Category Archives: Professional Development Plans

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.

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

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

Focus on Instructional Core: establish goals to focus learning

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:

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.

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.

#NCTMLive #T3Learns Webinar: Implement tasks that promote reasoning and problem solving, and Use and connect mathematical representations

On Wednesday, May 2, 2018, Jennifer Wilson (@jwilson828) and I co-facilitated the second webinar in a four-part series on the Eight Mathematics Teaching Practices from NCTM’s Principles to Actions: Ensuring Mathematical Success for All.

Implement tasks that promote reasoning and problem solving,
and Use and connect mathematical representations.

Effective teaching of mathematics facilitates discourse among learners to build shared understanding of mathematical ideas by analyzing and comparing approaches and arguments.

  • How might we implement and facilitate tasks that promote productive discussions to strengthen the teaching and learning of mathematics in all our teaching settings – teaching students and teaching teachers?
  • What types of tasks encourage mathematical flexibility to show what we know in more than one way?

Our slide deck:

Our agenda:

7:00 Jill/Jennifer’s Opening remarks

  • Share your name and grade level(s) or course(s).
  • Norm setting and Purpose
7:05 Number Talk: 81 x 25

  • Your natural way and Illustrate
  • Decompose into two or more addends (show it)
  • Show your work so a reader understands without asking questions
  • Share work via Twitter using #NCTMLive or bit.ly/nctmlive52
7:10 #LL2LU Use and connect mathematical representations

  • Self-assess where you are
  • Self-assessment effect size

Think back to a lesson you taught or observed in the past month. At what level did you or the teacher show evidence of using mathematical representations?

7:15 Task:  (x+1)^2 does/doesn’t equal x^2+1
7:25 Taking Action (DEI quote)
7:30 #LL2LU Implement Tasks That Promote Reasoning and Problem Solving
7:35 Graham Fletcher’s Open Middle Finding Equivalent Ratios
7:45 Illustrative Mathematics: Jim and Jesse’s Money
7:55 Close and preview next in the series

Some reflections from the chat window:

I learned to pay attention to multiple representations that my students will create when they are allowed the chance to think on their own.  I learned to ask myself how am I fostering this environment with my questioning.

I learned to pay attention to the diversity of representations that different students bring to the classroom and to wait to everyone have time to think

I learned to pay attention (more) to illustrating work instead of focusing so much on algebraic reasoning in my approach to teaching Algebra I. I learned to ask myself how could I model multiple representations to my students.

I learned to pay attention to multiple representations because students all think and see things differently.

I learned to make sure to give a pause for students to make the connections between different ways of representing a problem, rather than just accepting the first right answer and moving on.  

I learned to pay attention to the ways that I present information and concepts to children… I need to include more visual representations when I working with algebraic reasoning activities.

Cross posted on Easing the Hurry Syndrome

Leading Learners To Level Up: Deepening Understanding of Mathematical Practices #LL2LU with @jgough @jwilson828 #NCTMAnnual

At the National Council of Teachers of Mathematics conference in Washington D. C., Jennifer Wilson (@jwilson828) and I presented the following session.

Leading Learners To Level Up:
Deepening Understanding of Mathematical Practices

8:00 AM – 9:00 AM
Walter E. Washington Convention Center, Salon C

Here’s our agenda:

8:00

 

  1. Opening remarks
  2. Council (30 seconds each): Share your name, school and grade level(s) or course(s) with your table; How are you feeling this morning?
8:10

 

Make Sense of Tasks and Persevere Solving Them (SMP 1)

8:30 Practice like we play… Talent isn’t born. It is grown

  • Odell Beckham Jr videos
  • Discuss effort, skill, and craft
8:30 Look for & Make Use of Structure (SMP 7)

  • Read the CCSS SMP and Mark-Up (Sentence, Phrase, Word)
  • What does it look like in the classroom?
    • Area of an equilateral triangle
    • Difference of Perfect Square
8:55 Goal setting: Back with my learners … Next steps
9:00 End of Session

Here’s my sketch note of our plan:

Here’s the slide deck:

Cross posted on Easing The Hurry Syndrome

#SlowMath – Looking for Structure and Noticing Regularity in Repeated Reasoning from @jwilson828 & @jgough #NCTMAnnual

At the National Council of Teachers of Mathematics conference in Washington D. C., Jennifer Wilson (@jwilson828) and I presented the following session.

#SlowMath – Looking for Structure
and Noticing Regularity in Repeated Reasoning
4:30 PM – 5:30 PM
Walter E. Washington Convention Center, 145 AB

How do we provide opportunities for students to learn to use structure and repeated reasoning? What expressions, equations, and diagrams require making what isn’t pictured visible? Let’s engage in tasks where making use of structure and repeated reasoning can provide an advantage and think about how to provide that same opportunity for students.

Here’s my sketch note of our plan:

Here’s our slide deck:

Cross posted on The Slow Math Movement