Tag Archives: Embolden Your Inner Mathematician

Sheep Won’t Sleep #Mathematizing Read Alouds – implement tasks that promote reasoning and problem solving

How might we deepen our understanding of numeracy using children’s literature? What if we mathematize our read aloud books to use them in math as well as reading and writing workshop?

Have you read Sheep Won’t Sleep: Counting by 2’s, 5’s, and 10’s by Judy Cox?

This week’s Embolden Your Inner Mathematician session is designed to learn and practice both a Mathematics Teaching Practice and a Standard for Mathematical Practice.

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.

Jennifer Wilson and I use the following learning progression to help teachers and teaching teams calibrate their work.

From the Standards for Mathematical Practice,

Construct viable arguments and
critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

We choose to reword this for our students. Instead of I can construct a viable argument, we say I can show my work so a reader understands having to ask me questions.

We use the following learning progression to help students self-assess and reach to deepen their learning.

Now, Sheep Won’t Sleep: Counting by 2’s, 5’s, and 10’s by Judy Cox gives away the mathematical thinking on some pages. We decided to read the book and ask our students to listen and take notes as readers, writers, and mathematicians.  Mathematicians notice and note details, look for patterns, and ask questions.  To support listening and comprehension (a.k.a. empower learners to make sense and persevere), we created visuals for quasi-reader’s theater and spelled sheep, alpaca, llama, and yak.  (Level  2; check.)

We also practiced a keep the pace up and get kids collaborating instead of relying on the teacher strategy we are learning from Elizabeth Statmore.

And every day I used 10-2 processing to keep the pace up and get kids collaborating instead of relying on me. For every ten minutes of notes, I gave two minutes of processing time to catch up and collaborate on making their notes accurate. (Statmore, n pag.)

Instead of 10-2 processing, we took a minute after every couple of pages to intentionally turn and talk with a partner with the express purpose of comparing and improving our notes and mathematical communication.

As teachers, we are striving to implement tasks that promote reasoning and problem solving.   Sheep Won’t Sleep: Counting by 2’s, 5’s, and 10’s is a counting book so 1st graders can tackle the math. 2nd and 3rd graders can use this to connect skip counting and repeated addition to multiplication and to use and connect mathematical representations. 4th and 5th graders can use this to use and connect mathematical representations while attending to precision. (Level 1; check.)

Here’s a messy version of how we anticipated student work and thinking.

These read-aloud moments open up the opportunity for rich discussion and engaging questions. Students have the opportunity for more organic and deeper understanding of mathematical concepts thanks to the book that brought them to life, and it is an engaging way to look at math through a different lens.

As Professor of Mathematics Education at the Stanford Graduate School of Education Jo Boaler explains in her book Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching, “Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people.”


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

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

Standards for Mathematical Practice.” Standards for Mathematical Practice. N.p., n.d. Web. 15 Dec. 2014.

Statmore, Elizabeth. “Cheesemonkey Wonders.” First Week and AVID Strategies. 25 Aug. 2018.

Agenda: Embolden Your Inner Mathematician (09.12.18) Week 2

Week Two 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 show my work so that a reader understands without have to ask me questions.

From Principles to Actions: Ensuring Mathematical Success for All

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.

Learning Progressions for today’s goals:

  • I can useand connect mathematical representations.
  • I can use and connectmathematical representations.
  • I can show my work so that a reader understands without have to ask me questions.

Tasks:

  • Beanie Boos (see slide deck)
  • Number Talks
  • What do the standards say?

Addition and Subtraction

2nd Grade
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

3rd Grade
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

4th Grade
Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Multiplication

3rd Grade
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

4th Grade
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5th Grade
Fluently multiply multi-digit whole numbers using the standard algorithm.

Slide deck:

[Cross posted on 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.

“Number & Operations in Base Ten.” Number & Operations in Base Ten | Common Core State Standards Initiative, National Governors Association Center for Best Practices and Council of Chief State School Officers.

Available for learning

I feel it coming.

Have you seen surfers catch big waves? They paddle out, wait and watch.  Some waves pass by. Others crash over them. Sometimes the surfer gets up, punches through and rides it out.  Other times they wipe out. It is fascinating that they get back up and go back out. They persevere. I wonder how I can do that.

I feel it coming, but I cannot predict how I’m going to handle it. It is different every time. Sometimes I cry. Sometimes I turn and fight an internal battle to stand my ground to punch through the wave. Sometimes I can ask for help, but not always.

I am afraid it won’t be perfect.

I am afraid I can’t do it.

I am afraid others will laugh at me.

I am afraid I’ll disappoint my parents.

I am afraid I’m not good enough.

I am afraid I won’t be accepted.

I am afraid I don’t belong.

I am afraid I am not enough.

I am afraid.

I am afraid.

Labels make it easy to attribute student disengagement to a lack of ability or motivation, when disengagement often results from a lack of confidence. (Hassan and Lennard, 70 pag.)

The key to creating psychological safety, as Pentland and Edmondson emphasize, is to recognize how deeply obsessed our unconscious brains are with it. A mere hint of belonging is not enough; one or two signals are not enough. We are built to require lots of signaling, over and over. This is why a sense of belonging is easy to destroy and hard to build. (Coyle, 13 pag.)

How might we learn more about our learners? What actions are needed so that learners know they are psychologically safe?

What conditions must be set so that more learners punch through and rides out the wave?

CULTURE: from the Latin cultus, which means care.


Coyle, Daniel. The Culture Code: The Secrets of Highly Successful Groups. Random House Publishing Group. Kindle Edition.

Hasson, Julie, and Missy Lennard. Unmapped Potential: an Educator’s Guide to Lasting Change. Dave Burgess Consulting, Inc., 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.

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.

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.

Fall PD Opportunity: Embolden Your Inner Mathematician #TrinityLearns

How do we effectively lead mathematics education in the era of the digital age?  We commit to curation of best practices, connections between mathematical ideas, and communication to learn and share with a broad audience.  

To build confidence as well as a more visual approach to elementary mathematics learning and teaching, we have designed ongoing, early morning, job-embedded professional learning around teaching practices and current research. 

Goals:

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

  • 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.
  • I can work within NCTM’s Eight Mathematical Teaching Practices for strengthening the teaching and learning of mathematics.

Details:

Facilitators:

The weekly schedule of topics are as follows:


If you are  interested in emboldening your inner mathematician and would like to join us, please contact us for additional details.

Jill Gough | Director of Teaching & Learning
Experiments in Learning by Doing | Jill Gough notes
jgough@trinitatl.org | @jgough

Trinity School | www.trinityatl.org
4301 Northside Parkway | Atlanta, GA 30327
Phone 404.240.6220 | Fax 404.231.8111