All posts by jplgough

Learner, Love Questions, Problem-finding, Math w/technology. Interests: Collaborating, PLC, Formative assmt

Patient development of conceptual understanding

<true confession>

Sometimes I teach at my pace instead of the pace of the learners in my care.

<tragic>

To where am I racing?

Rule Three from The Talent Code by Daniel Coyle is SLOW IT DOWN.

“Why does slowing down work so well? The myelin model offers two reasons.  First, going slow allows you to attend more closely to errors, creating a higher degree of precision with each firing – and when it comes to growing myelin, precision is everything.  As football coach Tom Martinez likes to say ‘It’s not how fast you can do it. It’s how slowly you can do it correctly.’ Second, going slow helps the practitioner to develop something even more important: a working perception of the skill’s internal blueprint – the shape and rhythm of the interlocking skill circuits.”  (p. 85)

In her Shortest Path post, Jennifer Wilson (@jwilson828) asks:

How many of our students would choose a beautiful path over the shortest path to learn a new topic? Which of our students would always choose the shortest path over a happier path to learn a new topic?

I wonder how many learners would choose a beautiful path over the shortest path.  Listen to Daniele Quercia.

I have a confession to make. As a scientist and engineer, I’ve focused on efficiency for many years. But efficiency can be a cult, and today I’d like to tell you about a journey that moved me out of the cult and back to a far richer reality.

What is lost by the time we save being efficient?

How might we take up the challenge of teaching and learning procedural fluency through patient development of conceptual understanding? What if I can show what I know in more than one way is deemed essential to learn?

What if we guide our learners on a journey that offers beauty, understanding, quiet, more time, and then efficiency?

Let’s avoid the dangers of a single path. Choose patient development of beautiful paths to conceptual understanding.

It is not an impossible dream.

Be patient.

Learn.


Coyle, Daniel. The Talent Code: Greatness Isn’t Born : It’s Grown, Here’s How. New York: Bantam, 2009. 217.  Print.

Summer Reading 2015 – 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.  Below is the Summer Reading flyer announcing the choices for this summer.

 We will 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.)

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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.)

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We have the opportunity to model how to incorporate reading strategies into all classrooms.  Think about teaching young learners to read a section of their book and jot down a sentence, phrase, and word that has meaning to them.  Great formative assessment as the lesson begins!

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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?

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Berger, Warren (2014-03-04). A More Beautiful Question: The Power of Inquiry to Spark Breakthrough Ideas. Bloomsbury Publishing. Kindle Edition.

Boushey, Gail, and Joan Moser. The Daily 5: Fostering Literacy Independence in the Elementary Grades. Portland, Me.: Stenhouse, 2014. Print.

Brown, Sunni. The Doodle Revolution: Unlock the Power to Think Differently. New York: Portfolio/Penguin, 2014. Print.

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

Ritchhart, Ron; Church, Mark; Morrison, Karin (2011-03-25). Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners. Wiley. Kindle Edition.

#AmericanPromise – PD Reflection

Have you watched American Promise?

As part of our PD day, we gathered and watched a 45-minute version of the film.

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American Promise Sketchnotes Jill Gough

What happens when you don’t fit in? Are you coached to change to become like the norm? Do you choose to change to be more like the norm? Does the environment change to fit you?

How might we continue to grow as a community? What actions will we take?

Foster bravery, gain and maintain a strong sense of self, acknowledge and expand success.

For every learner.

SMP-6: attend to precision #LL2LU

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

I can attend to precision.
(CCSS.MATH.PRACTICE.MP6)

But what if I can’t attend to precision yet? What if I need help? How might we make a pathway for success?

Level 4:
I can distinguish between necessary and sufficient conditions for definitions, conjectures, and conclusions.

Level 3:
I can attend to precision.

Level 2:
I can communicate my reasoning using proper mathematical vocabulary and symbols, and I can express my solution with units.

Level 1:
I can write in complete mathematical sentences using equality and inequality signs appropriately and consistently.

 How many times have you seen a misused equals sign? Or mathematical statements that are fragments?

A student was writing the equation of a tangent line to linearize a curve at the point (2,-4).  He had written:  y+4=3(x-2)

And then he wrote:

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He absolutely knows what he means: y=-4+3(x-2).

But that’s not what he wrote.

Which student responses show attention to precision for the domain and range of y=(x-3)²+4? Are there others that you and your students would accept?

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How often do our students notice that we model attend to precision? How often to our students notice when we don’t model attend to precision?

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Attend to precision isn’t just about numerical precision. Attend to precision is also about the language that we use to communicate mathematically: the distance between a point and a line isn’t just “straight” – it’s the length of the segment that is perpendicular from the point to the line. (How many times have you told your Euclidean geometry students “all lines are straight”?)

But it’s also about learning to communicate mathematically together – and not just expecting students to read and record the correct vocabulary from a textbook.

[Cross posted on Easing the Hurry Syndrome]

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

Many students would struggle much less in school if, before we presented new material for them to learn, we took the time to help them acquire background knowledge and skills that will help them learn. (Jackson, 18 pag.)

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)

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But…what if I can’t? What if I have no idea what to look for, notice, take note of, or attempt to generalize?

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.)

Are we teaching for a solution, or are we teaching strategy to express patterns? What if we facilitate experiences where both are considered essential to learn?

We want more students to experience the burst of energy that comes from asking questions that lead to making new connections, feel a greater sense of urgency to seek answers to questions on their own, and reap the satisfaction of actually understanding more deeply the subject matter as a result of the questions they asked.  (Rothstein and Santana, 151 pag.)

What if we collaboratively plan questions that guide learners to think, notice, and question for themselves?

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

Indeed, sharing high-quality questions may be the most significant thing we can do to improve the quality of student learning. (Wiliam, 104 pag.)

How might we design for, expect, and offer feedback on procedural fluency and conceptual understanding?

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.

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.)

[Cross posted on Easing the Hurry Syndrome]


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.

Rothstein, Dan, and Luz Santana. Make Just One Change: Teach Students to Ask Their Own Questions. Cambridge, MA: Harvard Education, 2011. Print.

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

 

 

How to be a boring, bad writer…and other ideas (TBT Remix)

I hadn’t thought about it this way:

So, if you want to be a boring, bad writer:

  1. Never ever learn new words.
  2. Be afraid to say interesting things.
  3. Read as little as possible.
  4. Always play on your laptops.
  5. Never touch a dictionary.
  6. Copyright.
  7. Never make [the reader] see the action.
  8. Never revise your writing.
  9. Definitely take the easy way.

Since I want to be a better writer, I should practice 1) using new words, 2) saying interesting things, 3) reading as much as possible, 4) leveraging technology to enhance learning, 5) using available resources, 6) striving to be unique and citing my sources, 7) presenting a good story, 8) repeating a revision cycle several times, and 9) understanding to “embrace the struggle.”

I wonder if the same set of ideas can be applied to PBL.  How to avoid PBL, Design Thinking, and makery:

  1. Never ever learn new applications and strategies.
  2. Be afraid to try interesting, complex problems.  It might take too long.
  3. Read and research as little as possible. Don’t read and watch Edutopia, Deep Design Thinking, or It’s About Learning resources or ideas from 12k12.
  4. Always use technology for one-way communication.  Just tell them what to do.  Don’t offer students the opportunity to have voice and choice in learning.
  5. If you try PBL, and it doesn’t work; just give up.  Never seek additional support and resources.
  6. Never collaborate with others on projects and problems that integrate ideas and/or concentrate on community-issues.
  7. Avoid applications and real-world experiences.  Never offer the opportunity to present to an authentic audience.
  8. Never say “I don’t know,” or “let’s find out together.” Answer every question asked in class, or better yet, don’t allow questions.
  9. Definitely do the very same thing you did this time last year.  It’s easy.  Take the easy way. Remember…the E-Z-way!

How about applying these ideas to balanced assessment?  How to be single-minded about assessment:

  1. Never ever try new techniques, methods, and strategies.
  2. Be afraid to try alternate forms of assessment: performance based assessment, portfolios, etc.
  3. Read and research as little as possible. Don’t read anything by Tom Guskey, Jan Chapuis, Bob Marzanno, Dylan Wiliam etc.
  4. Always use assessment to generate grades.  Never try non-graded assessment to make adjustments to learning that improve achievement.
  5. If you use rubrics or standards-based grading, and students don’t respond; just give up.  Don’t allow students to revise their understanding and assess again.  Let them learn it next year or in summer school.
  6. Rely on results from standardized tests to compare students.  Just follow the model set by adults that have not met you and your learners.
  7. Never assess for learning and reteach prior to a summative assessment.  Think that you are teaching a lesson if failure occurs with no chance to revise.
  8. Never offer 2nd chance test or other opportunities to demonstrate learning has occurred.
  9. Definitely use the very same assessment you did this time last year.  It’s easy.  Take the easy way. Remember… E-Z-way!

I find this approach connected the anti-innovation ideas from Kelly Green in her 2/21/2012 ForbesWoman article I found by reading Bob Ryshke’s post, What schools can do to encourage innovation.  It also reminds me of Heidi Hayes Jacob’s style in her TEDxNYED talk I found by reading Bo Adam’s What year are you preparing your students for?” Heidi Hayes Jacobs #TEDxNYED post.

I like the provocation of the video and the anti-ideas.  I appreciate the challenge of rephrasing these ideas as statements of what I could do to get better.  I wonder how we should practice to become better at PBL, balanced assessment, innovation and creativity, etc.  In the comment field below, will you share how would you answer this prompt?

Since I want to be a better ___________, I should practice 1)  _____, 2)  _____, 3)  _____, 4)  _____, 5)  _____, 6)  _____, 7)  _____, 8)  _____, and 9)  _____.


How to be a boring, bad writer…and other ideas was originally published on February 26, 2012.