Tag Archives: Principles to Actions

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.
    • 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:

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)

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:

Overview: Embolden Your Inner Mathematician

Taking action on known national goals, 15 Trinity School teacher-learner-leaders will begin a semester-long professional learning journey to deepen our understanding of NCTM’s Effective Mathematics Teaching Practices.

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

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.

Facilitators:

Weekly schedule of topics:

Sep. 6 Subitizing and Number Talks:
 Elicit and use evidence of student thinking
Sep. 13 Numeracy and Visual Learning:
 Elicit and use evidence of student thinking
Sep. 20 Make sense of tasks and persevere in solving them:
 Facilitate meaningful mathematical discourse
Sep. 27 Attend to Precision and Construct a Viable Argument:
Facilitate meaningful mathematical discourse
Oct. 4 Strengthen Mathematical Flexibility:
Use and connect mathematical representations
Oct. 11 Visual Patterns – Strength Mathematical Flexibility:
Use and connect mathematical representations
Oct. 18 Mathematizing Children’s Literature (part 1):
Implement tasks that promote reasoning and problem solving
Oct. 25 Mathematizing Children’s Literature (part 2):
Implement tasks that promote reasoning and problem solving
Nov. 1 Designing Intentional Number Strings:
Building Procedural Fluency from Conceptual Understanding
Nov. 8 Using Appropriate Tools Strategically:
Building Procedural Fluency from Conceptual Understanding
Nov. 15 Empowering Learners:
Establish mathematical goals to focus learning
Nov. 22 Thanksgiving
Nov. 29 Deep Practice – challenged and learning
Support productive struggle in learning mathematics
Dec. 6 The Art of Questioning or Making Sense of Tasks part 2
Support productive struggle in learning mathematics
Dec. 13 14 Review and Reflection:
Pose purposeful questions

Anchor Resources:

Norms:


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

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 6-8. The National Council of Teachers of Mathematics, 2017.

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

Productive struggle with deep practice – what do experts say

NCTM’s publication, Principles to Action, in the Mathematics Teaching Practices, calls us to support productive struggle in learning mathematics. How do we encourage our students to keep struggling when they encounter a challenging task? How many learners are accustomed to giving up when they can’t solve a problem immediately and quickly. How do we change the practice of how our students learn mathematics?

Effective teaching not only acknowledges the importance of both conceptual understanding and procedural fluency but also ensures that the learning of procedures is developed over time, on a strong foundation of understanding and the use of student-generated strategies in solving problems. (Leinwand, 46 pag.)

Low floor, high ceiling tasks allow all students to access ideas and take them to very high levels. Fortunately, [they] are also the most engaging and interesting math tasks, with value beyond the fact that they work for students of different prior achievement levels. (Boaler, 115 pag.)

Deep learning focuses on recognizing relationships among ideas.  During deep learning, students engage more actively and deliberately with information in order to discover and understand the underlying mathematical structure. (Hattie, 136 pag.)

Deep practice is built on a paradox: struggling in certain targeted ways — operating at the edges of your ability, where you make mistakes — makes you smarter.  (Coyle, 18 pag.)

Or to put it a slightly different way, experiences where you’re forced to slow down, make errors, and correct them —as you would if you were walking up an ice-covered hill, slipping and stumbling as you go— end up making you swift and graceful without your realizing it. (Coyle, 18 pag.)

The second reason deep practice is a strange concept is that it takes events that we normally strive to avoid —namely, mistakes— and turns them into skills. (Coyle, 20 pag.)

We need to give students the opportunity to develop their own rich and deep understanding of our number system.  With that understanding, they will be able to develop and use a wide array of strategies in ways that make sense for the problem at hand. (Flynn, 8 pag.)

…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, 8 pag.)

This term productive struggle captures both elements we’re after:   we want students challenged and learning. As long as learners are engaged in productive struggle, even if they are headed toward a dead end, we need to bite our tongues and let students figure it out. Otherwise, we rob them of their well-deserved, satisfying, wonderful feelings of accomplishment when they make sense of problems and persevere. (Zager, 128-129 ppg.)

Encourage students to keep struggling when they encounter a challenging task.  Change the practice of how our students learn mathematics.

Let’s not rob learners of their well-deserved, satisfying, wonderful feelings of accomplishment when they make sense of problems and persevere.


Boaler, Jo. Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching (p. 115). Wiley. Kindle Edition.

Coyle, Daniel. The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. (p. 20). Random House, Inc.. Kindle Edition.

Flynn, Michael, and Deborah Schifter. Beyond Answers: Exploring Mathematical Practices with Young Children. Portland, ME: Stenhouse, 2017. (p. 8) Print.

Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy, Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series) (p. 136). SAGE Publications. Kindle Edition.

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

Zager, Tracy. Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Portland, ME.: Stenhouse Publishers, 2017. (pp. 128-129) Print.