Category Archives: #LL2LU

Traverse session: Experiential and Instructional: Promoting Productive Mathematical Struggle #tvrse18

At Traverse Boulder, I facilitated the following session on Tuesday, June 5, 2018.

Experiential and Instructional:
Promoting Productive Mathematical Struggle

How might we implement tasks that promote reasoning and problem solving to deepen conceptual understanding? Let’s identify and implement high quality tasks grounded in real experiences. Advancing the teaching and learning of mathematics cannot be accomplished with decontextualized worksheets. Discuss, sketch, and solve tasks that promote flexibility, creative and critical reasoning, and problem solving. Learning math should be anchored in depth of understanding through context – not pseudo context – and built on conceptual understanding as well as procedural fluency.

Here’s my sketch note of our plan:

Here’s the slide deck:

Just say no to worksheets.

Say YES to productive struggle and grappling.

Embolden your inner storyteller and leverage the art of questioning.

Context is key.

#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

Leading Learners To Level Up: Deepening Understanding of Mathematical Practices #LL2LU with @jgough @jwilson828 #NCTMAnnual

At the National Council of Teachers of Mathematics conference in Washington D. C., Jennifer Wilson (@jwilson828) and I presented the following session.

Leading Learners To Level Up:
Deepening Understanding of Mathematical Practices

8:00 AM – 9:00 AM
Walter E. Washington Convention Center, Salon C

Here’s our agenda:

8:00

 

  1. Opening remarks
  2. Council (30 seconds each): Share your name, school and grade level(s) or course(s) with your table; How are you feeling this morning?
8:10

 

Make Sense of Tasks and Persevere Solving Them (SMP 1)

8:30 Practice like we play… Talent isn’t born. It is grown

  • Odell Beckham Jr videos
  • Discuss effort, skill, and craft
8:30 Look for & Make Use of Structure (SMP 7)

  • Read the CCSS SMP and Mark-Up (Sentence, Phrase, Word)
  • What does it look like in the classroom?
    • Area of an equilateral triangle
    • Difference of Perfect Square
8:55 Goal setting: Back with my learners … Next steps
9:00 End of Session

Here’s my sketch note of our plan:

Here’s the slide deck:

Cross posted on Easing The Hurry Syndrome

#SlowMath – Looking for Structure and Noticing Regularity in Repeated Reasoning from @jwilson828 & @jgough #NCTMAnnual

At the National Council of Teachers of Mathematics conference in Washington D. C., Jennifer Wilson (@jwilson828) and I presented the following session.

#SlowMath – Looking for Structure
and Noticing Regularity in Repeated Reasoning
4:30 PM – 5:30 PM
Walter E. Washington Convention Center, 145 AB

How do we provide opportunities for students to learn to use structure and repeated reasoning? What expressions, equations, and diagrams require making what isn’t pictured visible? Let’s engage in tasks where making use of structure and repeated reasoning can provide an advantage and think about how to provide that same opportunity for students.

Here’s my sketch note of our plan:

Here’s our slide deck:

Cross posted on The Slow Math Movement

I can elicit and use evidence of student thinking #NCTMP2A #LL2LU

We strive to grow in our understanding of the Eight Mathematics Teaching Practices from NCTM’s Principles to Actions: Ensuring Mathematical Success for All. This research-informed framework of teaching and learning reflects a core set of high leverage practices and essential teaching skills necessary to promote deep learning of mathematics.

Elicit and use evidence of student thinking.

Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

In order to support our teaching teams as they stretch to learn more, we drafted the following learning progressions. We choose to provide a couple of pathways to focus teacher effort, understanding, and action.

When working with teacher teams to elicit and use evidence of student thinking, we refer to 5 Practices for Orchestrating Productive Mathematics Discussions by Peg Smith and Mary Kay Stein and Dylan Wiliam’s Embedding Formative Assessment: Practical Techniques for K-12 Classrooms along with Principles to Actions: Ensuring Mathematical Success for All by Steve Leinwand.

To deepen our understanding around eliciting evidence of student thinking, we anticipate multiple ways learners might approach a task, empower learners to make their thinking visible, celebrate mistakes as opportunities to learn, and ask for more than one voice to contribute.

From  NCTM’s 5 Practices for Orchestrating Productive Mathematics Discussions, we know that we should do the math ourselves, anticipate what learners will produce, and brainstorm how we might select, sequence, and connect learners’ ideas.

How will classroom culture grow as we focus on the five key strategies we studied in Embedding Formative Assessment: Practical Techniques for F-12 Classrooms by Dylan Wiliam and Siobhan Leahy?

  • Clarify, share, and understand learning intentions and success criteria
  • Engineer effective discussions, tasks, and activities that elicit evidence of learning
  • Provide feedback that moves learning forward
  • Activate students as learning resources for one another
  • Activate students as owners of their own learning

We call questions that are designed to be part of an instructional sequence hinge questions because the lessons hinge on this point. If the check for understanding shows that all students have understood the concept, you can move on. If it reveals little understanding, the teacher might review the concept with the whole class; if there are a variety of responses, you can use the diversity in the class to get students to compare their answers. The important point is that you do not know what to do until the evidence of the students’ achievement is elicited and interpreted; in other words, the lesson hinges on this point. (Wiliam, 88 pag.)

To strengthen our understanding of using evidence of student thinking, we plan our hinge questions in advance, predict how we might sequence and connect, adjust instruction based on what we learn – in the moment and in the next team meeting – to advance learning for every student. We share data within our team to plan how we might differentiate to meet the needs of all learners.

How might we team to strengthen and deepen our commitment to ensuring mathematical success for all?

What if we anticipate, monitor, select, sequence, and connect student thinking?

How might we elicit and use evidence of student thinking to advance learning for every learner?

Cross posted on Easing the Hurry Syndrome


Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

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

Wiliam, Dylan; Leahy, Siobhan. Embedding Formative Assessment: Practical Techniques for F-12 Classrooms. (Kindle Locations 2191-2195). Learning Sciences International. Kindle Edition.

#NCTMLive #T3Learns Webinar: Establish Mathematics Goals to Focus Learning, and Elicit and Use Evidence of Student Thinking.

On Wednesday, March 28, 2018, Jennifer Wilson (@jwilson828) and I co-facilitated the first webinar in a four-part series on the Eight Mathematics Teaching Practices from NCTM’s Principles to Actions: Ensuring Mathematical Success for All.
        .
Establish Mathematics Goals to Focus Learning, and
Elicit and Use Evidence of Student Thinking.

Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

  • How might we communicate with clarity to ensure that learners are focused on high quality mathematical goals?
  • What types of tasks provide opportunities for learners to notice, note, wonder, and take action as agents of their own learning?
                 .
Our slide deck:
Agenda:
7:00 Opening remarks

  • Share your name and grade level(s) or course(s).
  • Norm setting and Purpose
7:05 Establish mathematics goals to focus learning #LL2LU

7:10 Let’s Do Some Math:  Illustrative Math – Fruit Salad?

7:25 Quotes from Taking Action
7:30 Elicit and use evidence of student thinking #LL2LU

7:35 Let’s Do Some Math

7:45 Elicit and use student thinking – Social-Emotional
Talking Points – Elizabeth Statmore

7:55 Close and preview next webinar in the series.

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

Some reflections from the chat window:
  • I learned to pay attention to how my students may first solve the problem or think about it prior to me teaching it to try and see connections that are made or how I can meet them. ~C Heikkila
  • I learned how to pay attention to how I introduce tasks to students. Sometimes I place limits on their responses by telling them what I expect to see in their responses as it relates to content topics. I will be more mindful about task introduction. ~M Roland
  • I learned to pay more attention to mathematical operations, and to look for more solutions that can satisfy the given problem. ~B Hakmi
  •  I also learned the importance of productive struggle and to be patient with my students. ~M James
  • I’m thinking about how to encourage my teachers to intentionally teach the mathematical practices. ~M Hite
  • I learned to pay attention to the learning progressions so I can think of the work as a process and journey. ~B Holden
  • A new mathematical connection for me was the idea of graphing values for the product example. ~A Warden
  • I learned to pay attention to peer discussions to discover how well students are learning the concepts. ~M Grech
  • Am I anticipating the roadblocks to learning? ~L Hendry

An audio recording of the webinar and the chat transcript can be viewed at NCTM’s Partnership Series page.

Cross posted at Easing the Hurry Syndrome

I can establish mathematics goals to focus learning #NCTMP2A #LL2LU

We strive to grow in our understanding of the Eight Mathematics Teaching Practices from NCTM’s Principles to Actions: Ensuring Mathematical Success for All. This research-informed framework of teaching and learning reflects a core set of high leverage practices and essential teaching skills necessary to promote deep learning of mathematics.

Establish mathematics goals to focus learning.

Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.

In order to support our teaching teams as they stretch to learn more, we drafted the following learning progressions. We choose to provide a couple of pathways to focus teacher effort, understanding, and action.

When working with teacher teams to establish mathematics goals to focus learning, we refer to 5 Practices for Orchestrating Productive Mathematics Discussions by Peg Smith and Mary Kay Stein and Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning by John Hattie, Douglas Fisher, and Nancy Frey along with Principles to Actions: Ensuring Mathematical Success for All by Steve Leinwand.

To deepen our understanding around establishing mathematics goals, we anticipate, connect to prior knowledge, explain the mathematics goals to learners, and teach learners to use these goals to self-assess and level up.

From  NCTM’s 5 Practices for Orchestrating Productive Mathematics Discussions, 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.

Once prior knowledge is activated, students can make connections between their knowledge and the lesson’s learning intentions. (Hattie, 44 pag.)

To strengthen our understanding of using mathematics goals to focus learning, we make the learning goals visible to learners, ask assessing and advancing questions to empower students, and listen and respond to support learning and leveling up.

Excellent teachers think hard about when they will present the learning intention. They don’t just set the learning intentions early in the lesson and then forget about them. They refer to these intentions throughout instruction, keeping students focused on what it is they’re supposed to learn. (Hattie, 55-56 pag.)

How might we continue to deepen and strengthen our ability to advance learning for every learner?

What if we establish mathematics learning goals to focus learning?

Cross posted on Easing The Hurry Syndrome


Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy; Gojak, Linda M.; Moore, Sara Delano; Mellman, William L.. Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series). SAGE Publications. Kindle Edition.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 21) Print.

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