Category Archives: Creativity

Agenda: Embolden Your Inner Mathematician (10.10.18) Week 5

Week Five 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 implement tasks that promote reasoning and problem-solving. (#NCTMP2A)
  • I can show my work so that a reader understands without have to ask me questions.

From Principles to Actions: Ensuring Mathematical Success for All

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.

Learning Progressions for today’s goals:

  • I can implement tasks that promote reasoning and problem-solving. (#NCTMP2A)
  • I can show my work so that a reader understands without have to ask me questions.

Tasks:

  • Read and “do the math” from Each Orange Had 8 Slices by Paul Giganti Jr. (Author), Donald Crews (Illustrator).
  • Select, read, and mathematize a book of your choice. Plan a lesson for your students.

[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.

Agenda: Embolden Your Inner Mathematician (10.03.18) Week 4

Week Four 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 implement tasks that promote reasoning and problem-solving. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them. (#SMP-1)

From Principles to Actions: Ensuring Mathematical Success for All

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.

Learning Progressions for today’s goals:

  • I can implement tasks that promote reasoning and problem-solving. (#NCTMP2A)
  • I can make sense of tasks and persevere in solving them. (#SMP-1)

Tasks:

Anticipated ways to mathematize Sheep Won’t SleepSee the next blog post for additional details

[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.

The self-discipline to wait, watch, coach (revised)

My small extended family, there are just 10 of us, blazed through 12 dozen homemade cookies in three afternoons. Home for the holiday, my mother, my daughter, and I bake for pleasure, to help the house smell good, and to pass on important family traditions.  The cookie baking extravaganza has now extended into day 4. The demand for more cookies might be triggered by the smell of chocolate, peanut butter, and sugar wafting throughout the house, back porch, and driveway. Or, it could be gluttony. It’s a holiday; calories don’t count, right?

In her new red and green pjs, AS wakes up raring to go.  Jumping up and down in the kitchen in her new polka dot apron, she asks “How many cookies will we bake today, Mama? How many? How many?”

I hold back a sigh and try not to drop my head; I am tired. I have turkey, dressing, ham, and several casseroles to prepare to carry on our traditions, and I am experiencing cookie overload. I muster my best smile and say, “We need to bake at least 4 dozen cookies. Uncle Jack is coming today, and you know how much he loves your cookies.”

It is our 4th day of cookie baking. Once again, by popular request, we were making Reese’s peanut butter cup cookies.  We make peanut butter cookie dough, roll it into balls, and cook them in mini muffin pans.  As they come out of the oven, we press mini Reese’s peanut butter cups into the center of the cookies.  Delicious.

It is day 4 of this algorithmic work.  The learner is still excited, curious, and engaged.  Am I? Do I feel the same engagement, or am I bored and ready to move on?

For the first 2 dozen, I make the batter, and three generations work together in concert to roll the cookies into balls. The tins come out of the oven holding peanut butter goodness just waiting to receive the Reese’s peanut butter cup candies.  Together, my mother, AS, and I press the candy into the cookies as they come out of the oven. I can still picture my grandmother’s hands doing this work with my mother and me.

Apprenticeship as learning is so important.

I am struck by the lessons my sweet 6-year old, AS, is teaching me about learning with my students. How often do our students watch us do the work to solve the problem or answer the question and pitch in at the last step?   

Baking the second 2 dozen is a very different story.  Thanks to my mother, AS her very own measuring spoons, spatula, and mini muffin pan that bakes 1 dozen muffins.  Empowered now that she has her own pan, she takes charge. It would have been so much faster for me to roll the cookies.  But, no…her pan; her cookies. Her mantra: “I can do it myself!”

So, I watch, wait, and coach.  I try not to cringe. I hold my comments so that I do not undermine her independence and confidence. Too small, the balls will be difficult to press candy into after baking in the oven.  Too big and they will blob out on the pan during baking. Patiently, I ask, “I wonder, honey, if the peanut butter cup will fit into that ball once baked. What do you think?” She fixes most of these problems with a little coaching from me.

Isn’t this happening in our classrooms?  It is so much faster and more efficient for the teacher to present the material.  We can get so much more done in the short amount of time we have. But, how much does the learner “get done” or learn?  When efficiency trumps learning, does anyone really have success? How do we encourage “I can do it myself!”? How do we find the self-discipline to watch, wait, and coach?

As she demands more independence, her confidence grows.  Can you believe that she would alter my recipe for the first 2 dozen cookies?  As our second dozen bakes, I press the peanut butter cups into my cookies. Miss I-Can-Do-It-Myself decides that Hershey kisses will be just as good or better.  With no prompting (or permission) she creates a new (to her) cookie. She has Hershey Kisses, and she wants to use them.

Worth repeating: “As she demands more independence, her confidence grows.” When we intervene too soon, are we stripping learners of their confidence and independence? Are we promoting productive struggle? Do we let them grapple enough?  

Does it really matter which method a learner uses to solve a problem or answer a question?  Isn’t it okay if they use the distributive property or an area model to multiply? Does it really matter which method is used to find the solution to a system of equations?  Shouldn’t they first find success? Don’t we want our learners to understand more than one way? Is our way always the best way?

Is AS pleased with herself and her creativity?  You bet. Are her cookies just as good as the original recipe?  Sure! How can you go wrong combining chocolate and peanut butter?

We must applaud the process that learners use to solve a problem or respond to a question.  We must praise them when they try something different. We must promote and encourage risk-taking, creativity, and problem-solving.

We must find the self-discipline to be patient while learning is in progress, to watch, wait, and coach.  We must embrace and promote the “I can do it myself!” attitude.

We must.


The self-discipline to wait, watch, coach was originally published on Dec 26, 2010.  This revision is inspired by what we are learning in Embolden Your Inner Writer.

I am grateful for the thoughtful, challenging, advancing feedback from Marsha Harris, Amanda Thomas, Kate Burton, Becky Holden, Cathrine Halliburton, and Lauren Kinnard.

#MVIFI Collider session Sketchnoting: Show what you know more than one way

At the February 16th MVIFI Collider event for professional learning, I facilitated the following 50-minute session on sketch noting twice.

Sketchnoting:
Show what you know more than one way

Up your note taking skills by being visual. Learn this invaluable method for recording, showcasing understanding, and deepening comprehension.

We will meet and greet, norm, touch on research, play with words and word art, discuss tools, practice, participate in a feedback look, and close by setting a micro-goal.

Here’s my sketch note of the plan:

We watched Simon Sinek’s TED talk to practice live sketch noting.

Here are artifacts of learning from Twitter:

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?

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.

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.
  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 SplatsSteve Wyborney (@SteveWyborney)
8:25 Fraction SplatsSteve 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.

Summer PD: Day 3 Empower Learners

Summer Literacy and Math Professional Learning
June 5-9, 2017
Day 3 – Empower Learners
Jill Gough and Becky Holden

I can empower learners to reach for the next independent level in their learning.

Learning target and pathway:

It is not easy, but we need to shift from being the givers of knowledge to becoming the facilitators of knowledge development.  (Flynn, 8 pag.)

UED: 8:45 – 11:15  / EED: 12:15 – 2:45

image5

Slide deck

Resources: