Tag Archives: @jwilson828

Agenda: Embolden Your Inner Mathematician (10.24.18) Week 7

Week Seven 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.

Tasks:

  • Poetry and watercolor (a.k.a., the beauty of mathematics)
  • Phases of the moon (See slide deck)

What the research says:

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.)

Equitable teaching of mathematics focuses on going deep with mathematics, including developing a deep understanding of computational procedures and other mathematical rules, formulas, and facts. When students learn procedures with understanding, they are then able to use and apply those procedures in solving problems. When students learn procedures as steps to be memorized without strong links to conceptual understanding, they are limited in their ability to use the procedure. (Smith, 93 pag.)

Evidence of work and thinking:

Slide deck:

[Cross posted at Sum it up and  Multiply it out]


Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or 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.

Agenda: Embolden Your Inner Mathematician (10.17.18) Week 6

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:

[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.

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.

Agenda: Embolden Your Inner Mathematician (09.19.18) Week 3

Week Three 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 a reader understand without asking 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 use and 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:

What the research says:

From Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5:

High-level tasks not only hold high mathematical expectations for every student, one aspect of equitable classrooms, they also “allow multiple entry points and varied solution strategies” (NCTM 2014, p. 17).

…Positioning students as valuable contributors to mathematical work, even as authors and owners of mathematical ideas, supports the development of positive mathematical identities and agency as mathematical thinkers. [p. 72-73]

Too often students see mathematics as isolated facts and rules to be memorized. … students are expected to develop deep and connected knowledge of mathematics and are engaged in learning environments rich in use of multiple representations.

Mathematics learning is not a one size fits all approach …, meaning not every child is expected to engage in the mathematics in the same way at the same time. … the diversity of their sense-making approaches is reflected in the diversity of their representations. [p. 140]

Examples of Anticipated thinking and outcomes:

[Cross posted on Sum it up and Multiply it out]


Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or 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.

Smith, Margaret, and Mary Kay Stein. 5 Practices for Orchestrating Productive Mathematics Discussions.The National Council of Teachers of Mathematics, 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.

Establish goals to focus learning – Reading Workshop 5th Grade

What if we design a lesson to orchestrate productive discussion, critique the reasoning of others, grow as readers and writers, and deepen understanding through reflection?

The 5th grade team invited me to co-labor with them to help our young learners deepen their understanding of reader’s response journals. As a team, they are focused on implementing and deepening their understanding of Wiliam and Leahy’s  five strategies in Embedding Formative Assessment: Practical Techniques for K-12 Classrooms :

  • Clarify, share, and understand learning intentions and success criteria
  • Engineer effective discussions, tasks, and activities that elicit evidence of learning
  • Provide feedback that moves learning forward
  • Activate students as learning resources for one another
  • Activate students as owners of their own learning

From our Instructional Core work during Pre-Planning, we are working to  establish goals to focus learning.

The 5th Grade team drafted the following learning progressions to make their thinking visible to our new students. As a team, they have established these goals for students. (Level 3 for I can establish goals.)

How might we use these established goals to focus learning? What student outcomes should we anticipate, and what teacher moves should we plan based on prior experience?

At their invitation (#soexcited), I facilitated a lesson on using the drafts above to improve and strengthen reader’s response journal entries while modeling the use of assessing and advancing questions to focus student learning. (Level 4 for I can establish goals and Level 3 for I can focus learning.)

Here’s the plan:

And, the slide deck:

These learning progressions are in each student’s reader’s response journal so they can use them in class and at home.

It was a crisp 30-minute lesson. All of our anticipated outcomes presented during the mini-lesson.

We wanted our students to learn more about

  • making their thinking visible to another reader,
  • adding text evidence to support their ideas,
  • including details that support understanding,
  • participating in productive discussion,
  • critiquing the reasoning of others,
  • growing as readers and writers,
  • using learning progressions to improve their work.

After reading one of my reader’s response entries, our students’ frustration at not having read Bud, Not Buddy by Christopher Paul Curtis surfaced during  their feedback loop to me. This offered me the opportunity to ask their teacher if he or she would have read every independent reading selection made by his or her students. It was a strong “ah ha” moment for our students.

The students’ comments could be categorized in themes. Samples of our students’ reflections are shared as evidence of effort and learning.

  • An ah-ha for me is that my teacher has not read every single book in the universe.
  • I learned to pay attention to text evidence and explaining my text evidence so the reader understands why I added the quotes and page numbers.  I also learned to pay attention to visuals and formatting.
  • I don’t know what an ah-ha moment is. (Oops! Needs more instruction and time to learn.)
  • I know that everyone has not read the book and that I need to add enough detail for people who haven’t read the book.
  • An ah-ha for me is that I think that adding the definitions was smart because I didn’t know some of the words.
  • I learned to pay attention to science experiments. (Yikes! Needs more instruction and time to make sense of the task.)
  • I learned to ask myself if it makes sense and if another person could understand.
  • I learned to ask myself “how can I improve this? What details should I add?”

We know this is not a one-and-done event for our students and our team. We learned about our students and know what me should work on next. We must continue to practice making our thinking visible and hone our skills to use goals to focus learning.

Our school’s mission calls for us to deepen students’ educational experiences and empower students as agents of their own learning while we help them build strong academic foundation.  We strive to make our thinking visible to each other and to our students.

What is to be gained when we make our thinking visible to our students and use established goals to focus learning?


Wiliam, Dylan; Leahy, Siobhan. Embedding Formative Assessment: Practical Techniques for F-12 Classrooms. (Kindle Locations 493-494). Learning Sciences International. Kindle Edition.