Category Archives: Sketch Notes

#LL2LU, Algebra, Connecting Ideas, Professional Development Plans, Sketch Notes

Agenda: Embolden Your Inner Mathematician (10.17.18) Week 6

October 17, 2018 Jill Gough Leave a comment

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.

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.

From Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-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.)

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.

Tasks:

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:

View this document on Scribd

[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.

#LL2LU, Connecting Ideas, Professional Development Plans, Questions, Reading, Sketch Notes

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

October 3, 2018 Jill Gough 1 Comment

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.

From NCTM’s 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.

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.

Connecting Ideas, Learning, Peer Observations, Professional Development Plans, Reflection, Sketch Notes

Lesson Study: different teachers, common lesson plan, guaranteed and viable curriculum

August 17, 2018 Jill Gough Leave a comment

What if we share common mission and vision? How might we express our style, individuality, and personality while holding true to a plan and the essentials to learn?

My team, the Academic Leadership Team, includes the Head of School, both Division Heads, the Director of Curriculum, the Director of Technology, and me. We strategically plan using our agreed upon essential learnings.

This week, I had the honor and privilege of observing members of my team launch learning based on our goals and plans. Can you see our connectedness, themes, and common language?

All School Meeting
with Joe Marshall, Head of School

Upper Elementary Division Meeting
with Sarah Barton Thomas, Division Head

Early Elementary Division Meeting
with Rhonda Mitchell, Division Head

Instructional Core Meeting
with Jill Gough, Director of Teaching and Learning
and Marsha Harris, Director of Curriculum

Early Elementary Division Meeting
with Rhonda Mitchell, Division Head

Upper Elementary Division Meeting
with Sarah Barton Thomas, Division Head

How might we team to meet the needs of our diverse learners? What if teaching teams plan common lessons based on guaranteed and viable curriculum? And, what can we learn when we observe each other?

#BeTogetherNotTheSame
#GrowAndLearnTogether

#LL2LU, Connecting Ideas, Learning, Learning Progressions, Professional Development Plans, Questions, Reflection, Sketch Notes

Focus on Instructional Core: establish goals to focus learning

August 8, 2018 Jill Gough 1 Comment

As part of our school’s Pre-Planning, Marsha Harris and I facilitated a faculty-teams workshop to continue our work and learning in the Instructional Core.

Here are my notes from the session.

The agenda, shared ahead of the meeting, looked like this:

The slide deck that accompanies this plan looks like this:

View this document on Scribd

As seen in the slides, we checked in with John Hattie’s research around teacher clarity.

Teacher clarity involves the instructional moves a teacher makes that begin with carefully planning a lesson and making the learning intentions for that lesson or unit clear to herself and her students.

It extends to consistently evaluating where students are in the learning process and describing the success criteria on which students can assess their own progress and on which the teacher bases her evaluation of a student’s progress with a idea or concept. (Hattie, 38 pag.)

To model teacher clarity, we looked at two drafts for

I can establish goals to focus learning.

First, establish goals:

Then, focus learning:

How might we partner together to establish learning goals? What if we by “do the task as a learner” to notice and note needed prerequisites and anticipate potential learning obstacles? Can we deepen learning experiences by connecting to prior learning standards and strategies?

What if we make learning goals visible so that learners are able to identify what they know and need to know next? How might we team to anticipate needed questions to assess and advance learning? What if we teach learners to ask more questions to forward and deepen learning? How might we empower learners to level up?

When we focus on learning,
we strengthen the Instructional Core.

Hattie, John A. (Allan); Fisher, Douglas B.; Frey, Nancy; Gojak, Linda M.; Moore, Sara Delano; Mellman, William L.. Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning (Corwin Mathematics Series) (p. 38). SAGE Publications. Kindle Edition.

#LL2LU, Learning, Learning Progressions, Presentations, Professional Development Plans, Questions, Reading, Sketch Notes

Traverse session: Experiential and Instructional: Promoting Productive Mathematical Struggle #tvrse18

June 6, 2018 Jill Gough Leave a comment

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:

View this document on Scribd

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.

#LL2LU, Conferences, Connecting Ideas, Learning Progressions, Professional Development Plans, Questions, Reading, Sketch Notes

#KSULit2018: Mathematizing Read Alouds

March 20, 2018 Jill Gough 1 Comment

At the 27th Annual KSU Conference on Literature for Children and Young Adults where the theme was Reimagining the Role of Children’s and Young Adult Literature, I presented the following 50-minute session on Tuesday, March 20, 2018.

Mathematizing Read Alouds

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 literacy? We invite you to notice and note, listen and learn, and learn by doing while we share ways to deepen understanding of numeracy and literacy.

Let’s debunk the myth that mathematicians do all work in their heads. Mathematicians notice, wonder, note, identify patterns, ask questions, revise thinking, and share ideas. Mathematicians show their thinking with details so that a reader understands without having to ask questions.

What if we pause during read-alouds to give learners a chance to analyze text features, to notice and wonder, to ask and answer questions in context?

How might we inspire and teach learners to make their thinking visible so that a reader understands?

Here’s my sketch note of the plan:

Here are more of the picture books highlighted in this session:

And, a list by approximate grade levels:

Early Learners, Pre-K, and Kindergarten

Pete the Cat and the Missing Cupcakes
Little Penguins
Who Sank the Boat?
Roxaboxen

Kindergarten and 1st Grade

2nd, 3rd, 4th Grade

4th, 5th, 6th Grade

Conferences, Connecting Ideas, Creativity, Learning, Presentations, Professional Development Feedback, Professional Development Plans, Sketch Notes

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

February 16, 2018 Jill Gough Leave a comment

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:

#LL2LU, Connecting Ideas, Learning, Professional Development Plans, Questions, Sketch Notes

Instructional Core practice #WordsMatter How will we show we CARE?

August 9, 2017 Jill Gough Leave a comment

As part of our school’s Pre-Planning, I facilitated a faculty-teams workshop to continue our work and learning in the Instructional Core.

Here are my notes from the session.

The agenda, shared ahead of the meeting, looked like this:

The slide deck that accompanies this plan looks like this:

View this document on Scribd

We watched 4:05 minutes of Practice is Everything to renew and review our norms around teaming.

How we practice, how we team, makes a difference. The words we choose and use when offering feedback contribute to how our learners author their identity. As we work to calibrate our expectations, we can also hone and enhance our ability to offer high-quality, positive, actionable feedback that empower learners to reach for their next independent level.

As seen in the slides, I used video timers to pace the teamwork time. What I learned is that the timers held me accountable for the work time promised to teachers. I was forced to wait, to be patient, and to not rush. So helpful to hold the time for our teachers.

When we focus on learning,
we hold time for learners.

And, just as we carefully plan and hold time for learning, we carefully choose what we notice and note. Words matter; the story you tell impacts how a learner is thought of and seen.

Amanda Thomas (@TrinityMrsT) found and shared the video below. I used it in our session to illustrate the power of story.

As we begin a new school year with new learners, how will we seek a balanced story, describe what we want to see next, and balance our feedback to highlight success?

What story will we notice and note?
What feedback will we offer?
What will we contribute to how learners author their identity?

How will we show we C.A.R.E.?

Connecting Ideas, Professional Development Plans, Questions, Sketch Notes, Social-Emotional

Lesson Study: different teachers, common lesson plan, guaranteed and viable curriculum

August 8, 2017 Jill Gough Leave a comment

What if we share common mission and vision? How might we express our style, individuality, and personality while holding true to a plan and the essentials to learn?

Today, I had the honor and privilege of observing members of my team launch learning based on our goals and plans. Can you see our connectedness, themes, and common language?

All School Meeting
with Joe Marshall, Head of School

Early Elementary Division Meeting
with Rhonda Mitchell, Division Head

Upper Elementary Division Meeting
with Maryellen Berry, Division Head

How might we team to meet the needs of our diverse learners? What if teaching teams plan common lessons based on guaranteed and viable curriculum? And, what can we learn when we observe each other?

#BeTogetherNotTheSame
#GrowAndLearnTogether

Algebra, Conferences, Connecting Ideas, Questions, Sketch Notes

Sketch notes from #TMC17 (a.k.a. Twitter Math Camp)

July 30, 2017 Jill Gough Leave a comment

Becky Holden (@bholden86) and I attended Twitter Math Camp (#TMC17) at Holy Innocents Episcopal School in Atlanta, GA from Thursday, July 27 to Sunday, July 30.

This conference is by teachers, for teachers. The structure of TMC contains the following lengths of presentations:

Morning sessions (One session that meets Thursday, Friday and Saturday mornings for 2 hours each morning)
Afternoon sessions (Individual 1/2 hour sessions on Thursday)
Afternoon sessions (Individual 1 hour sessions Thursday, Friday and Saturday)

To honor Carl Oliver‘s (@carloliwitter) #PushSend request/challenge, here are my sketch notes from the sessions I attended.

Differentiating CCSS Algebra 1
— from drab to fab using Exeter Math 1 & Exploratory Talk
Elizabeth Statmore (@cheesemonkeysf)

The Politics(?) of Mathematics Teaching
Grace Chen (@graceachen)

What does it mean to say that mathematics teaching is political, and what does that mean for our moral and ethical responsibility as mathematics teachers?