Tag Archives: SMP-1

#ShowYourWork, make sense and persevere, flexibility with @IllustrateMath

How might we learn to show our work so that a reader understanding without having to ask questions? As we work with our young learners, we want them to grow as mathematicians and as communicators.

We ask students to show their work so that a reader understands without having to ask them questions. What details should we add so that our thinking is visible to others?

To show (and to assess) comprehension, we are looking for mathematical flexibility.

I taught 6th grade math today while Kristi and her team attended ASCD.  She asked me to work with our students on showing their work.  Here’s the plan:

Learning goals:

  • I can use ratio and rate reasoning to solve real-world and mathematical problems.
  • I can show my work so that a reader can understanding without having to ask questions.

Activities:

Learning progressions:

Level 4:
I can demonstrate mathematical flexibility with ratio and rate reasoning to show what I know more than one way using tables, equations, double number lines, etc..

Level 3:
I can use ratio and rate reasoning to solve real-world and mathematical problems.

Level 2:
I can make tables of equivalent ratios relating quantities with whole-number measurements, and I can use tables to compare ratios.

Level 1:
I can use guess and check to solve real-world and mathematical problems.

Anticipated solutions:

Sample student work:

Learner choice: using appropriate tools strategically takes time and tools

All students benefit from using tools and learning how to use them for a variety of purposes.  If we don’t make tools readily available and value their use, our students miss out on major learning opportunities. (Flynn, 106 pag.)

I’m taking the #MtHolyokeMath #MTBoS course, Effective Practices for Advancing the Teaching and Learning of Mathematics.  Zachary Champagne facilitated the second session and used The Cycling Shop task from Mike Flynn‘s TMC article.

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You can see the notes I started on paper.

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Jim, Casey and I used a pre-made Google slide deck provided to us to collaborate since we were located in GA, MA, and CA.  We challenged ourselves to consider wheels after working with 8 wheels.

Here’s what our first table looked like.

cyclingshop1

Now, I was having trouble keeping up with the number of wheels and the number of cycles.  So I did this:

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This made it both better and worse for me (and for my group).

Here’s an interesting thing.  I’ve been studying, practicing, and teaching the Standards for Mathematical Practices. Jennifer Wilson and I have written a learning progression to help learners learn to say I can use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. (Sage, 6 pag.)

Clearly, I was not even at Level 1 during class.  Not once – not once – during class did it occur to me how much a spreadsheet would help me, strategically.

8wheelsspreadsheet

The spreadsheet would calculate the number of wheels automatically for each row so that I could confirm correct combinations.  (You can view this spreadsheet and make a copy to play with if you are interested.)

When making mathematical models, [mathematically proficient students] know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. (Sage, 6 pag.)

With a quick copy and paste, I could tackle any number of wheels using my spreadsheet.  I can look for and make use of structure emerged quickly when using the spreadsheet strategically.  (I want to also highlight color as a strategic tool.) Play with it; you’ll see.

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[Mathematically proficient students] are able to use technological tools to explore and deepen their understanding of concepts. (Sage, 6 pag.)

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There is no possible way I would have the stamina to seek all the combinations for 25 or 35 wheels by hand, right?

Students have access to a wide assortment of tools that they must learn to use for their mathematical work. The sheer volume of possibilities can seem overwhelming, but with time and experience, students can learn how to choose the right tool for the task at hand and how to use it strategically to reach their goal. (Flynn, 106 pag.)

Important to repeat, “with time and experience, students can learn how to choose the right tool for the task at hand and how to use it strategically to reach their goal.

For this to happen, we need to have a solid understanding of the kinds of tools available, the purpose of each tool, and how students can learn to use them flexibly and strategically in any given situation. This also means that we have to make these tools readily available to students, encourage their use, and provide them with options so they can decide which tool to use and how to use it. If we make all the decisions for them, we remove that critical component of MP5 where students make decisions based on their knowledge and understanding of the tools and the task at hand. (Flynn, 106 pag.)

To be clear, a spreadsheet was available to me during class, but I didn’t see it.  How might we make tools readily available and visible for learners to choose?

When we commit to empower students to deepen their understanding, we make tools available and encourage exploration and use, so that each learner makes decisions for themselves. In other words, how do we help learners to level up in both content and practice?

What if we make I can look for and make use of structure; I can use appropriate tools strategically; and I can make sense of tasks and persevere in solving them essential to learn for every learner?

How might we offer tools and time?

It’s about learning by doing, right?


Flynn, Michael. Beyond Answers: Exploring Mathematical Practices with Young Children. Portland, Maine.: Stenhouse, 2017. Print.

Flynn, Mike. “The Cycling Shop.” Nctm.org. Teaching Children Mathematics, Aug. 2016. Web. 03 Feb. 2017.

Common Core State Standards.” The SAGE Encyclopedia of Contemporary Early Childhood Education (n.d.): n. pag. Web.

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.

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.

Deep Dive into Standards of Mathematical Practice

As a team, we commit to make learning pathways visible. We are working on both horizontal and vertical alignment.  We seek to calibrate our practices with national standards.

On Friday afternoon, we met to take a deep dive into the Standards of Mathematical Practice. Jennifer Wilson joined us to coach, facilitate, and learn. We are grateful for her collaboration, inspiration, and guidance.

The pitch:

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The plan:

Goals:

  • I can anticipate Standards for Mathematical Practice that learners will employ during this lesson.
  • I can begin to design lessons incorporating national standards, a learning progression, and a formative assessment plan.

Norms:

  • Safe space
    • I can talk about what I know, and I can talk about what I don’t know.
    • I can be brave, vulnerable, kind, and considerate to myself and others while learning.
  • Celebrate opportunities to learn
    • I can learn from mistakes, and I can celebrate what I thought before and now know.

Resources:

Learning Plan:

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The learning progressions:

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The slide deck:

As a community of learners, we

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#ILoveMySchool