#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:

Revealing Reader’s Thinking: Doodling, Digitalizing, and Deepening Learning

Revealing Reader’s Thinking:
Doodling, Digitalizing, and Deepening Learning
KSU Conference on Literature for Children and Young Adults
March 20 and March 21
Amanda Thomas, Trinity School
Jill Gough, Trinity School

We invite you to listen and learn while we share ways to enhance the Reader’s Notebook. We will demonstrate ways to reveal student thinking through multiple strategies and modalities inspired by Lester Laminack, Kylene Beers, Robert Probst, Jennifer Serravallo, Lucy Calkins, and more! Experience something you can try out tomorrow!

Don’t miss the artifacts of student learning in our slide deck. Just click on this slide to access the complete deck.

Resources

Sample Reader’s Response learning progressions  

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.

This slideshow requires JavaScript.

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.

Goal Work: design and implement a differentiated action plan

As an Academic Leadership Team, Maryellen BerryRhonda MitchellMarsha Harris, and I continue to work on our common goal.

By the end of this year, all teachers should be able to say We can design and implement a differentiated action plan across our grade to meet all learners where they are.

To highlight our commitment to empowering learners to act as agents of their own learning, we continue to share the following progression as a pathway for teams to learn and stretch.

You can see our previous plans here and here. For today’s Wednesday Workshop, we only had about 45 minutes to work and learn together.  As the Academic Leadership Team, we asked ourselves how we might make time for faculty to learn in targeted ways?  We challenged ourselves to model what we want to see from our faculty. So today’s goal is

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

Here is the big picture for our plan.Here are the details from the Pre-K – 6th literacy PD:

Here are the details for Early Leaners PD: Here are the details for Math PD:

Teachers of Specials and Learning Team also had different learning plans to differentiate for our readers and the social-emotional and character building work.

We hope our faculty can see that we strive to serve as their teacher team and that we embrace the norm be together, not the same.

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

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

Sneak peek: Leading Mathematics Education in the Digital Age

Leading Mathematics Education in the Digital Age
2017 NCSM Annual Conference
Pre-Conference Session
Sunday, April 2, 2017 from 1:00-5:00 p.m.
Jennifer Wilson
Jill Gough

How can leaders effectively lead mathematics education in the era of the digital age? There are many ways to contribute in our community and the global community, but we have to be willing to offer our voices. How might we take advantage of instructional tools to purposefully ensure that all students and teachers have voice: voice to share what we know and what we don’t know yet; voice to wonder what if and why; voice to lead and to question.

Sneak peek for our session includes:

How might we strengthen our flexibility to make sense and persevere? What if we deepen understanding to show what we know more than one way?

Interested? Here’s a sneak peek at a subset of our slides as they exist today. Disclaimer: Since this is a draft, the slides may change before we see you in San Antonio.

I wonder what Jennifer’s sneak peek looks like? Do you?

Using technology alongside #SlowMath to promote productive struggle

Using technology alongside #SlowMath
to promote productive struggle
2017 T³™ International Conference
Sunday, March 12, 8:30 – 10 a.m.
Columbus AB, East Tower, Ballroom Level
Jennifer Wilson
Jill Gough

One of the Mathematics Teaching Practices from the National Council of Teachers of Mathematics’ (NCTM) “Principles to Actions” is to support productive struggle in learning mathematics.

  • How does technology promote productive struggle?
  • How might we provide #SlowMath opportunities for all students to notice and question?
  • How do activities that provide for visualization and conceptual development of mathematics help students think deeply about mathematical ideas and relationships?

[Cross posted at Easing the Hurry Syndrome]