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.

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 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 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.
Principles to Actions: Ensuring Mathematical Success for All

Slide deck

 7:15 Welcome, Materials, Q&A Closest to One – warm up Open Middle worksheet 7:30 Establishing Intent, Purpose, Norm Setting Ambitious Teaching NCTM’s Principles to Action Read The Dot 7:45 Break for Birthday Breakfast 7:55 Talking Points from Elizabeth Statmore (@chessemonkeysf) 8:10 Subitizing (a.k.a. Dot Talks) 8:30 Number Talk 8:55 Planning Anticipate Plan to Monitor Sequence anticipated responses 9:05 Closure 9:15 End of session

Homework:

• Number talks with students – subitizing first
• Seek flexibility and multiple ways to show what you know.
• What examples did you select?
• Why did you select the examples you used?
• What examples of student thinking did you document?

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.

Summer PD: Day 1 Make Sense; Persevere

Summer Literacy and Mathematics Professional Learning
June 5-9, 2017
Day 1 – Make Sense and Persevere
Jill Gough and Becky Holden

Today’s focus and essential learning:

We want all mathematicians to be able to say:

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

(but… what if I can’t?)

Great teachers lead us just far enough down a path so we can challenge for ourselves. They provide us just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out the solution to the world, makes me want to step to the next higher level.  Great teachers somehow make us want to ask the questions that they want us to answer, overcome the challenge that they, because they are our teacher, believe we need to overcome. (Lichtman, 20 pag.)

… designed to help students slow down and really think about problems rather than jumping right into solving them. In making this a routine approach to solving problems, she provided students with a lot of practice and helped them develop a habit of mind for reading and solving problems.  (Flynn, 19 pag.)

Resources:

#ObserveMe – the other side – invitation and purpose

Observation by invitation and with purpose.

For context, stop and read Robert Kaplinsky’s
(@robertkaplinsky) #ObserveMe challenge if you haven’t.

How might we serve one another? What if we have questions about our practice? In a community of confident, competent risk-takers, it is safe to declare what we’d like to learn, our goals, and hoped for feedback.

Today, I served as observer-learner for two such teacher-learners.

Julia Kuipers (@J_kuipers3) 6th Grade Spanish:

Since Julia was seeking feedback on how much time they spoke in the target language, I tried to incorporate a timestamp in my sketch.

I could share my sketch in real-time prior to leaving the classroom for immediate feedback.  Later in the day, I could reflect on Julia’s class and use my sketch, I could offer additional feedback in her feedback collection form.

Her feedback form:

I liked that I could write about what I noticed and what I wonder.  I made sure that I commented on what I saw that could be used as evidence of time in the target language, students empowered to level up and stretch themselves, and students serving as resources for each other.  I wondered about extending formative assessment to include performance as well as efficacy.

Megan Hayes-Golding (@mgolding) Physics:

First, it is important to note that we are not at the same school, though this is still observation by invitation and with purpose.

While my sketch chronicled my observation, I noticed and noted when Megan provided levels of challenge within an activity and when students were set up for success when working independently.

Since it was at the end of the day, I had the opportunity to debrief and offer direct feedback in conversation with Megan.

I am thankful for the learning experiences today.  I am grateful for the invitations. I appreciate knowing what to observe so that I can learn and serve.

Observation by invitation and with purpose.

Everyone learns.

Wow!