Category Archives: Learning

Thinking from different angles. Facing challenges. (TBT Remix)

Thinking from different angles. Facing challenges. Making thinking more visible.

The modern world demands that we all think a bit more productively, more creatively, more rationally; that we think from a different angle, with a different set of muscles, with a different set of expectations; that we think with neither fear nor favor, with neither blind optimism nor sour skepticism. (Levitt and Dubner)

This means that facing challenges, both problems and opportunities, is vital to personal success. This is the arena in which we can grow, excel, create, and expand. Without these challenges, we wither. Because of this importance, it is equally vital that we examine the way in which we meet the challenges by questioning our path from the outset. (Lichtman)

So, if we really believe that good communication is core to intelligent strategy, to seamless teamwork, to the pursuit of excellence, we must take seriously the limitation of being literally blinded to larger realities. We don’t know what we don’t know until we ask others to add their perspectives and until we start drawing it out for everyone to see. (Brown)

The costs of changing nothing are stagnation and resignation to the status quo. But the benefits of changing your reality— and sharing that positive reality with others— are the kinds of successes, discoveries, and breakthroughs that can transform not only your own life but the world. (Achor)

What if we examine the way we meet challenges, think from different angles,  share perspectives, and share successes? How might we change our part of the world?

Thinking from different angles. Facing challenges. was originally published on December 22, 2014.

Achor, Shawn (2013-09-10). Before Happiness: The 5 Hidden Keys to Achieving Success, Spreading Happiness, and Sustaining Positive Change (p. 232). Crown Publishing Group. Kindle Edition.

Levitt, Steven D.; Dubner, Stephen J. (2014-05-12). Think Like a Freak: The Authors of Freakonomics Offer to Retrain Your Brain (p. 8). HarperCollins. Kindle Edition.

Lichtman, Grant (2010-05-25). The Falconer (Kindle Locations 1330-1332). iUniverse. Kindle Edition.

Silos Suck: How to Doodle Everyone Onto the Same Page.” Sunni Brown. Sunni Brown, 21 Nov. 2014. Web. 22 Dec. 2014.

Move the fulcrum to a positive mindset; find a path forward (TBT remix)

Move the fulcrum so that all the advantage goes to a negative mindset, and we never rise off the ground. Move the fulcrum to a positive mindset, and the lever’s power is magnified— ready to move everything up. (Achor, 65 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.)

How are we intentionally teaching growth mindset? How might we coach ourselves and our learners using Carol Dweck’s first steps to changing your mindset?

Step1. Learn to hear your fixed mindset “voice.”

Step 2. Recognize that you have a choice.

Step 3. Talk back to it with a growth mindset voice.

Step 4. Take the growth mindset action.

“Mostly though, I feel it in a changed attitude toward failure, which doesn’t feel like a setback or the writing on the wall anymore, but like a path forward.” (Coyle, 217 pag.)

Move the fulcrum to a positive mindset’ find a path forward was originally published on January 12, 2015.

Achor, Shawn. The Happiness Advantage: The Seven Principles of Positive Psychology That Fuel Success and Performance at Work. New York: Broadway, 2010. Print.

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

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



Deep Practice, Leveling, and Communication (TBT Remix)

Does a student know that they are confused and can they express that to their teacher? We need formative assessment and self-assessment to go hand-in-hand.

I agree that formative self-assessment is the key. Often, I think students don’t take the time to assess if they understand or are confused. I think that it is routine and “easy” in class. The student is practicing just like they’ve been coached in real time. When they get home, do they “practice like they play” or do they just get through the assignment? I think that is where deep practice comes into play. If they practice without assessing (checking for success) will they promote their confusion?  I tell my students that it is like practicing shooting free throws with your feet perpendicular to each other. Terrible form does not promote success. Zero practice is better than incorrect practice.

With that being said, I think that teachers must have realistic expectations about time and quality of assignments. If we expect students to engage in deep practice (to embrace the struggle) then we have to shorten our assignments to accommodate the additional time it will take to engage in the struggle.  We now ask students to complete anywhere from 1/3 to 1/2 as many problems as in the past with the understanding that these problems will be attempted using the method of deep practice.

Our version of deep practice homework:
“We have significantly shortened this assignment from years past in order to allow you time to work these questions correctly. We want you do work with deep practice.

  • Please work each problem slowly and accurately.
  • Check the answer to the question immediately.
  • If correct, go to the next problem.
  • If not correct, mark through your work – don’t eraseleave evidence of your effort and thinking.
    • Try again.
    • If you make three attempts and can not get the correct answer, go on to the next problem. “

I also think that the formative assessments with “leveling” encourage the willingness to struggle. How many times has a student responded to you “I don’t get it”? Perhaps it is not a lack of effort. Perhaps it is a lack of connected vocabulary. It is not only that they don’t know how, is it that they don’t know what it is called either. It is hard to struggle through when you lack vocabulary, skill, and efficacy all at the same time. How might we help our learners attend to precision, to communicate in the language of our disciplines?

Now is the time to guide our young learners to develop voice, confidence (and trust), and a safe place to struggle.

Deep Practice, Leveling, and Communication was originally published on November 20, 2010


#ShowYourWork: words, pictures, numbers

In her Colorful Learning post, Learning: Do our students know we care about that?, Kato shared the following learning progression for showing your work.

What if we guide our learners to

I can describe or illustrate ow I arrived at a solution so that the reader understands without talking to me?

Isn’t this really about making thinking visible and clear communication?  Anyone who has taught learners who take an AP exam can attest to the importance of organized, clear pathways of thinking. It is not about watching the teacher show work, it is about practicing, getting feedback, and revising.

Compare the following:

What if a learner submits the following work?

Screen Shot 2015-11-09 at 8.43.46 AM

Can the reader understand how the writer arrived at this solution without asking any questions?

What if the learner shared more thinking? Would it be clearer to the reader? What do you think?


How often do we tell learners that they need to show their work? What if they need to show more work? What if they don’t know how?

How might we communicate and collaborate creatively to show and tell how to level up in showing work and making thinking visible?

How might we grow in the areas of comprehension, accuracy, flexibility, and deeper understanding if we learn to communicate clearly using words, pictures, and numbers?

#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.

#TEDTalkTuesday: Brave space a.k.a. turning collisions into connections

Yesterday, I had the privilege of attending a session at GISA on Implicit Bias facilitated by Trinity’s very own Gina Quiñones () and Lauren Kinnard ().

Lauren and Gina began the session by setting norms, challenging us to level up from a safe space to a brave space. How might we dare to be brave enough to express what we think and feel? What if we listen to others to learn?

Screen Shot 2015-11-03 at 6.53.47 PM

They challenged us to consider how might we turn our own cultural collisions into more meaningful connections and shared the following TED talk.

Turning cultural collisions into cultural connections: Nadia Younes at TEDxMontrealWomen

I am grateful to work and learn with brave leaders, and I am thankful for all who trust enough to share brave space.

Fluency: comprehension, accuracy, flexibility, and efficiency

No strategy is efficient for a student who does not yet understand it. (Humphreys & Parker, 27 pag.)

If both sense and meaning are present, the likelihood of the new information getting encoded into longterm memory is very high. (Sousa, 28 pag.)

When we teach for understanding we want comprehension, accuracy, fluency, and efficiency. If we are efficient but have no firm understanding or foundation, is learning – encoding into longterm memory – happening?

We don’t mean to imply that efficiency is not important. Together with accuracy and flexibility, efficiency is a hallmark of numerical fluency. (Humphreys & Parker, 28 pag.)

What if we make I can make sense of problems and persevere in solving them and I can demonstrate flexibility essential to learn?


Flexibility #LL2LU

If we go straight for efficiency in multiplication, how will our learners overcome following commonly known misconception?

common misconception: (a+b)²=a² +b²


correct understanding: (a+b)²=a² +2ab+b²

The strategies we teach, the numeracy that we are building, impacts future understanding.  We teach for understanding. We want comprehension, accuracy, fluency, and efficiency.

How might we learn to show what we know more than one way? What if we learn to understand using words, pictures, and numbers?

What if we design learning episodes for sense making and flexibility?

Humphreys, Cathy, and Ruth E. Parker. Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4-10. Portland, ME: Steinhouse Publishers, 2015. Print.

Sousa, David A. Brain-Friendly Assessments: What They Are and How to Use Them. West Palm Beach, FL: Learning Sciences, 2014. Print.