Tag Archives: A More Beautiful Question

Number Talks: how AND why

Listening informs questioning. (Berger, 98 pag.)

How do we know learning has occurred? How do we know how learning has happened? What if we pause and listen to learn?

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

How would you add 39 to 67? Would you use the traditional algorithm? Would you need paper? How might we teach flexibility, sense making, and numeracy to build fluency and confidence?

Number talks are about students making sense of their own mathematical ideas. (Humphrey & Parker, 13 pag.)

How might we seize the opportunity to confer with our learners to see if they are making sense of what is being taught?

This is the challenge – and joy – of teaching by listening to students. (Humphrey & Parker, 13 pag.)

If interested in additional examples of number talks, both the how and the why, listen to Jo Boaler and her students from the Stanford Online MOOC How to Learn Math: For Teachers and Parents.

Do we believe our learners – every one of them – are capable of developing proficiency in mathematics?

How might we show what we know more than one way?

How might we continue to send the message I believe in you and mean it?

What if we listen to learn?


I am grateful to Kristin Gray (@MathMinds) and Crystal Morey (@themathdancer) for their leadership and facilitation as a dozen #TrinityLearns faculty participate in an online book club (#mNTmTch) for Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding Grades 4-10 along with over 600 educators across the globe.


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

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.

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 http://sigmaa.maa.org/rume/crume2010/Archive/JohnsonEtAl.pdf 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.

#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.

Confidence, strengths, gratitude – A More Beautiful Question VTR SPW

Why do we begin to fear asking questions?

If you fear not having answers to the questions you might ask yourself, remember that one of the hallmarks of innovative problem solvers is that they are willing to raise questions without having any idea of what the answer might be. (Berger, 186 pag.)

How might we develop as questioners comfortable with uncertainty?

When you change one small thing and it works, it can help breed the confidence to change other things— including bigger ones. (Berger, 197 pag.)

If you don’t know, you don’t know.  How often do we hear questions that show uncertainty? I don’t even know where to begin.  I have no idea what question to ask. What if we offer actionable feedback, in the form of positive questions, to highlight what is known to get to what is not known? How might we bolster confidence and bravery to ask the next uncertain-of-the-answer question?

The main premise of appreciative inquiry is that positive questions, focusing on strengths and assets, tend to yield more effective results than negative questions focusing on problems or deficits. Strength-based questioning focuses on what is working in our lives— so that we can build upon that and get more out of it. (Berger, 190 pag.)

AMBQ-Chpt5

Summer Reading using VTR: Sentence-Phrase-Word:
A More Beautiful Question
Chapter 5: Questioning for Life

Usually, my choice of Sentence-Phrase-Word combinations connect to form an idea for me.  In this case, experiment, should be my choice for “the word” from this chapter, particularly pages 198-199.

However, the word I keep coming back to is gratitude.

Happiness researchers such as Tal Ben-Shahar, author of Happier and Being Happy and a professor at Harvard University, believe it’s important to “cultivate the habit of gratitude.” Simply by asking, at the end of each day, What am I grateful for? and writing down the answers in a “gratitude journal,” people tend to be “happier, more optimistic, more successful, more likely to achieve their goals,” according to Ben-Shahar. (Berger, 190 pag.)

What if this is an essential to learn? How might we focus on taking actions to help ourselves and others be happier, more optimistic, more successful than we were yesterday?


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

Teaching the art of questioning – A More Beautiful Question VTR SPW

How are we teaching the art of questioning? Are we frustrated by the questions or lack of questions? What if we are more intentional about thoughtful questioning and reflection? How might we adjust the protocols and processes in our learning environments?

If a [community] is going to encourage questioning, it must teach people to do it well— or risk being besieged by nonproductive questions. (Berger, 171 pag.)

I’m intrigued by the idea not being besieged by precocious and nonproductive questions. How often do we address the first question that is launched? What if we collect many questions and then collaboratively select a questioning path to follow?

AMBQ - Chapt 4

Summer Reading using VTR: Sentence-Phrase-Word:
A More Beautiful Question
Chapter 4: Questioning in Business

How might we enhance our ability to think deeply about the questions that we dwell on and value?

…that clear vision is arrived at, and constantly modified and sharpened, through deep reflection and questioning. (Berger, 161 pag.)

What if we pause to facilitate question-storming to generate many questions?

The Right Question Institute— which specializes in teaching students to tackle problems by generating questions, not solutions— has found that groups of students (whether children or adults) seem to think more freely and creatively using the “question-storming” method, in which the focus is on generating questions. (Berger, 153 pag.)

What if we take up the challenge of teaching the art of questioning? How might we change the conversations and experiences  around learning?


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

Listening, trust, and feedback – A More Beautiful Question VTR SPW

Bennett says that within IDEO, the company recognizes it’s important to create an environment where it’s safe to ask “stupid” questions. (Berger, 80 pag.)

It’s about culture and atmosphere and bravery. Are we striving for progress or perfection?

As the writer Peter Sims noted in Harvard Business Review, most of us, throughout our school years and even in the business world, have been taught to hold back ideas until they are polished and perfect. (Berger 120 pag.)

What if we embrace risk-taking to show our work and thinking early and often? Are we taking actions to teach and model constructive critique for learning?

In committing to an idea, it becomes critical to find a way to share it in order to get feedback. (Berger, 118 pag.)

If we show work in progress, are we fearful that the feedback will cause a shutdown rather than a new iteration?

Which brings us back to culture and climate.

AMBQ-Chpt3

Summer Reading using VTR: Sentence-Phrase-Word:
A More Beautiful Question
Chapter 3: The Why, What if, and How of Innovative Questioning

How are we listening to learners – every learner? What if we use technology to offer everyone a voice and an opportunity to question, to see the thinking of others, and to offer feedback to themselves and others?

Are we listening deeply to each other? Are we observing – paying attention – closely to learn?

Why are we afraid to show our work? What if feedback is asked for as well as given? How might we shift our culture?


Note:

Chapter 3 is also full of interesting, important questions and ideas to ponder. These ideas and questions connect, for me, to assessment, design thinking, and makery.

I have many notes in my book. I am part of a cohort reading this book. I know that others will highlight and help discuss additional ideas from this chapter.


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

Be curious; overcome fear; ask – A More Beautiful Question VTR SPW

[learners] may be self-censoring their questions due to cultural pressures. (Berger, 58 pag.)

What are the cultural norms  in our learning community around asking questions? Who has permission to ask questions?

But this issue of “Who gets to ask the questions in class?” touches on purpose, power, control, and, arguably, even race and social class. (Berger, 56 pag.)

If learners are self-censoring their questions because of cultural pressures, who really has permission to ask questions?

How might we create space and opportunity for additional voices to contribute questions? What if we leverage tools – technology, protocols, strategies – to offer every learner new ways to have a voice?

What would it look and sound like in the average classroom if we wanted to make “being wrong” less threatening? (Berger, 50 pag.)

What is to be gained from using  feedback loops as a way to make the possibility of “being wrong” less threatening?

Screen Shot 2015-05-28 at 12.55.21 PM

Image from Kato Nim's 4th Grade Class

How might we show that what we don’t know gives direction for learning and growth?

AMBQ-Chpt2

Summer Reading using VTR: Sentence-Phrase-Word:
A More Beautiful Question
Chapter 2: Why We Stop Questioning?

If learners are self-censoring their questions because of cultural pressures, what actions should/can/will be taken?


Note:

Chapter 2 is full of interesting, important questions and ideas to ponder.

Why do kids ask so many questions? (And how do we really feel about that?) Why does questioning fall off a cliff? Can a school be built on questions? Who is entitled to ask questions in class? If we’re born to inquire, then why must it be taught? (Berger, 39 pag.)

I have many notes in my book. I am part of a cohort reading this book. I know that others will highlight and help discuss additional ideas from this chapter.


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