# #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

# 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?