when you can.

#LessonClose with @TracyZager at #MtHolyokeMath

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.

Summer Learning 2017 – Choices and VTR

How do we learn and grow when we are apart? We workshop, plan, play, rest, and read to name just a few of our actions and strategies.

We make a commitment to read and learn every summer.  This year, in addition to books and a stream of TED talks, Voices of Diversity, we offer the opportunity to read children’s literature and design learning intentions around character and values.

Below is the Summer Learning flyer announcing the choices for this summer.

We will continue to use the Visible Thinking Routine Sentence-Phrase-Word to notice and note important, thought-provoking ideas. This routine aims to illuminate what the reader finds important and worthwhile.

Sentence-Phrase-Word helps learners to engage with and make meaning from text with a particular focus on capturing the essence of the text or “what speaks to you.” It fosters enhanced discussion while drawing attention to the power of language. (Ritchhart, 207 pag.)

However, the power and promise of this routine lies in the discussion of why a particular word, a single phrase, and a sentence stood out for each individual in the group as the catalyst for rich discussion . It is in these discussions that learners must justify their choices and explain what it was that spoke to them in each of their choices. (Ritchhart, 208 pag.)

Continuing to work on our goal, We can design and implement a differentiated action plan across our divisions school to meet all learners where they are, we make our thinking visible on ways to level up.

When we share what resonates with us, we offer others our perspective.  What if we engage in conversation to learn and share from multiple points of view?

Ritchhart, Ron, Mark Church, and Karin Morrison. Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners. San Francisco, CA: Jossey-Bass, 2011. Print

Building and Sustaining the Culture of Problem Solving in our Classroom with @FawnPNguyen #MtHolyokeMath

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

Here are my notes from Session 7, Building and Sustaining the Culture of Problem Solving in our Classroom, with Fawn Nguyen

I am struck by Fawn’s initial purpose. Building and sustaining a culture of problem solving in our classrooms demands vision with plans and commitment with continual growth through feedback.

How to we make use of structure in our planning to narrow our resources to build and sustain coherence and connectedness? Wen we plan, are we intentionally connecting to standards and intentionally stepping away from them to promote problem solving, visual learning, and deepening understanding?

What tasks do we select? How much time do we spend? And, most importantly, how do we show faith in our learners to promote productive, creative struggle?

Notes from previous sessions:


Anticipating @IllustrateMath’s Jim and Jesse’s Money

How might we learn to show our work so that a reader understanding without having to ask questions? As we work with our young learners, we want them to grow as mathematicians and as communicators.

We ask students to show their work so that a reader understands without having to ask them questions. What details should we add so that our thinking is visible to others?

To show (and to assess) comprehension, we are looking for mathematical flexibility.

Learning goals:

  • I can use ratio and rate reasoning to solve real-world and mathematical problems.
  • I can show my work so that a reader can understanding without having to ask questions.


Learning progressions:

Level 4:
I can demonstrate mathematical flexibility with ratio and rate reasoning to show what I know more than one way using tables, equations, double number lines, etc..

Level 3:
I can use ratio and rate reasoning to solve real-world and mathematical problems.

Level 2:
I can make tables of equivalent ratios relating quantities with whole-number measurements, and I can use tables to compare ratios.

Level 1:
I can use guess and check to solve real-world and mathematical problems.

Anticipated solutions:

Using Appropriate Tools Strategically:

I wonder if any of our learners would think to use a spreadsheet. How might technology help with algebraic reasoning? What is we teach students to create tables based on formulas?

How might we experiment with enough tools to display confidence when explaining my reasoning, choices, and solutions?

Choice of an appropriate tool is learner based. How will we know how different tools help unless we experiment too?

#NCSM17 #Sketchnotes Wednesday Summary

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.

Seeking brightspots and dollups of feedback about learning and growth.

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