Category Archives: Questions

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

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?

Deep Practice: Building Conceptual Understanding in the Middle Grades

2017 NCSM Annual Conference
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.

Deep practice is built on a paradox: struggling in certain targeted ways — operating at the edges of your ability, where you make mistakes — makes you smarter. Or to put it a slightly different way, experiences where you’re forced to slow down, make errors, and correct them —as you would if you were walking up an ice-covered hill, slipping and stumbling as you go— end up making you swift and graceful without your realizing it. (Coyle, 18 pag.)

The second reason deep practice is a strange concept is that it takes events that we normally strive to avoid —namely, mistakes— and turns them into skills. (Coyle, 20 pag.)

This term productive struggle captures both elements we’re after: we want students challenged and learning. As long as learners are engaged in productive struggle, even if they are headed toward a dead end, we need to bite our tongues and let students figure it out. Otherwise, we rob them of their well-deserved, satisfying, wonderful feelings of accomplishment when they make sense of problems and persevere. (Zager, 128 pag.)


Coyle, Daniel. The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. (p. 18-20). Random House, Inc.. Kindle Edition.

Zager, Tracy. Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Portland, ME.: Stenhouse Publishers, 2017. (pp. 128-129) Print.

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?

Productive struggle with deep practice – what do experts say

NCTM’s publication, Principles to Action, in the Mathematics Teaching Practices, calls us to support productive struggle in learning mathematics. How do we encourage our students to keep struggling when they encounter a challenging task? How many learners are accustomed to giving up when they can’t solve a problem immediately and quickly. How do we change the practice of how our students learn mathematics?

Effective teaching not only acknowledges the importance of both conceptual understanding and procedural fluency but also ensures that the learning of procedures is developed over time, on a strong foundation of understanding and the use of student-generated strategies in solving problems. (Leinwand, 46 pag.)

Low floor, high ceiling tasks allow all students to access ideas and take them to very high levels. Fortunately, [they] are also the most engaging and interesting math tasks, with value beyond the fact that they work for students of different prior achievement levels. (Boaler, 115 pag.)

Deep learning focuses on recognizing relationships among ideas.  During deep learning, students engage more actively and deliberately with information in order to discover and understand the underlying mathematical structure. (Hattie, 136 pag.)

Deep practice is built on a paradox: struggling in certain targeted ways — operating at the edges of your ability, where you make mistakes — makes you smarter.  (Coyle, 18 pag.)

Or to put it a slightly different way, experiences where you’re forced to slow down, make errors, and correct them —as you would if you were walking up an ice-covered hill, slipping and stumbling as you go— end up making you swift and graceful without your realizing it. (Coyle, 18 pag.)

The second reason deep practice is a strange concept is that it takes events that we normally strive to avoid —namely, mistakes— and turns them into skills. (Coyle, 20 pag.)

We need to give students the opportunity to develop their own rich and deep understanding of our number system.  With that understanding, they will be able to develop and use a wide array of strategies in ways that make sense for the problem at hand. (Flynn, 8 pag.)

…help students slow down and really think about problems rather than jumping right into solving them. In making this a routine approach to solving problems, she provided students with a lot of practice and helped them develop a habit of mind for reading and solving problems. (Flynn, 8 pag.)

This term productive struggle captures both elements we’re after:   we want students challenged and learning. As long as learners are engaged in productive struggle, even if they are headed toward a dead end, we need to bite our tongues and let students figure it out. Otherwise, we rob them of their well-deserved, satisfying, wonderful feelings of accomplishment when they make sense of problems and persevere. (Zager, 128-129 ppg.)

Encourage students to keep struggling when they encounter a challenging task.  Change the practice of how our students learn mathematics.

Let’s not rob learners of their well-deserved, satisfying, wonderful feelings of accomplishment when they make sense of problems and persevere.


Boaler, Jo. Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (p. 115). Wiley. Kindle Edition.

Coyle, Daniel. The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. (p. 20). Random House, Inc.. Kindle Edition.

Flynn, Michael, and Deborah Schifter. Beyond Answers: Exploring Mathematical Practices with Young Children. Portland, ME: Stenhouse, 2017. (p. 8) Print.

Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy, Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series) (p. 136). SAGE Publications. Kindle Edition.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.

Zager, Tracy. Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Portland, ME.: Stenhouse Publishers, 2017. (pp. 128-129) Print.

#ShowYourWork, make sense and persevere, flexibility with @IllustrateMath

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.

I taught 6th grade math today while Kristi and her team attended ASCD.  She asked me to work with our students on showing their work.  Here’s the plan:

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.

Activities:

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:

Sample student work:

Mathematizing Read-Alouds

Mathematizing Read-Alouds
KSU Conference on Literature for Children and Young Adults
March 21, 2017
Becky Holden, Trinity School
Megan Noe, Trinity School
Jill Gough, Trinity School

How might we deepen our understanding of numeracy using Children’s literature? What if we mathematize our read aloud books to use them in math as well as reading and writing workshop? We invite you to listen and learn while we share ways to deepen understanding of numeracy and literacy. Come exercise your mathematical flexibility to show what you know more than one way.

Books on which to practice: