Category Archives: Reading

Listeners: evaluative, interpretive, generative

What type of listener are am I right now? Do I know what modes of listening I use? How might I improve as a listener? What if I actively choose to practice?

Listening informs questioning. Paul Bennett says that one of the keys to being a good questioner is to stop reflexively asking so many thoughtless questions and pay attention— eventually, a truly interesting question may come to mind. (Berger, 98 pag.)

I’ve been studying a paper Gail Burrill (@GailBurrill) shared with us a couple of weekends ago.  The paper, Mathematicians’ Mathematical Thinking for Teaching: Responding to Students’ Conjectures by Estrella Johnson, Sean Larsen, Faith Rutherford of Portland State University, discusses three types of listening: evaluative, interpretive, and generative.

The term evaluative listening is characterized by Davis (1997) as one that “is used to suggest that the primary reason for listening in such mathematical classrooms tends to be rather limited and limiting” (p. 359). When a teacher engages in evaluative listening the goal of the listening is to compare student responses to the “correct” answer that the teacher already has in mind. Furthermore, in this case, the student responses are largely ignored and have “virtually no effect on the pre-specified trajectory of the lesson” (p. 360).

When a teacher engages in interpretive listening, the teacher is no longer “trying simply to assess the correctness of student responses” instead they are “now interested in ‘making sense of the sense they are making’” (Davis, 1997, p. 365). However, while the teacher is now actively trying to understand student contribution, the teacher is unlikely to change the lesson in response.

Finally, generative listening can “generate or transform one’s own mathematical understanding and it can generate a new space of instructional activities” (Yackel et al., 2003, p. 117) and is “intended to reflect the negotiated and participatory nature of listening to students mathematics” (p. 117). So, when a teacher is generatively listening to their students, the student contributions guide the direction of the lesson. Rasmussen’s notion of generative listening draws on Davis’ (1997) description of hermeneutic listening, which is consistent with instruction that is “more a matter of flexible response to ever-changing circumstances than of unyielding progress towards imposed goals” (p. 369).

If you’d like to read about these three types of listening the authors continue their paper with a case study.

Evaluative listeners seek correct answers, and all answers are compared to the one deemed correct from a single point of view.

Interpretive listeners seek sense making.  How are learners processing to produce solutions to tasks? What does the explanation show us about understanding?

Generative listeners seek next steps and questions themselves. In light of what was just heard, what should we do next? And, then they act.

For assessment to function formatively, the results have to be used to adjust teaching and learning; thus a significant aspect of any program will be the ways in which teachers make these adjustments. (William and Black, n. pag)

“Great teachers focus on what the student is saying or doing,” he says, “and are able, by being so focused and by their deep knowledge of the subject matter, to see and recognize the inarticulate stumbling, fumbling effort of the student who’s reaching toward mastery, and then connect to them with a targeted message.” (Coyle, 177 pag.)

What if we empower and embolden learners to ask the questions they need to ask by improving the way we listen and question?

Unless you ask questions, nobody knows what you are thinking or what you want to know.” (Rothstein and Santana, 135 pag.)

How might we practice generative listening to level up in the art of questioning? What is we listen to inform our questioning?

How might we collaborate to learn and grow as listeners and questioners?

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

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

Davis, B. (1997). Listening for difference: An evolving conception of mathematics teaching. Journal for Research in Mathematics Education. 28(3). 355–376.

Johnson, E., Larsen, S., Rutherford (2010). Mathematicians’ Mathematicians’ Mathematical Thinking for Teaching: Responding to Students’ Conjectures. Thirteenth Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education Conference on Research in 
Undergraduate Mathematics Education. Raleigh, NC. Retrieved from on September 12, 2015.

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

Wiliam, Dylan, and Paul Black. “Inside the Black Box: Raising Standards Through Classroom Assessment.” The College Cost Disease (2011): n. pag. WEA Education Blog. Web. 13 Sept. 2015.

Yackel, E., Stephan, M., Rasmussen, C., Underwood, D. (2003). Didactising: Continuing the work of Leen Streefland. Educational Studies in Mathematics. 54. 101–126.

Intersection of struggle and hope (TBT Remix)

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.)

When learners are thrashing around blindly, how might we serve as refuge for support, encouragement, and a push in a new direction? (And, what if one of the learners is me?)

Many days we stand in the intersection of struggle and hope.

We can observe our children carefully and look into their eyes and say, “Can I tell you what a great person you are?” and follow-up with concrete examples of the way they give amazing hugs and how kindly they treat their friends.  This is the stuff of our most important relationships: Aiming to understand and be understood. (Lehman, Christopher, and Kate Roberts)

… some teachers preached and practiced a growth mindset. They focused on the idea that all children could develop their skills, and in their classrooms a weird thing happened. It didn’t matter whether students started the year in the high- or the low-ability group. Both groups ended the year way up high. It’s a powerful experience to see these findings. The group differences had simply disappeared under the guidance of teachers who taught for improvement, for these teachers had found a way to reach their “low-ability” students. (Dweck, Carol)

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, Shawn.)

To pursue bright spots is to ask the question “What’s working, and how can we do more of it?” Sounds simple, doesn’t it? Yet, in the real world, this obvious question is almost never asked. Instead, the question we ask is more problem focused: “What’s broken, and how do we fix it?” (Heath, Chip and Dan Heath)

And so the challenge of our future is to say, are we going to connect and amplify positive tribes that want to make things better for all of us?  (Godin, Seth)

Move the fulcrum. Pursue bright spots. Amplify to make things better.

Aim to understand and to be understood.

Intersection of struggle and hope was originally published on December 10, 2014.

Achor, Shawn (2010-09-14). The Happiness Advantage: The Seven Principles of Positive Psychology That Fuel Success and Performance at Work (Kindle Locations 947-948). Crown Publishing Group. Kindle Edition.

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 (2006-02-28). Mindset: The New Psychology of Success (Kindle Locations 1135-1138). Random House, Inc.. Kindle Edition.

Heath, Chip; Heath, Dan (2010-02-10). Switch: How to Change Things When Change Is Hard (p. 45). Random House, Inc.. Kindle Edition.

Lehman, Christopher, and Kate Roberts. Falling in Love with Close Reading: Lessons for Analyzing Texts and Life. N.p.: n.p., n.d. Print.

Transcript: Seth Godin – The Art of Noticing, and Then Creating.” On Being. N.p., n.d. Web. 09 Dec. 2014.

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: 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.

Deep practice: struggle, mistakes, learning – The Talent Code VTR SPW

How might we deepen learning experiences? What if we see small mistakes and failures as opportunities to learn?

Deep practice is built on a paradox: struggling in certain targeted ways—operating at the edges of your ability, where you make mistakes—makes you smarter. Or to put it a slightly different way, experiences where you’re forced to slow down, make errors, and correct them—as you would if you were walking up an ice-covered hill, slipping and stumbling as you go—end up making you swift and graceful without your realizing it. (Coyle, 18 pag.)

What if, in school (and out), we become serious about learning from mistakes? How will we learn from a mistake if it is erased, hidden, or ignored? What if we learn and share and seek feedback?

The second reason deep practice is a strange concept is that it takes events that we normally strive to avoid—namely, mistakes—and turns them into skills. To understand how deep practice works, then, it’s first useful to consider the unexpected but crucial importance of errors to the learning process. (Coyle, 20 pag.)

How can we tell when deep practice happens and deep learning is in progress?

Making progress became a matter of small failures, a rhythmic pattern of botches, as well as something else: a shared facial expression. (Coyle, 13 pag)


Summer Reading using VTR: Sentence-Phrase-Word:
The Talent Code
Chapter 1: The Sweet Spot

How do we find and get into “the zone” to learn deeply? How might we help every learner dwell in their sweet spot, learning at the edge of their capabilities?

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

#TEDTalkTuesday from A More Beautiful Question

One of the choices for summer reading in our community is A More Beautiful Question: The Power of Inquiry to Spark Breakthrough Idea by Warren Berger (@GlimmerGuy).

The following three are featured in the book, and I thought we might want to hear from them to add depth to the reading.

Mick Ebeling: The invention that unlocked a locked-in artist

Jack Andraka: A promising test for pancreatic cancer … from a teenager

Dan Meyer: Math class needs a makeover


Summer Reading using VTR: Sentence-Phrase-Word

Reading nonfiction. Close reading of nonfiction.

How do we annotate the text, look for patterns, and ask questions to engage deeply when reading?

Tracking content using imagery, color, word pictures and typography can change the way you understand information and also dramatically increase your level of knowledge and retention. (Brown, n. pag.)

How do we engage with and make meaning and connections from text? How might we notice and note the big ideas from a text to capture what speaks to us?

How do we show and share what we are thinking? What if we use the Sentence-Phrase-Word visible thinking routine as we read this summer?

Screen Shot 2015-05-12 at 7.14.20 PM Screen Shot 2015-05-12 at 7.25.04 PM

…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, 207 pag.)

What might we learn when we discuss what speaks to us?

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

Brown, Sunni. “VISUAL NOTE-TAKING 101 / PERSONAL INFODOODLING™.” Visual Thinking/Literacy/Gaming/Facilitation for a Smarter World. Sunni Brown, n.d. Web. 12 May 2015.

How to Do a Close Reading.” Harvard College Writing Center. Harvard Writing Project, n.d. Web. 12 May 2015.

Ritchhart, Ron, Mark Church, and Karin Morrison. Making Thinking Visible: How to Promote Engagement, Understanding, and Independence for All Learners. San Francisco, CA: Jossey-Bass, 2011. Print.