Tag Archives: #LL2LU

Embolden Your Inner Mathematician: week 7 agenda

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.

Principles to Actions: Ensuring Mathematical Success for All

Slide deck

15 min Homework discussion, Q&A,
Problem of the Week
15 min Number talk and
birthday breakfast
45 min Numeracy through Literature –
Notice and Note

Those Darn Squirrels!

35 min

 

Designing for Learning

Read, select, and design –
anticipate and connect

  • Read and discuss
  • Brainstorm important concepts and
    anticipate how learners will think and
    share using Post-it notes
  • Connect to essential learnings or skills
10 min Closure
End of session

Possibilities:

Learning Progressions:

  • I can demonstrate mathematical flexibity to show what I know more than one way.
  • I can show my work so that a reader understands without asking questions.

Standards for Mathematical Practice

  • I can make sense of tasks and persevere in solving them.

  • I can construct a viable argument and critique the reasoning of others.

“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.

Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.


Previous Embolden Your Inner Mathematician agendas:

Embolden Your Inner Mathematician: week 6 agenda

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.

Principles to Actions: Ensuring Mathematical Success for All

Slide deck

15 min Homework discussion, Q&A, Problem of the Week
15 min Deepening: Use and connect representations
15 min Construct a viable argument and critique the reasoning of others
20 min 5 Practices: Anticipate, Monitor, Select, Sequence, Connect
40 min Visual Patterns – Routines for Reasoning
15 min Closure
End of session

Homework:

  • Practice finding and connecting multiple representations in our Number Talks
  • Read: Use and Connect Mathematical Representations
    • What the Research Says: Representations and Student Learning (pp. 138-140)
    • Promoting Equity by Using and Connecting Mathematical Representations (pp. 140-141)
    • Check out Kristin Gray’s (@MathMinds) response to Vicki’s tweet (shown below) and try to answer the question for yourself for a Number Talk you’ve done or will do this week.

Standards for Mathematical Practice

  • I can make sense of tasks and persevere in solving them.

  • I can construct a viable argument and critique the reasoning of others.

“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.

Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.


Previous Embolden Your Inner Mathematician agendas:

Summer PD: Day 1 Make Sense; Persevere

Summer Literacy and Mathematics Professional Learning
June 5-9, 2017
Day 1 – Make Sense and Persevere
Jill Gough and Becky Holden

Today’s focus and essential learning:

We want all mathematicians to be able to say:

I can make sense of tasks
and persevere in solving them.

(but… what if I can’t?)

Great teachers lead us just far enough down a path so we can challenge for ourselves. They provide us just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out the solution to the world, makes me want to step to the next higher level.  Great teachers somehow make us want to ask the questions that they want us to answer, overcome the challenge that they, because they are our teacher, believe we need to overcome. (Lichtman, 20 pag.)

… designed to help students slow down and really think about problems rather than jumping right into solving them. In making this a routine approach to solving problems, she provided students with a lot of practice and helped them develop a habit of mind for reading and solving problems.  (Flynn, 19 pag.)

Screen Shot 2017-06-06 at 7.53.02 AM.png

Agenda and Tasks:

Slide deck:

Resources:

Summer Learning 2017 – Choices and VTR

How do we learn and grow when we are apart? We workshop, plan, play, rest, and read to name just a few of our actions and strategies.

We make a commitment to read and learn every summer.  This year, in addition to books and a stream of TED talks, Voices of Diversity, we offer the opportunity to read children’s literature and design learning intentions around character and values.

Below is the Summer Learning flyer announcing the choices for this summer.

We will continue to use the Visible Thinking Routine Sentence-Phrase-Word to notice and note important, thought-provoking ideas. This routine aims to illuminate what the reader finds important and worthwhile.

Sentence-Phrase-Word helps learners to engage with and make meaning from text with a particular focus on capturing the essence of the text or “what speaks to you.” It fosters enhanced discussion while drawing attention to the power of language. (Ritchhart, 207 pag.)

However, the power and promise of this routine lies in the discussion of why a particular word, a single phrase, and a sentence stood out for each individual in the group as the catalyst for rich discussion . It is in these discussions that learners must justify their choices and explain what it was that spoke to them in each of their choices. (Ritchhart, 208 pag.)

Continuing to work on our goal, We can design and implement a differentiated action plan across our divisions school to meet all learners where they are, we make our thinking visible on ways to level up.

When we share what resonates with us, we offer others our perspective.  What if we engage in conversation to learn and share from multiple points of view?


Ritchhart, Ron, Mark Church, and Karin Morrison. Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners. San Francisco, CA: Jossey-Bass, 2011. Print

#LL2LU Mathematical Communication at an early age (TBT Remix)

Continue the pattern:  18, 27, 36, ___, ___, ___, ___

Lots of hands went up.

18, 27, 36, 45, 54, 63, 72
Yes! How did you find the numbers to continue the pattern?

S1:  I added 9.
(Me: That’s what I did.)
S2: I multiplied by 9.
(Me: Uh oh…)
S3: The ones go down by 1 and the tens go up by 1.
(Me: Wow, good connection.)

Arleen and Laura probed and pushed for deeper explanations.

S1: To get to the next number, you always add 9.
(Me: That’s what I did.)
S2: I see 2×9, 3×9, and 4×9, so then you’ll have 5×9, 6×9, 7×9, and 8×9.
(Me: Oh, I see! She is using multiples of 9, not multiplying by 9. Did she mean multiples not multiply?)
S3: It’s always the pattern with 9’s.
(Me: He showed the trick about multiplying by 9 with your hands.)

Without the probing and pushing for explanations, I would have thought some of the children did not understand.  This is where in-the-moment formative assessment can accelerate the speed of learning.

There were several more examples with probing for understanding. Awesome work by this team to push and practice. Arleen and Laura checked in with every child as they worked to coach every learner to success.  Awesome!

24, 30, 36, ___, ___, ___, ___
49, 42, 35, ___, ___, ___, ___
40, 32, 24,  ___, ___, ___, ___

I was so curious about the children’s thinking.  Look at the difference in their work and their communication.

By analyzing their work in the moment, we discovered that they were seeing the patterns, getting the answers, but struggled to explain their thinking.  It got me thinking…How often in math do we communicate to children that a right answer is enough? And the faster the better??? Yikes!  No, no, no! Show what you know, not just the final answer.

My turn to teach.

It is not enough to have the correct numbers in the answer.  It is important to have the correct numbers, but that is not was is most important.  It is critical to learn to describe your thinking to the reader.

How might we explain our thinking? How might we show our work? This is what your teachers are looking for.

The children gave GREAT answers!

We can write a sentence.
We can draw a picture.
We can show a number algorithm. (Seriously, a 4th grader gave this answer. WOW!)

But, telling me what I want to hear is very different than putting it in practice.

It makes me wonder… How can I communicate better to our learners? How can I show a path to successful math communication? What if our learners had a learning progression that offered the opportunity to level up in math communication?

What if it looked like this?

Level 4
I can show more than one way to find a solution to the problem.  I can choose appropriately from writing a complete sentence, drawing a picture, writing a number algorithm, or another creative way.

Level 3
I can find a solution to the problem and describe or illustrate how I arrived at the solution in a way that the reader does not have to talk with me in person to understand my path to the solution.

Level 2
I can find a correct solution to the problem.

Level 1
I can ask questions to help me work toward a solution to the problem.

show-your-work
Learning progression in 4th grade student-friendly language from Kato Nims (@katonims129)
IMG_8439
Learning progression developed by #TrinityLearns 2nd Grade community learners-of-all-ages.

What if this became a norm? What if we used this or something similar to help our learners self-assess their mathematical written communication? If we emphasize math communication at this early age, will we ultimately have more confident and communicative math students in middle school and high school?

What if we lead learners to level up in communication of understanding? What if we take up the challenge to make thinking visible? … to show what we know more than one way? … to communicate where the reader doesn’t have to ask questions?

How might we impact the world, their future, our future?


#LL2LU Mathematical Communication at an early age was originally published on October 30, 2013.

Struggle: pay attention; keep moving forward – The Talent Code VTR SPW

What if we reframe mistakes to be billed as opportunities to learn? If we truly believe in fail up, fail forward, fail faster, how do we leverage the quick bursts of failure mistakes struggle to propel learning in a new direction?

Struggle is not optional—it’s neurologically required: in order to get your skill circuit to fire optimally, you must by definition fire the circuit suboptimally; you must make mistakes and pay attention to those mistakes; you must slowly teach your circuit. You must also keep firing that circuit—i.e., practicing—in order to keep myelin functioning properly. After all, myelin is living tissue. (Coyle, 43 pag.)

How might we position each learner to work at the edge of their ability, reaching to a new goal,  capture failure and turn it into skill?

Because the best way to build a good circuit is to fire it, attend to mistakes, then fire it again, over and over. Struggle is not an option: it’s a biological requirement. (Coyle, 34 pag.)

How might we establish a community norm that calls for a trail of mistakes to show struggle and evidence of learning? What if paying attention to mistakes is an essential to learn? How might we celebrate the trail that leads to success, to keep moving forward?

TalentCode-Chpt2

Summer Reading using VTR: Sentence-Phrase-Word:
The Talent Code
Chapter 2: The Deep Practice Cell

How might we target struggle so that it is productive? For what should we reach? What if expand our master coach toolkit to include a pathway to sense making and perseverance?

SMP-1: Make Sense of Problems and Persevere #LL2LU

What if we target productive struggle through process? How might we lead learners to level up by helping them reach? When learners are thrashing around blindly, how might we serve as refuge for support, encouragement, and a push in a new direction?


Coyle, Daniel (2009-04-16). The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. Random House, Inc.. Kindle Edition.

productive struggle vs. thrashing blindly

The trick is to choose a goal just beyond your present abilities; to target the struggle. Thrashing blindly doesn’t help. Reaching does. (Coyle, 19 pag.)

What if we teach how to reach? How might we offer targeted struggle for every learner in our care?

SMP-1: Make Sense of Problems and Persevere #LL2LU

Investing time in teaching students how to learn is never wasted; in doing so, you deepen their understanding of the upcoming content and better equip them for future success. (Jackson, 19 pag.)

SMP-8: Look for and Express Regularity in Repeated Reasoning #LL2LU

If we are to harness the power of feedback to increase student learning, then we need to ensure that feedback causes a cognitive rather than an emotional reaction—in other words, feedback should cause thinking. It should be focused; it should relate to the learning goals that have been shared with the students; and it should be more work for the recipient than the donor. (Wiliam, 130 pag.)

Math Flexibility

When people believe their basic qualities can be developed, failures may still hurt, but failures don’t define them.   And if abilities can be expanded – if change and growth are possible – then there are still many paths to success.” (Dweck, 39 pag.)

What pathways to learning are illuminated in order to highlight learning = struggle + perseverance?


Coyle, Daniel (2009-04-16). The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. Random House, Inc. Kindle Edition.

Dweck, Carol S. Mindset: the New Psychology of Success. New York: Random House, 2006. 39. Print.

Jackson, Robyn R. (2010-07-27). How to Support Struggling Students (Mastering the Principles of Great Teaching series) (Pages 18-19). Association for Supervision & Curriculum Development. Kindle Edition.

Wiliam, Dylan (2011-05-01). Embedded Formative Assessment (Kindle Locations 2679-2681). Ingram Distribution. Kindle Edition.