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?

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.)

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.)

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.

Filed under: #LL2LU, 21st Century Learning, Learning, Learning Progressions, Questions, Reading Tagged: #LL2LU, Carol Dweck, Daniel Coyle, Dylan Wiliam, Embedded Formative Assessment, How to Support Struggling Students, make sense of problems and persevere, mathematical flexibility, Mindset, regularity in repeated reasoning, Robyn Jackson, SMP, SMP-1, SMP-8, The Talent Code ]]>

How are we facilitating experience where learners can risk and grow in sense making and perseverance? We want every learner to be able to say:

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

An important and powerful aspect of teachers’ practice concerns the ways in which they treat mistakes in mathematics classrooms. Research has shown that mistakes are important opportunities for learning and growth, but students routinely regard mistakes as indicators of their own low ability. (Boaler, n. pag.)

Do we teach mistakes as opportunities to learn? What if we slow down – pause – to reflect on what didn’t work well and plan a new tact?

In analyzing a series of setbacks, a key question to ask is Am I failing differently each time? “If you keep making the same mistakes again and again,” the IDEO founder David Kelley has observed, “you aren’t learning anything. If you keep making new and different mistakes, that means you are doing new things and learning new things.”(Berger, 124 pag.)

How might we take up the challenge to focus on learning? What if we teach the importance of struggle?

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, 43-44 pag.)

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

How might we amplify the important practice of how we treat mistakes? What if we teach and learn how to pay attention to mistakes and how to change based on what we learn?

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

What if we slow down to focus on learning?

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

Boaler, Jo. “Ability and Mathematics: The Mindset Revolution That Is Reshaping Education.” *Forum* 55.1 (2013): 143. *FORUM: For Promoting 3-19 Comprehensive Education*. SYMPOSIUM BOOKS Ltd, 2013. Web. 2015.

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

Filed under: Connecting Ideas, Learning, Questions, Reflection Tagged: A More Beautiful Question, Daniel Coyle, Jo Boaler, Talent Code, Warren Berger ]]>

No one threw rocks at me last week when I launched WODB with our entire teaching faculty, not just the math faculty. Actually, I think it was quite fun.

How might we lend each other our observations and thinking? What if we improve the way we notice and note our observations? Can we help the young learners in our care to construct viable arguments and critique the reasoning of others?

What if we try? Can we slowly hack away at the “one right answer” culture in our classrooms?

Suppose you choose which one doesn’t belong and it is different from the one I selected. Is it possible that we can both be correct? Can we construct a viable argument to make our case? In other words, can we say why we see things the way we do? Can we critique the reasoning of someone who sees it differently? Are we able to teach listening to and seeing another’s point of view?

Will listening to another add to our understanding and the flexibility of our thinking?

Do we apply what we learn? If teaching very young learners, run – don’t walk – to check out Christopher Danielson’s *A Better Shapes Book*.

As a faculty, we played with WODB on Friday. On Monday, it was put into practice with our youngest learners.

Click to view slideshow.What might we learn if we risk trying new things? How might we learn and grow?

Be brave.

Risk.

Experiment.

Learn by doing.

Bourassa, Mary. *Which One Doesn’t Belong?* N.p., n.d. Web.

Danielson, Christopher. *Which One Doesn’t Belong: A Shapes Book*. A Talking Math with Your Kids Production, 07 Jan. 2015. Web. 30 Apr. 2015.

Filed under: 21st Century Learning, Ask Don't Tell, Connecting Ideas, Creativity, Learning, Professional Development Plans, Questions ]]>

In the video below, Dylan Wiliam discusses the subtle difference between assessment for learning and formative assessment.

From the video:

*Formative assessment – assessment that actually shapes learning*.

“In order to engage inhigh-quality assessment, teachers need to firstidentify specific learning targetsand then to know whether the targets are asking students to demonstrate their knowledge, reasoning skills, performance skills, or ability to create a quality product.

“The teacher must alsounderstand what it will take for students to become masters of the learning targets.

It is not enough that the teacher knows where students are headed; the students must also know where they are headed, and both theteacher and the students must be moving in the same direction.”(Conzemius, O’Neill, 66 pag.)

If we are to continue to learn and improve, how might we create actionable experiences that form learning?

Conzemius, Anne; O’Neill, Jan. The Power of SMART Goals: Using Goals to Improve Student Learning. Bloomington, IN: Solution Tree, 2006. Print.

Filed under: #LL2LU, Assessment, Connecting Ideas, Learning Progressions, Questions Tagged: Anne Conzemius, Assessment for Learning, Dylan Wiliam, formative assessment, Jan O'Neill ]]>

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.

Filed under: Connecting Ideas, Questions, Reflection, TED talk Tagged: #SlowMath, #TEDTalkTuesday, Daniel Coyle, Daniele Quercia, efficiency, happiness, Jennifer Wilson, The Talent Code ]]>

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.)

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.)

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!

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?

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.

Filed under: Connecting Ideas, Creativity, Professional Development Plans, Questions, Reading Tagged: A More Beautiful Question, Daniel Coyle, Gail Boushey, Joan Moser, Making Thinking Visible, Ron Ritchhart, Sentence-Phrase-Word, Steve Long-Nguyen Robbins, Summer Reading, Sunni Brown, The Daily 5, The Doodle Revolution, The Talent Code, Visible Thinking Routine, Warren Berger, What If?: Short Stories to Spark Diversity Dialogue ]]>

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

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.

Filed under: Professional Development Plans, Questions, Sketch Notes Tagged: American Promise, doodle, questions, sketch note ]]>

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:

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?

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**?

**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]

Filed under: #LL2LU, Algebra, Questions Tagged: attend to precision, SMP, SMP-6 ]]>

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)**

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.

Filed under: #LL2LU, Algebra, Assessment, Connecting Ideas, Learning, Learning Progressions Tagged: #LL2LU, Dan Rothstein, Dylan Wiliam, Embedded Formative Assessment, feedback, How to Support Struggling Students, Luz Santana, Make just one change, regularity in repeated reasoning, Robyn Jackson, SMP, SMP-8 ]]>

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
**

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?

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?

Or over the set of complex numbers?** **

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?** **

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

What if we are looking at powers of **i**?

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]

Filed under: #LL2LU, Algebra, Ask Don't Tell, Connecting Ideas, Learning, Questions, Synergy 8 Tagged: #LL2LU, @jwilson828, CAS, regularity in repeated reasoning, SMP, SMP-8, TI-Nspire CAS ]]>