# Category Archives: Professional Learning & Pedagogy

## #NCTMLive and #T3Learns webinar: Implement tasks that promote reasoning and problem solving, and use and connect mathematical representations.

On Wednesday, May 2, 2018, Jill Gough (@jgough) 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:

View this document on Scribd

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 Experiments in Learning by Doing

## I can elicit and use evidence of student thinking

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

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 Experiments in Learning by Doing

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.

Posted by on March 29, 2018 in Professional Learning & Pedagogy

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

On Wednesday, March 28, 2018, Jill Gough (@jgough) 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). – Maybe a poll? Norm setting and Purpose 7:05 Establish mathematics goals to focus learning #LL2LU 7:10 Task:  Illustrative Math – Fruit Salad? Demonstrate flexibility Look for and make use of structure Share your work via Twitter using #NCTMLive or http://bit.ly/IMfruitsalad-dropyourwork 7:25 Quotes from Taking Action 7:30 Elicit and use evidence of student thinking #LL2LU Dylan Wiliam James Popham #LL2LU 7:35 Let’s Do Some Math Robert Kaplinsky: Open Middle Biggest Product ? 7:45 Talking Points – Elizabeth Statmore Suggestion One talking about learning math Suggestion Two talking about mathematics Geometry Talking Points example Ratios and Proportional reasoning Talking Points example 7:55 Close and preview next in the series
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.

Cross posted at Experiments in Learning by Doing

## I can establish mathematics goals to focus learning

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 Experiments in Learning by Doing

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.

Posted by on March 27, 2018 in Professional Learning & Pedagogy

## Leading Mathematics Education in the Digital Age

Leading Mathematics Education in the Digital Age
2017 NCSM Annual Conference
Pre-Conference Sessions
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.

[Cross-posted at Experiments in Learning by Doing]

## Sneak Peek: Leading Mathematics Education in the Digital Age

Leading Mathematics Education in the Digital Age

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 empower our learners to own their learning? How might we provide opportunities for our learners to level up to the learning target, knowing what they know and what they don’t know yet? How might we encourage our learners to add to the learning of their classmates?

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

Here is Jill’s sneak peek, in case you missed it.

Posted by on March 16, 2017 in Professional Learning & Pedagogy

## 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 Experiments in Learning by Doing]

Posted by on March 12, 2017 in Professional Learning & Pedagogy

2017 T³™ International Conference
Saturday, March 11, 8:30 – 10 a.m.
Columbus H, East Tower, Ballroom Level
Jennifer Wilson
Jill Gough

How might we take action on current best practices and research in learning and assessment? What if we make sense of new ideas and learn how to apply them in our own practice? Let’s learn together; deepen our understanding of formative assessment; make our thinking visible; push ourselves to be more flexible; and more. We will explore some of the actions taken while tinkering with ideas from Tim Kanold, Dylan Wiliam, Jo Boaler and others, and we will discuss and share their impact on learning.

[Cross posted at Experiments in Learning by Doing]

1 Comment

Posted by on March 11, 2017 in Professional Learning & Pedagogy

## Deep practice: building conceptual understanding in the middle grades

Deep practice:
building conceptual understanding in the middle grades

2017 T³™ International Conference
Friday, March 10, 10:00 – 11:30 a.m.
Dusable, West Tower, Third Floor
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.

[Cross posted at Experiments in Learning by Doing]

1 Comment

Posted by on March 10, 2017 in Professional Learning & Pedagogy

## Who Will Work with Whom?

How do you and your students determine who will work with whom?

Elizabeth has been reflecting on teaming her speed demons with other speed demons and her katamari with other katamari. She is grouping and regrouping often, paying attention both to how students work and how students work together.

As part of SREB’s Mathematics Design Collaborative, we use the work from student pre-assessments to pair students homogenously on days when we are doing a formative assessment lesson from the Mathematics Assessment Project. Many of our teachers have worried about homogenous pairing. They wonder how two students who have little understanding of the material will learn anything if they are paired with each other. What we are finding, though, is twofold. Since we don’t have to spend as much time with pairs of students who have demonstrated understanding or some understanding, we can focus our time on the pairs of students who have little understanding. In addition, neither student can sit back and rely on the other student to do all of the work. Together, they end up doing something. The formative assessment lessons are written so that all students have entry to the content. Some items are more challenging than others, and we are slowly learning that every student doesn’t have to get to the same place in the collaborative activity. Students work for a certain amount of time and share what they have learned, even though they might not finish the entire activity.

Others (Alex Overwijk and Dylan Kane) cite Peter Liljedahl’s work on visible, random assignment of student teams.

It takes me a long time to get to know someone and feel comfortable sharing my ideas. For many years I let students choose their teams and work together for the entire year. More recently, though, my coworkers and I have used a card sort activity for teaming students on the first day of a unit. Teams work together throughout the unit unless we are enacting a Formative Assessment Lesson (FAL), in which case we team students homogenously based on their pre-assessment.

In geometry, we’ve made card sorts that introduce students to some of the terms and diagrams that we will study in the unit, often leading right in to the first lesson. It often takes a while for students to find their other team members since they don’t already know the content. Alternatively, we could use content/card matches from the previous unit to team them randomly and visibly on the first day.

For the first team sort, I emailed a preview to students the night before class so that they would have some idea of what to expect/what they might do with their card when they came to class.

Many students noted in their end of course feedback that we should keep the team sorts:

I think you should keep putting us into teams, as we can learn from others who think differently or similarly to us. I think you should also keep switching the classes some. I feel like this helped me a lot this year.

I would keep the different groups that are paired up. I feel that the groups helped me to see others point of view not just my own.

switching classes to see different teaching styles and having different groups throughout the year.

The changing of groups because it has helped me make friends and learn to work together with people who frustrate me.

All of our geometry team sorts are linked here.

I’ve heard others talk about teaming and re-teaming several times during a single lesson based on what students know and don’t know yet. I’m not there yet, but I am intrigued by the idea and would like to learn more both about the value of moving around so often and the logistics of what happens to students’ stuff.

And so the journey to figure out who will work with whom continues …