# #NCTMLive #T3Learns Webinar: Implement tasks that promote reasoning and problem solving, and Use and connect mathematical representations

On Wednesday, May 2, 2018, Jennifer Wilson (@jwilson828) and I co-facilitated the second webinar in a four-part series on the Eight Mathematics Teaching Practices from NCTM’s Principles to Actions: Ensuring Mathematical Success for All.

Implement tasks that promote reasoning and problem solving,
and Use and connect mathematical representations.

Effective teaching of mathematics facilitates discourse among learners to build shared understanding of mathematical ideas by analyzing and comparing approaches and arguments.

• How might we implement and facilitate tasks that promote productive discussions to strengthen the teaching and learning of mathematics in all our teaching settings – teaching students and teaching teachers?
• What types of tasks encourage mathematical flexibility to show what we know in more than one way?

Our slide deck:

Our agenda:

 7:00 Jill/Jennifer’s Opening remarks Share your name and grade level(s) or course(s). Norm setting and Purpose 7:05 Number Talk: 81 x 25 Your natural way and Illustrate Decompose into two or more addends (show it) Show your work so a reader understands without asking questions Share work via Twitter using #NCTMLive or bit.ly/nctmlive52 7:10 #LL2LU Use and connect mathematical representations Self-assess where you are Self-assessment effect size Think back to a lesson you taught or observed in the past month. At what level did you or the teacher show evidence of using mathematical representations? 7:15 Task:  (x+1)^2 does/doesn’t equal x^2+1 7:25 Taking Action (DEI quote) 7:30 #LL2LU Implement Tasks That Promote Reasoning and Problem Solving 7:35 Graham Fletcher’s Open Middle Finding Equivalent Ratios 7:45 Illustrative Mathematics: Jim and Jesse’s Money 7:55 Close and preview next in the series

Some reflections from the chat window:

I learned to pay attention to multiple representations that my students will create when they are allowed the chance to think on their own.  I learned to ask myself how am I fostering this environment with my questioning.

I learned to pay attention to the diversity of representations that different students bring to the classroom and to wait to everyone have time to think

I learned to pay attention (more) to illustrating work instead of focusing so much on algebraic reasoning in my approach to teaching Algebra I. I learned to ask myself how could I model multiple representations to my students.

I learned to pay attention to multiple representations because students all think and see things differently.

I learned to make sure to give a pause for students to make the connections between different ways of representing a problem, rather than just accepting the first right answer and moving on.

I learned to pay attention to the ways that I present information and concepts to children… I need to include more visual representations when I working with algebraic reasoning activities.

Cross posted on Easing the Hurry Syndrome

# Overview: Embolden Your Inner Mathematician

Taking action on known national goals, 15 Trinity School teacher-learner-leaders will begin a semester-long professional learning journey to deepen our understanding of NCTM’s Effective Mathematics Teaching Practices.

We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.

Goals:

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

• I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.
• 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.

Facilitators:

Weekly schedule of topics:

 Sep. 6 Subitizing and Number Talks:  Elicit and use evidence of student thinking Sep. 13 Numeracy and Visual Learning:  Elicit and use evidence of student thinking Sep. 20 Make sense of tasks and persevere in solving them:  Facilitate meaningful mathematical discourse Sep. 27 Attend to Precision and Construct a Viable Argument: Facilitate meaningful mathematical discourse Oct. 4 Strengthen Mathematical Flexibility: Use and connect mathematical representations Oct. 11 Visual Patterns – Strength Mathematical Flexibility: Use and connect mathematical representations Oct. 18 Mathematizing Children’s Literature (part 1): Implement tasks that promote reasoning and problem solving Oct. 25 Mathematizing Children’s Literature (part 2): Implement tasks that promote reasoning and problem solving Nov. 1 Designing Intentional Number Strings: Building Procedural Fluency from Conceptual Understanding Nov. 8 Using Appropriate Tools Strategically: Building Procedural Fluency from Conceptual Understanding Nov. 15 Empowering Learners: Establish mathematical goals to focus learning Nov. 22 Thanksgiving Nov. 29 Deep Practice – challenged and learning Support productive struggle in learning mathematics Dec. 6 The Art of Questioning or Making Sense of Tasks part 2 Support productive struggle in learning mathematics Dec. 13 14 Review and Reflection: Pose purposeful questions

Anchor Resources:

Norms:

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-. The National Council of Teachers of Mathematics, 2017.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 6-8. The National Council of Teachers of Mathematics, 2017.

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

# #NCTMRegionals Day 1 notes

Sharing my day one notes from the NCTM Regional Conference in Philadelphia:

Peg Cagle: Teacher Leadership – Advocating for ourselves, our students, our profession.

“The difference between listening and pretending to listen, I discovered, is enormous. One is fluid, the other is rigid. One is alive, the other is stuffed. Eventually, I found a radical way of thinking about listening. Real listening is a willingness to let the other person change you. When I’m willing to let them change me, something happens between us that’s more interesting than a pair of dueling monologues.” – Alan Alda

Becky Holden: Building Understanding – Meeting Students Where They Are

Kristin Gray: Lesson Planning That Begins with Student Thinking

# #NCTMRegionals Inspire, Innovate, IGNITE! sketchnote

I had the opportunity to attend, live tweet, and sketch the 2016 Regional Conference & Exposition in Philadelphia opening session Inspire, Innovate, IGNITE! delivered by Chike Akua, Jimmie L. Davis, Matthew Larson, Sara Moore, Tom Reardon, Michael Steele, and Rose Mary Zbiek.

I am grateful to Bob Lochel for sharing an artifact of evidence of my work.

If interested, you can check out the presenters’ slide decks to add context to my notes at NCTM’s blog.