Category Archives: Learning

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.

Activity:

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.

PD Planning: #Mathematizing Read Alouds part 2

Time. We need more of it.

How might we gain time without adding minutes to our schedule?

What if we mathematize our read-aloud books to use them in math as well as reading and writing workshop? Could it be that we gain minutes of reading if we use children’s literature to offer context for the mathematics we are learning? Could we add minutes of math if we pause and ask mathematical questions during our literacy block?

Becky Holden and I planned the following professional learning session to build common understanding and language as we expand our knowledge of teaching numeracy through literature.  Every Kindergarten, 1st Grade, 2nd Grade, and 3rd Grade math teacher participated in 3.5-hours of professional learning over the course of two days.

Have you read How Many Seeds in a Pumpkin? by Margaret McNamara, G. Brian Karas?

Learning Targets:

Mathematical Practice:

  • I can make sense of tasks and persevere in solving them.

2nd Grade

  • I can work with equal groups of objects to gain foundations for multiplication.
  • I can skip-count by 2s, 5, 10s, and 100s within 1000 to strengthen my understanding of place value.

3rd Grade

  • I can represent and solve problems involving multiplication and division.
  • I can use place value understanding and properties of operations to perform multi-digit arithmetic.

Learning Progressions:

I can apply mathematical flexibility.
#ShowYourWork Algebra

Here’s what it looked like:

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Here’s some of what the teacher-learners said:

I learned to look at books with a new critical eye for both literacy and mathematical lessons. I learned that I can read the same book more than once to delve deeper into different skills. This is what we are learning in Workshop as well. Using a mentor text for different skills is such a great way to integrate learning.

I learned how to better integrate math with other subjects as well as push pass the on answer and look for more than one way to answer the question as well as show in more than one way how I got that answer and to take that to the classroom for my students.

I learned how to integrate literacy practice and math practice at once. In addition, I also learned how to deepen learning and ask higher thinking questions, as well as how to let students answer their own questions and have productive struggle.

I learned that there are many different ways to notice mathematical concepts throughout books. It took a second read through for me to see the richness in the math concepts that could be taught.

I learned that there are many children’s literature that writes about multiple mathematical skills and in a very interesting way!

How might we notice and note opportunities to pause, wonder, and question? What is to be gained by blending learning?

Harnessing the Power of the Purposeful Task with @GFletchy #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 6, Harnessing the Power of the Purposeful Task, with Graham Fletcher.


Notes from previous sessions:

Anticipating @IllustrateMath’s 6.RP Overlapping Squares

To anchor our work in differentiation and mathematical flexibility, we use NCTM’s 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret Smith and Mary Kay Stein.

Kristi Story, Becky Holden, and I worked together during our professional learning time to meet the goals for the session shown below.

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.

The learning goals for students include:

I can use ratio reasoning to solve problems and understand ratio concepts.

I can make sense of tasks and persevere in solving them.

I can look for and make use of structure.

I can notice and note to make my thinking visible.

Kristi selected Illustrative Math’s  6.RP Overlapping Squares task for students. Here are the ways we anticipated how students would approach and engage with the task.

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Our plan for helping students who are stuck includes providing and encouraging the use of a graphing tool such as graph paper or TI-Nspire software installed on their MacBooks. We also intend to use the following learning progressions.

I can make sense of tasks and persevere in solving them.

I can look for and make use of structure.

Finally, we also want our learners to work on how they show their work.

#ShowYourWork Subtraction

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


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.

Stein, Mary Kay., and Margaret Smith. 5 Practices for Orchestrating Productive Mathematics Discussions. N.p.: n.p., n.d. Print.