Tag Archives: @steve_leinwand

#LL2LU, Assessment, Connecting Ideas, Learning, Questions

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

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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.

#LL2LU, Assessment, Connecting Ideas, Learning Progressions, Questions

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

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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.

#LL2LU, Ask Don't Tell, Connecting Ideas, Learning, Learning Progressions, Professional Development Plans

Embolden Your Inner Mathematician: week 4 agenda

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Facilitate meaningful mathematical discourse.

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

Principles to Actions: Ensuring Mathematical Success for All

Slide deck

15 min Homework discussion using Connect-Extend-Challenge
Visible Thinking Routine
35 min Which pizza is the better deal?
– Robert Kaplinsky (@robertkaplinsky)
10 min Break
30 min the Whopper Jar 3-Act Task
– Graham Fletcher (@gfletchy)
20 min Number Talks
10 min Closure
End of session

Homework:

  • Facilitate meaningful mathematical discourse using Number Talks.
    • Select a number talk.
    • Anticipate student answers with your team.
    • Notice and note which students used each strategy.
    • What will/did you learn?
  • Read pp. 146-151 from TAKING ACTION: Implementing Effective Mathematics Teaching Practices in K-Grade 5
    • Examining Mathematical Discourse
  • Deeply Read pp. 175-179 from TAKING ACTION: Implementing Effective Mathematics Teaching Practices in K-Grade 5
    • What the Research says: Meaningful Mathematical Discourse
    • Promoting Equity through Facilitating Meaningful Mathematical Discourse

Standards for Mathematical Practice 

  • I can make sense of tasks and persevere in solving them.

  • I can construct a viable argument and critique the reasoning of others.

“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.

Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.

Previous Embolden Your Inner Mathematician agendas:

#LL2LU, Ask Don't Tell, Connecting Ideas, Learning, Learning Progressions, Professional Development Plans

Embolden Your Inner Mathematician: week 3 agenda

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Facilitate meaningful mathematical discourse.

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

Principles to Actions: Ensuring Mathematical Success for All

Slide deck

7:15 Homework Splats! discussion, Q&A, Problem of the Week
7:35 Open Middle: Closest to One (recap)

7:55 3-Act Task:  The Cookie Thief
8:25 3-Act Task: How big is the World’s Largest Deliverable Pizza?
8:55 Book discussion from homework
9:10 Closure
9:15 End of session

Homework:

  • Read pp. 146-151 from TAKING ACTION: Implementing Effective Mathematics Teaching Practices in K-Grade 5
    • Examining Mathematical Discourse
  • Deeply Read pp. 175-179 from TAKING ACTION: Implementing Effective Mathematics Teaching Practices in K-Grade 5
    • What the Research says: Meaningful Mathematical Discourse
    • Promoting Equity through Facilitating Meaningful Mathematical Discourse

Standards for Mathematical Practice 

  • I can make sense of tasks and persevere in solving them.

  • I can construct a viable argument and critique the reasoning of others.

“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.

Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.

Previous Embolden Your Inner Mathematician agendas:

Connecting Ideas, Creativity, Professional Development Plans, Questions, Reading, Reflection

Embolden Your Inner Mathematician Week 2: Contemplate then Calculate (#CthenC)

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For our second session of Embolden Your Inner Mathematician, we focus on Numeracy and Visual Learning: Elicit and use evidence of student thinking.

What is we use powerful tools to elicit student thinking? How might we learn about students to deeply understand them as mathematicians? And then, what actions do we take to ensure mathematical success for all?

This week’s session began with a gallery walk using Amy Lucenta and Grace Kelemanik’s first five Contemplate then Calculate (#CthenC) lessons found on at Fostering Math Practices.

From Ruth Parker and Cathy Humphreys in Making Number Talks Matter:

No matter what grade you teach, even high school, so-called “dot” cards (which may not have dots) are a great way to start your students on the path to mathematical reasoning. We say this because, from experience, we have realized that with dot cards, students only need to describe what they see— and people have many different ways of seeing! Arithmetic problems, on the other hand, tend to be emotionally loaded for many students. Both of us have found that doing several dot talks before we introduce Number Talks (with numbers) helps establish the following norms:

  • There are many ways to see, or do, any problem.

  • Everyone is responsible for communicating his or her thinking clearly so that others can understand.

  • Everyone is responsible for trying to understand other people’s thinking.

To embolden mathematicians and to prepare to elicit and use evidence of student thinking, teaching teams must practice to develop the habits put forth in 5 Practices for Orchestrating Productive Mathematics Discussions.

You can see our teacher-learner-leaders working to deepen their understanding of and commitment to the Making Number Talks Matter: norms, Smith and Stein’s 5 Practices for Orchestrating Productive Mathematics Discussions, and NCTM’s Principles to Actions: Ensuring Mathematical Success for All.

How might we continue to deepen our understanding of NCTM’s teaching practices? What if we team to learn and practice?

From Principles to Actions: Ensuring Mathematical Success for All

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.

And, from Taking Action: Implementing Effective Mathematics Teaching Practices in K-Grade 5

In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry, and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners.  The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy. (Smith, 4 pag.)

Worth repeating:

The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy.

We continue to foster creativity, visual and algebraic representation to strengthen our mathematical flexibility as we learn together.

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

#ChangeTheFuture

#EmbraceAmbitiousTeaching

#EmboldenYourInnerMathematician

“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.

Humphreys, Cathy; Parker, Ruth. Making Number Talks Matter (Kindle Locations 339-346). Stenhouse Publishers. Kindle Edition.

Kelemanik, Grace, and Amy Lucent. “Starting the Year with Contemplate Then Calculate.” Fostering Math Practices.

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-5. The National Council of Teachers of Mathematics, 2017.

Algebra, Assessment, Connecting Ideas, Creativity, Professional Development Plans, Reading

Embolden Your Inner Mathematician: Week 2 agenda

5 Comments

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.
  Principles to Actions: Ensuring Mathematical Success for All

Slide deck

7:15 Establishing Intent, Purpose, Norm Setting
8:00 Continuing Talking Points – Elizabeth Statmore (@chessemonkeysf)
8:15 Number Splats – Steve Wyborney (@SteveWyborney)
8:25 Fraction Splats – Steve Wyborney (@SteveWyborney)
8:45 Planning for Splats
9:00 Closure and Reflection

  • I learned to pay attention to…
  • I learned to ask myself…
  • A new mathematical connection is…
9:15 End of session

Homework:

  • Elicit and use evidence of student thinking using Splats. What will/did you learn?
  • Write to describe your quest for Closest to One using Open Middle worksheet with I can show my work so a reader understands without asking me questions.
  • Deeply Read pp. 207-211 from TAKING ACTION: Implementing Effective Mathematics Teaching Practices in K-Grade 5
    • What the Research says: Elicit and Use Evidence of Student Thinking
    • Promoting Equity by Eliciting and Using Evidence of Student Thinking
  • Read one of the following from TAKING ACTION: Implementing Effective Mathematics Teaching Practices in K-Grade 5
    • pp.183-188 Make a Ten
    • pp.189-195 The Odd and Even Task
    • pp. 198-207 The Pencil Task

 

Kelemanik, Grace, and Amy Lucent. “Starting the Year with Contemplate Then Calculate.” Fostering Math Practices.

Kaplinsky, Robert, and Peter Morris. “Closest to One.” Open Middle.

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-5. The National Council of Teachers of Mathematics, 2017.

Statmore, Elizabeth. “Cheesemonkey Wonders.” #TMC14 GWWG: Talking Points Activity – Cultivating Exploratory Talk through a Growth Mindset Activity, 1 Jan. 1970.

Wyborney, Steve. “The Fraction Splat! Series.” Steve Wyborney’s Blog: I’m on a Learning Mission., 26 Mar. 2017.
#LL2LU, Ask Don't Tell, Connecting Ideas, Learning Progressions, Professional Development Plans, Questions, Reflection

Embolden Your Inner Mathematician Week 1: Number Talks

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How might we deepen our understanding of NCTM’s teaching practices? What if we team to learn and practice?

For our first session of Embolden Your Inner Mathematician, we focus on Subitizing and Number Talks: Elicit and use evidence of student thinking.

From Principles to Actions: Ensuring Mathematical Success for All

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.

And, from Taking Action: Implementing Effective Mathematics Teaching Practices in K-Grade 5

Meeting the demands of world-class standards for student learning requires teachers to engage in what as been referred to as “ambitious teaching.” Ambitious teaching stands in sharp contrast to what many teachers experienced themselves as learners of mathematics. (Smith, 3 pag.)

In ambitious teaching, the teacher engages students in challenging tasks and collaborative inquiry, and then observes and listens as students work so that she or he can provide an appropriate level of support to diverse learners.  The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy. (Smith, 4 pag.)

Worth repeating:

The goal is to ensure that each and every student succeeds in doing meaningful, high-quality work, not simply executing procedures with speed and accuracy.

How might we foster curiosity, creativity, and critical reasoning while deepening understanding? What if we listen to what our students notice and wonder?

My daughter (7th grade) and I were walking through our local Walgreens when I hear her say “Wow, I wonder…” I doubled back to take this photo.

To see how we used this image in our session to subitize (in chunks) and to investigate the questions that arose from our wonderings, look through our slide deck for this session.

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. What if we build the habit of showing what we know more than one way to add layers of depth to understanding?

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

What if we ask ourselves what other ways can we add layers of depth so that students make sense of this task? How might we better serve our learners if we elicit and use evidence of student thinking to make next instructional decisions? 

#ChangeTheFuture

#EmbraceAmbitiousTeaching

#EmboldenYourInnerMathematician

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.

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-5. The National Council of Teachers of Mathematics, 2017.