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Connecting Ideas, Creativity, Professional Development Plans, Questions, Reading, Reflection

Embolden Your Inner Mathematician Week 2: Contemplate then Calculate (#CthenC)

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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.

#LL2LU, Ask Don't Tell, Connecting Ideas, Learning Progressions, Professional Development Plans, Questions, Reflection

Embolden Your Inner Mathematician Week 1: Number Talks

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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.

Connecting Ideas, Learning, Presentations, Professional Development Plans

Summer PD: Day 2 Mathematical Flexibility

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Summer Literacy and Mathematics Professional Learning
June 5-9, 2017
Day 2 – Mathematical Flexibility
Jill Gough and Becky Holden

Today’s focus and essential learning:

I can demonstrate mathematical flexibility to show what I know in more than one way.

(but , what if I can’t?)

Learning target and pathway:

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, 58 pag.)

…we know that what separates high achievers from low achievers is not that high achievers know more math, it is that they interact with numbers flexibly and low achievers don’t.  (Boaler, n. pag.)

UED: 8:45 – 11:15  / EED: 1:15 – 2:45

 Slide deck

Resources:

Assessment, Connecting Ideas, Information Age Learning, Time

Time, accuracy, speed, & precision (TBT Remix)

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It is critical that we take a moment to review the emerging evidence on the impact of timed testing and the ways in which it transforms children’s brains, leading to an inevitable path of math anxiety and low math achievement. (Boaler, Jo)

Her name was Mrs. Hughes.  I can still hear her:

F … F … J … J … F … F … J … J.

Time, accuracy, speed, and precision were ultimately important in the typing class I took my sophomore year of high school.  I am glad that I touch-type.  At typingtest.com, you can assess your typing speed and accuracy.  Here are my latest results:

Screen Shot 2014-12-06 at 11.31.17 AM

And, later in the day…

Screen Shot 2014-12-06 at 6.02.14 PM

There are plenty of people that do not touch type, some hunt-and-peck.  Is their work some how diminished because they may need more time than a touch typist?  If not witnessing the time and effort, would the reader of the product even know whether the author was speedy or not?

Are accuracy and precision when typing more important than speed and time?  Wouldn’t it be better to take more time and have an accurate product than to be quick with errors?

This has me thinking about assessment, testing, and time.  In a perfect world, we want both speed and accuracy.  What if we can’t have both?  What if a learner needs more time to demonstrate what they know?  Do we really expect all children to perform and produce at the same speed?  Are we sacrificing accuracy and precision for the sake of time?  Should it be the other way around? Are we assessing what our learners know and can show or how fast they can think and work?

How important is it to complete an assessment
within a fixed, pre-determined period of time?

How might we offer learners more time to demonstrate what they know and have learned?

Time is the variable; learning is the constant.

Time, accuracy, speed, & precision was first posted on April 30, 2012

Boaler, Jo. “Timed Tests and the Development of Math Anxiety.” Web log post. Jo Boaler. N.p., 06 July 2012. Web. 09 Nov. 2014.

 

Connecting Ideas, Creativity, Information Age Learning, Learning, Professional Development Plans

Doodling the C’s – Lesson 05: Listening

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How do we practice Information Age skills?  Which of the C’s do we actively engage with, share in the-struggle-to-learn with others, and intentionally insert into daily practice?

Creativity and innovation, Communication, Critical thinking and problem solving, Collaboration, …

Last week’s lesson was on memory boosters.  Lesson 05 is on listening.

Project:  Listen to a couple of TED talks of your choice.
(suggestions below).

1st TED Talk:

  1. Practice the technique of visually thinking about what you are hearing.
  2. Listen to the video twice.
    1. During the first time, stop the video when needed to pause to sketch.
    2. On the second time through, do not stop the video. Work your way through and see how much you can sketch note.
2nd TED Talk:
  1. Be brave.  Practice what we’ve learned in Lesson 4: Memory Booster.
  2. Sketch-note the chosen TED talk without stopping the video.  It is ok to miss some things.
  3. Share your doodle using the hastags #ShowYourWork and YourSchoolsHashtag #TrinityLearns or #WALearns, etc.

Remember… It takes practice.

  • Share your poster with someone and ask for feedback.
  • Scan or take a photo of your work and insert it in your Doodling the C’s Google doc, on your blog, or in your My Learning portfolio.
  • Bonus: Tweet a copy of your poster using the hashtags #ShowYourWork #TrinityLearns (or your school’s hashtag)

Connecting Ideas, Creativity, Information Age Learning, Learning, Professional Development Plans

Doodling the C’s – Lesson 04: Memory Boosters

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How do we practice Information Age skills?  Which of the C’s do we actively engage with, share in the-struggle-to-learn with others, and intentionally insert into daily practice?

Creativity and innovation, Communication, Critical thinking and problem solving, Collaboration, …

Last week’s lesson was on faces and figures.  Lesson 04 is on memory boosters.

Complete the five Memory Boosters Lessons:

Project (pick one):

  • Create a 7.5 x 10 poster of Lessons Learned from the Building Blocks, Lettering, Faces & Figures lessons using these building block.
  • Create a 7.5 x 10 poster for an upcoming class or lesson.
    • Mind map of connected ideas
    • Important message
    • Pathway of success for an essential learning.

Remember… It takes practice.

  • Share your poster with someone and ask for feedback.
  • Scan or take a photo of your work and insert it in your Doodling the C’s Google doc, on your blog, or in your My Learning portfolio.
  • Bonus: Tweet a copy of your poster using the hashtags #ShowYourWork #TrinityLearns (or your school’s hashtag)
Connecting Ideas, Creativity, Information Age Learning, Learning, Professional Development Plans

Doodling the C’s – Lesson 03: Faces and Figures

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How do we practice Information Age skills?  Which of the C’s do we actively engage with, share in the-struggle-to-learn with others, and intentionally insert into daily practice?

Creativity and innovation, Communication, Critical thinking and problem solving, Collaboration, …

Last week’s lesson was on lettering.  Lesson 03 is on faces and figures.

Complete the four Faces & Figures Lessons:

  1. Stick Peeps
  2. Faces
  3. Emotions
  4. Sketch-note Example

Want more practice?  Experiment with these ideas.

Project (pick one):

  • Create a 7.5 x 10 poster of Lessons Learned from the Building Blocks and Lettering lessons using the building block.  (I like Jo Boaler’s stem:  I wish everyone my age knew…)
  • Create a 7.5 x 10 poster to describe
    • an important person or event
    • an important idea(s) from our current Read Aloud
 Remember… It takes practice.
  • Share your poster with someone and ask for feedback.
  • Scan or take a photo of your work and insert it in your Doodling the C’s Google doc, on your blog, or in your My Learning portfolio.
  • Bonus: Tweet a copy of your poster using the hashtags #ShowYourWork #TrinityLearns (or your school’s hashtag)