Category Archives: Connecting Ideas

#TEDTalkTuesday: Explore more than one path

Yesterday, I wrote that efficiency should never trump understanding.  Today, I’d like to ponder efficiency as one of many paths.

Daniele Quercia: Happy maps
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.

On this cartography, you’re not only able to see and connect from point A to point B the shortest segments, but you’re also able to see the happy segment, the beautiful path, the quiet path. In tests, participants found the happy, the beautiful, the quiet path far more enjoyable than the shortest one, and that just by adding a few minutes to travel time.

How might we encourage our learners to explore paths in addition to the most efficient?

In context: review, new ideas, norms, and inquiry

Learning in context.  Answering questions based on our collected data.

How might we review what we already know and build upon it at the same time?  And, how are we teaching our learners about the social norms and the sociomathematical norms in the context of our community?

I love it when co-learning happens.  Kristi Story (@kstorysquared) facilitated another great lesson in statistics with our 6th graders this morning.  Our learners collected data to investigate statistical questions and distribution of data in terms of shape, center, and spread.

Collecting data (love this organization):

  • I usually spend about _____ MINUTES taking a shower or bath.
  • There is a total of _____ LETTERS in my first, middle, and last names.
  • There are _____ PEOPLE living in my home.

Collaboratively analyzing the data:

  • Data sets were collected for each question.
  • Each group was given one set of the collected data to organize and analyze.

Establishing both social and sociomathematical norms in context.

  • What if we collect data to answer statistical questions?
  • What if we grow as a community to continue to embrace a norm of challenging and questioning each other?
  • How might we take messy data and organize it?
  • How will we summarize the data to communicate center, shape, and spread?
  • How might we show what we know in more than one way?
  • What if we organize collected data and discuss the distribution of data in terms of center, shape, and spread?

Learners were not told to answer the above questions.  The questions and the necessary answers came up organically as the learners grappled with the data.

My Learning

I joined the group working on minutes taking a shower.  Here’s what it looked like.

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Here’s my messy attempt to organize and analyze the collected data.

We could compute the landmark data points.  We could quickly represent the data as a dot plot.  What happens when or if we want to represent the data using a box plot? I really didn’t know how to draw a box plot of this data since the median=Q3.

What can we learn by using technology to aid in the visualization process?

dot-box1

What if we leverage technology to show us more than we might see when we graph by hand?

dot-box3
What if we are intentional in our commitment to #AskDontTell inquiry approach to learning? How might we continue to teach the norm of challenging and questioning? What if we learn about and practice both social norms and sociomathematical norms in context as we learn in grow together?


Norms and Mathematical Proficiency.” Teaching Children Mathematics. National Council of Teachers of Mathematics, Aug. 2013. Web. 31 Aug. 2015.

What we don’t remember about the foundation…

I wonder if, when the house is finished, we forget the foundational infrastructure required for function.  How does water get into and out of my house? Who ran the wires so that our lamps illuminate our space? Who did the work, and what work was done, prior to the slab being poured?

When we recall a basic multiplication fact, it’s like flipping a light switch in our house. The electrical wiring allowing us to turn on the light is linked to sound, safe, and deeply connected infrastructure. (K. Nims, personal communication, August 30, 2015)

Just like the light switch is not part of the foundation, memorization of multiplication facts is also not foundational. It is efficient and functional.  Efficiency must not trump understanding.

We need people who are confident with mathematics, who can develop mathematical models and predictions, and who can justify, reason, communicate, and problem solve. (Boaler, n. pag.)

Screen Shot 2015-08-30 at 7.45.22 PMStudents who rely solely on the memorization of math facts often confuse similar facts. (O’Connell, 4 pag.)

Students must first understand the facts that they are being asked to memorize. (O’Connell, 3 pag.)

What if we have forgotten all the hard work that came prior to the task of memorizing our multiplication facts?

Do we remember learning about multiplication as repeated addition? Have we forgotten the connection between multiplication, arrays, and area?

Conceptual understanding of multiplication lays a foundation for deeper understanding of many mathematical topics.  Memorizing facts denies learners the opportunity to connect ideas, exercise flexibility, and interact with multiple strategies.

The goal is to have confident, competent, critical thinkers. Let’s remember that a strong foundation has many unseen components.  What if we slow down to develop deep understanding of the numeracy of multiplication?

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.”  (Coyle, 85 pag.)

How might we serve our learners by expecting them to show what they know more than one way?


Boaler, Jo. “The Stereotypes That Distort How Americans Teach and Learn Math.” The Atlantic. Atlantic Media Company, 12 Nov. 2013. Web. 30 Aug. 2015.

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

O’Connell, Susan, and John SanGiovanni. Mastering the Basic Math Facts in Multiplication and Division: Strategies, Activities & Interventions to Move Students beyond Memorization. Portsmouth, NH: Heinemann, 2011. Print.

#TEDTalkTuesday: community problem solving

How are we engaging learners in community-issues problem solving? This week’s TED talk celebrates our own.

Andrew Hennessy – Turning “Lost” Into “Found”

My school faced a problem: An unruly Lost and Found space filled with multiple examples of the same clothing, namely blue fleece cover-ups. My goal was to reinvent the process for labeling, sorting, storing and returning items that get left behind at my school. The solution involved applying a wear-proof QR code that contains critical information used to help reunite the lost item with the owner.  Teachers use a phone based QR app complete with automated parental notification to make the magic happen.

How might we continue to teach community problem solving? What if we teach and learn more about perseverance?

How might we help our learners choose and collaborate projects that they care about?  What if we join a team of learners to discover how the content of our discipline can be used in the process of finding, working on, and solving problems?

community, Community, COMMUNITY? (TBT Remix)

To which level of community are you and your learners connected:  community, Community, or COMMUNITY?  How connected are you and your learners to a community, any community?

This week I attended the Trinity School 60th Anniversary Speaker Series featuring Dr. Heidi Hayes Jacobs since I am invited and included in this learning community.  Dr. Jacobs asked

“Who owns the learning?”

How do we use technology to broaden the learning community for the children in our care so that they own their learning?  How do we use technology to broaden our own learning community so that we continue to learn and grow?

I’ve been thinking about the literal meaning of being a member of a community which has inspired me to ask:

  • Do the learners that assemble in my classroom form a community?
  • Do the learners in my school form a community?
  • Do the faculty in my school form a community?
  • Are our learners’ parents part of our learning community?
  • Are our learners’ parents part of their child’s learning community?
  • What about the authors, teachers, learners, etc. outside my school – are they part of our community?
  • Are the teachers that learn with me at conferences part of a community of learners that contribute to the success of my learners?

I have to ask myself if my learners are in a community that is restricted only to the 26 people that assemble during Xnd period.  Are my colleagues or the parents of my learners invited to be in our Xnd period learning community, creating Community?  Are our national and international colleagues, friends, and experts invited to join our Xnd period community, creating COMMUNITY?

How will learners own their learning, and how will they encounter opportunities to question, to reason, to express themselves, to discover and pursue a passion?  With whom will our learners question, reason, express themselves, discover and pursue a passion?

How open are we, really, to these ideas?  What actions do we take?  How are we modeling learning and owning our learning?

To which do we belong: community, Community, COMMUNITY?

To which should we belong: community, Community, COMMUNITY?


community, Community, COMMUNITY? was originally posted on September 30, 2011.

#TEDTalkTuesday: Noticing a.k.a. practicing neoteny

When innovators talk about the virtues of beginner’s mind or neoteny, to use the term favored by MIT Media Lab’s Joi Ito, one of the desirable things they’re referring to is that state where you see things without labels, without categorization. Because once things have been labeled and filed, they become known quantities— and we don’t think about them, may not even notice them. (Berger, 41 pag.)

Tony Fadell: The first secret of design is … noticing

You see, there are invisible problems all around us, ones we can solve. But first we need to see them, to feel them.

Look broader. Look closer. Think younger.

We must become, in a word, neotenous (neoteny being a biological term that describes the retention of childlike attributes in adulthood). To do so, we must rediscover the tool that kids use so well in those early years: the question. Ito puts it quite simply: “You don’t learn unless you question.” (Berger, 24 pag.)


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

Try on a new lens – (TBT Remix)

We perceive only the sensations we are programmed to receive, and our awareness is further restricted by the fact that we recognize only those for which we have mental maps or categories. (Zander, 10 pag.)

The following was posted on the last day of Pre-Planning my first year at Trinity.  While no longer a stranger, I continue to need and learn from  the stories of our children and colleagues.

From August 14, 2012:

I am new to my community – a stranger, if you will.  As a fledgling member of the community, I need and want to hear the stories of the children and my colleagues, the history of the people and the place. One spectacular opportunity afforded me is to hear the same story from multiple perspectives.  I value the luxury of learning and seeing through multiple lenses.

Through which lens do I choose to look at my surroundings?  On what do I choose to focus?  How do I practice seeing bright spots?  How often do I focus on success rather than struggle?  How do I make the practice of bright-spot-seeking a habit?  Do I teach this habit to others?

For our children, school begins tomorrow. What will they want and need from us, their teachers?  How will we offer feedback as they learn and grow?  Is it our habit to highlight their success or their struggle?  When we mark student papers, do we “award credit” or do we “take points off?” Literally, what do we mark?  What is our habit? What are we teaching through our habit?

How do our actions impact the lens through which our learners see themselves? How does our habit impact the way we see our learners? I am learning to make a point to change my lens to see with different clarity.  What does the story say if I change my view? What do we learn as we try on a new lens?

The frames our minds create define – and confine – what we perceive to be possible.  (Zander, 14 pag.)

Draw a different frame around the same set of circumstances and new pathways come into view. (Zander, 1 pag.)

How do our actions impact the lens through which our learners see themselves? How does our habit impact the way we see our learners? I am learning to make a point to change my lens to see with different clarity.

What does the story say if I change my view? What do we learn as we try on a new lens?


[This post was originally cross published as Try on a new lens – edu180atl: jill gough 8.14.12 and “edu180atl: jill gough 8.14.12“]

Zander, Rosamund Stone, and Benjamin Zander. The Art of Possibility: Transforming Professional and Personal Life. Camberwell, Vic.: Penguin, 2002. Print.