Tag Archives: @jwilson828

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.)

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Agenda and Tasks:

Slide deck:


#SlowMath: look for meaning before the procedure

In her #CMCS15 session, Jennifer Wilson (@jwilson828) asks:

How might we leverage technology to build procedural fluency from conceptual understanding?  What if we encourage sketching to show connections?

What if we explore right triangle trigonometry and  equations of circles through the lens of the Slow Math Movement?  Will we learn more deeply, identify patterns, and make connections?

How might we promote and facilitate deep practice?

This is not ordinary practice. This is something else: a highly targeted, error-focused process. Something is growing, being built. (Coyle, 4 pag.)

What if we S…L…O…W… down?

How might we leverage technology to take deliberate, individualized dynamic actions? What will we notice and observe? Can we Will we What happens when we will take time to note what we are noticing and track our thinking?


What is lost by the time we save being efficient, by telling? How might we ask rather than tell?

#SlowMath Movement = #DeepPractice + #AskDontTell

What if we offer more opportunities to deepen understanding by investigation, inquiry, and deep practice?

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

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?


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.

SMP-8: look for and express regularity in repeated reasoning #LL2LU

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We want every learner in our care to be able to say

I can look for and express regularity in repeated reasoning. (CCSS.MATH.PRACTICE.MP8)

But what if I can’t look for and express regularity in repeated reasoning yet? What if I need help? How might we make a pathway for success?

Level 4
I can attend to precision as I construct a viable argument to express regularity in repeated reasoning.

Level 3
I can look for and express regularity in repeated reasoning.

Level 2
I can identify and describe patterns and regularities, and I can begin to develop generalizations.

Level 1
I can notice and note what changes and what stays the same when performing calculations or interacting with geometric figures.

What do you notice? What changes? What stays the same?

Can we use CAS (computer algebra system) to help our students practice look for and express regularity in repeated reasoning?

What do we need to factor for the result to be (x-4)(x+4)?
What do we need to factor for the result to be (x-9)(x+9)?
What will the result be if we factor x²-121?
What will the result be if we factor x²-a2?

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We can also explore over what set of numbers we are factoring using the syntax we have been using. And what happens if we factor x²+1. (And then connect the result to the graph of y=x²+1.)

What happens if we factor over the set of real numbers?

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Or over the set of complex numbers? 

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What about expanding the square of a binomial? 

What changes? What stays the same? What will the result be if we expand (x+5)²?  Or (x+a)²?  Or (x-a)²? 

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What about expanding the cube of a binomial?  Or expanding (x+1)^n, or (x+y)^n?

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What if we are looking at powers of i?

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We can look for and express regularity in repeated reasoning when factoring the sum or difference of cubes. Or simplifying radicals. Or solving equations.

Through reflection and conversation, students make connections and begin to generalize results. What opportunities are you giving your students to look for and express regularity in repeated reasoning? What content are you teaching this week that you can #AskDontTell?

[Cross-posted on Easing the Hurry Syndrome]



Making #LL2LU Learning Progressions Visible

From Chapter 3: Grading Strategies that Support and Motivate Student Effort and Learning of Grading and Learning: Practices That Support Student Achievement, Susan Brookhart writes:

First, these teachers settled on the most important learning targets for grading. By learning targets, they meant standards phrased in student-friendly language so that students could use them in monitoring their own learning and, ultimately, understanding their grade.

One of these learning targets was ‘I can use decimals, fractions, and percent to solve a problem.’ The teachers listed statements for each proficiency level under that target and steps students might use to reach proficiency.

The [lowest] level was not failure but rather signified ‘I don’t get it yet, but I’m still working.’ (Brookhart, 30 pag.)

How are we making learning progressions visible to learners so that they monitor their own learning and understand how they are making progress?

Yet is such a powerful word. I love using yet to communicate support and issue subtle challenges.  Yet, used correctly, sends the message that I (you) will learn this.  I believe in you, and you believe in me. Sending the message “you can do it; we can help” says you are important.  You, not the class.  You.  You can do it; we can help.

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Self-assessment, self-directed learning, appropriate level of work that is challenging with support, and the opportunity to try again if you struggle are all reasons to have learning progressions visible to learners.

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Making the learning clear, communicating expectations, and charting a path for success are all reasons to try this method.Screen Shot 2014-11-09 at 6.32.15 PM

In addition to reading the research of Tom Guskey, Doug Reeves, Rick Stiggins, Jan Chappius, Bob Marzano and many others, we’ve been watching and learning from TED talks.  My favorite for thinking about leveling formative assessments is Tom Chatfield: 7 ways games reward the brain.

As a community, we continue the challenging work of writing commonly agreed upon essential learnings for our student-learners.  Now that we are on a path of shared models of communication, we are able to develop feedback loops and formative assessments for student-learners to use to monitor their learning as well as empower learners to ask more questions.

By learning to insert feedback loops into our thought, questioning, and decision-making process, we increase the chance of staying on our desired path. Or, if the path needs to be modified, our midcourse corrections become less dramatic and disruptive. (Lichtman, 49 pag.)

Are learning progressions visible and available for every learner?

  • If yes, will you share them with us using #LL2LU on Twitter ?
  • If no, can they be? What is holding you back from making them visible?

Brookhart, Susan M. Grading and Learning: Practices That Support Student Achievement. Bloomington, IN: Solution Tree, 2011. Print.

Lichtman, Grant, and Sunzi. The Falconer: What We Wish We Had Learned in School. New York: IUniverse, 2008. Print.

Lesson and Assessment Design – #T3Learns

What are we intentional about in our planning, process, and implementation?

  • Are the learning targets clear and explicit?
  • What are important check points and questions to guide the community to know if learning is occurring?
  • Is there a plan for actions needed when we learn we must pivot?

On Saturday, a small cadre of T3 Instructors gathered to learn together, to explore learning progressions, and to dive deeper in understanding of the Standards for Mathematical Practice.

The pitch:

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Jennifer and I fleshed out the essential learning in more detail:

  • I can design lessons anchored in CCSS or NGSS.
    • I can design a lesson incorporating national standards, an interactive TI-Nspire document, a learning progression, and a formative assessment plan.
    • I can anticipate Standards for Mathematical Practice that learners will employ during this lesson.
  • I can design a learning progression for a skill, competency, or process.
    • I can use student-friendly language when writing “I can…” statements.
    • I can design a leveled assessment for students based on a learning progression.
  • I can collaborate with colleagues to design and refine lessons and assessments.
    • I can calibrate learning progressions with CCSS and/or NGSS.
    • I can calibrate learning progressions with colleagues by giving and receiving growth mindset oriented feedback, i.e. I can offer actionable feedback to colleagues using I like… I wonder… what if…
    • I can refine my learning progressions and assessments using feedback from colleagues.

The first morning session offered our friends and colleagues an opportunity to experience a low-floor-high-ceiling task from Jo Boaler combined with a SMP learning progression.  After the break, we transitioned to explore the Standards for Mathematical Practice in community. The afternoon session’s challenge was to redesign a lesson to incorporate the design components experienced in the morning session.

Don’t miss the tweets from this session.

Here are snippets of the feedback:

I came expecting…

  • To learn about good pedagogy and experience in real time examples of the same. To improve my own skills with lesson design and good pedagogy.
  • Actually, I came expecting a great workshop. I was not disappointed. I came expecting that there would be more focus using the TI-Nspire technology (directly). However, the structure and design was like none other…challenging at first…but then stimulating!
  • to learn how to be more deliberate in creating lessons. Both for the students I mentor and for T3 workshops.
  • I came expecting to deepen my knowledge of lesson design and assessment and to be challenged to incorporate more of this type of teaching into my classes.

I have gotten…

  • so much more than I anticipated. I learned how to begin writing clear “I can” statements. I also have been enriched by those around me. Picking the brains of others has always been a win!
  • More than I bargained. The PD was more of an institute. It seemed to have break-out sessions where I could learn through collaboration, participation, and then challenging direct instruction, … and more!
  • a clear mind map of the process involved in designing lessons. A clarification of what learning progressions are. Modeling skills for when I present trainings. Strengthening my understanding of the 8 math practices.
  • a better idea of a learning progression within a single goal. I think I had not really thought about progressions within a single lesson before. Thanks for opening my eyes to applying it to individual lesson goals.

I still need (or want)…

  • To keep practicing to gain a higher level of expertise and comfort with good lesson design. Seeing how seamlessly these high quality practices can be integrated into lessons inspires me to delve into the resources provided and learn more about them. I appreciate the opportunity to stay connected as I continue to learn.
  • days like this where I can collaborate and get feedback on activities that will improve my teaching and delivery of professional development
  • I want to get better at writing the “I can” statements that are specific to a lesson.
  • I want to keep learning about the use of the five practices and formative assessment.

We want to see more collaborative productive struggle, pathways for success, opportunities for self- and formative assessment, productive conversation to learn, and more.

As Jennifer always says … and so the journey continues…

[Cross-posted at Easing the Hurry Syndrome]