# Agenda: Embolden Your Inner Mathematician (10.17.18) Week 6

Week Six of Embolden Your Inner Mathematician

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

Course 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.

Today’s Goals

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

• I can use and connect mathematical representations. (#NCTMP2A)
• I can make sense of tasks and persevere in solving them. (#SMP-1)
• I can show my work so that a reader understands without have to ask me questions.

Use and connect mathematical representations: Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

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.)

Learning Progressions for today’s goals:

• I can use and connect mathematical representations. (#NCTMP2A)

• I can show my work so that a reader understands without have to ask me questions.

• Visual representation of multiplication, exponents, subtraction. (Connect 2nd-5th grade with Algebra I and II.)
• Apples and Bananas task (see slide deck)

What the research says:

Not only should students be able to understand and translate between modes of representations but they should also translate within a specific type of representation. [Smith, pag. 139]

Equitable teaching of mathematics includes a focus on multiple representations. This includes giving students choice in selecting representations and allocating substantial instructional time and space for students to explore, construct, and discuss external representations of mathematical ideas. [Smith, pag. 141]

Too often students see mathematics as isolated facts and rules to be memorized. [Smith, pag. 141]

\Anticipated work and thinking:

Slide deck:

[Cross posted at Sum it up and Multiply it out]

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

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

# Embolden Your Inner Mathematician: week 7 agenda

Implement tasks that promote reasoning and problem solving.

Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Principles to Actions: Ensuring Mathematical Success for All

Slide deck

 15 min Homework discussion, Q&A, Problem of the Week 15 min Number talk and birthday breakfast 45 min Numeracy through Literature – Notice and Note Those Darn Squirrels! 35 min Designing for Learning Read, select, and design – anticipate and connect Read and discuss Brainstorm important concepts and anticipate how learners will think and share using Post-it notes Connect to essential learnings or skills 10 min Closure End of session

Possibilities:

Learning Progressions:

• I can demonstrate mathematical flexibity to show what I know more than one way.
• I can show my work so that a reader understands without asking questions.

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:

# Embolden Your Inner Mathematician: week 6 agenda

Use and connect mathematical representations.

Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

Principles to Actions: Ensuring Mathematical Success for All

Slide deck

 15 min Homework discussion, Q&A, Problem of the Week 15 min Deepening: Use and connect representations 15 min Construct a viable argument and critique the reasoning of others 20 min 5 Practices: Anticipate, Monitor, Select, Sequence, Connect 40 min Visual Patterns – Routines for Reasoning 15 min Closure End of session

Homework:

• Practice finding and connecting multiple representations in our Number Talks
• Read: Use and Connect Mathematical Representations
• What the Research Says: Representations and Student Learning (pp. 138-140)
• Promoting Equity by Using and Connecting Mathematical Representations (pp. 140-141)
• Check out Kristin Gray’s (@MathMinds) response to Vicki’s tweet (shown below) and try to answer the question for yourself for a Number Talk you’ve done or will do this week.

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:

# Embolden Your Inner Mathematician: week 5 agenda

Use and connect mathematical representations.

Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

Principles to Actions: Ensuring Mathematical Success for All

Slide deck

 15 min Homework discussion, Q&A 45 min Apples and Bananas Task 30 min Number Talk – Flexibility: Show what you know more than one way. 10 min Break 20 min Connecting multiple representations End of session

Homework:

• Practice finding and connecting multiple representations in our Number Talks
• Read: Use and Connect Mathematical Representations
• What the Research Says: Representations and Student Learning (pp. 138-140)
• Promoting Equity by Using and Connecting Mathematical Representations (pp. 140-141)
• Check out Kristin Gray’s (@MathMinds) response to Vicki’s tweet (shown below) and try to answer the question for yourself for a Number Talk you’ve done or will do this week.

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:

# Embolden Your Inner Mathematician: week 4 agenda

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.
• 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:

# Embolden Your Inner Mathematician: week 3 agenda

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) Robert Kaplinsky (@robertkaplinsky) 7:55 3-Act Task:  The Cookie Thief Graham Fletcher (@gfletchy) 8:25 3-Act Task: How big is the World’s Largest Deliverable Pizza? Robert Kaplinsky (@robertkaplinsky) 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:

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

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?

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 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.

# Embolden Your Inner Mathematician: Week 2 agenda

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.

Slide deck

 7:15 Establishing Intent, Purpose, Norm Setting Contemplate then Calculate (#CthenC) Amy Lucenta (@AmyLucenta) Grace Kelemanik (@GraceKelemanik) 8:00 Continuing Talking Points – Elizabeth Statmore (@chessemonkeysf) Talking Points activity 8:15 Number Splats – Steve Wyborney (@SteveWyborney) 8:25 Fraction Splats – Steve Wyborney (@SteveWyborney) 8:45 Planning for Splats Select specific Number Splats or Fraction Splats Anticipate Connect 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.

# Embolden Your Inner Mathematician Week 1: Number Talks

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.

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.

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.

# Embolden Your Inner Mathematician Week 1: Talking Points

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.

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.

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.

Let’s pay attention to the whole child. Content is mission critical, but so are disposition and efficacy.  What if we learn more about our students disposition to support the social/emotional well-being of our mathematicians?  How might we elicit and use evidence of student thinking to understand  assumptions/beliefs about learning math?

We used the following exploratory talking points from Elizabeth Statmore:

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?

#ChangeTheFuture

#EmbraceAmbitiousTeaching

#EmboldenYourInnerMathematician

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.