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Tag Archives: The Art of Questioning

The Magic Octagon – Dan’s, Andrew’s, and mine

I had saved Andrew’s post in my folder for a recent lesson, which was about Dan’s video.

We paused halfway in, and students decided where it would be. They answered a Quick Poll to let me know, and by the time they had all answered, some had changed their minds.

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We quickly looked at the responses, and they decided using time would be easier to decipher than some of the other descriptions.

I sent a second poll. I waited for everyone to answer, even the ones who wanted to take their time thinking about it.

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And then we continued to watch.

We paused for the last question, they discussed with their team, and then we finished watching.

Good conversation. But we didn’t get to the sequel proposed by one of Andrew’s students: If the front side arrow is pointed at 5:00, would the other arrow point at 5:00, too? Why or why not?

So I emailed that question to my students.

  • Yes, the two points move like opposite hands on a clock moving closer to each other and overlapping at 5:00. At about 11:00 they would overlap again. Otherwise, there is no overlap.
  • They would be at 5:00. This is because when he flips the magic octagon, the back arrow also flips, causing the new time to be 3:00 instead of 9:00. This means that if you were to find a line of reflection, you could flip the octagon on that line and the arrow would always land right where the previous one did. If this was on transparent paper, you can see that if one arrow points to 5:00, then the other one would be pointing at 7:00. But if you were to flip the octagon on the reflection line which intersects 12:00 and 6:00, then you would continuously get 5:00 because of the reflection.

As I got the responses from students, I realized that I wished I had asked a different question. While I did include why or why not, and it was obvious from the responses that students didn’t just answer yes or no, I wish I had asked “At what time(s), if any, are the front side and back side arrows at the same time?”

I am reminded of something I can no longer find that I read in a book. A group of teachers observed a “master” teacher for a lesson and then went back to their own classrooms to teach the lesson. The teachers asked the same questions that the master teacher asked; however, the lessons didn’t go as hoped. The teachers were not asking questions based on what was happening in their own classrooms; they were asking questions based on what had happened in the other classroom.

I love reading blog posts and learning from so many mathematics educators. They give me ideas that I wouldn’t have on my own. In fact, as my classroom moved toward more asking and less telling, I used to say that my most important work happened before the lesson, collaborating with other teachers and deciding what questions to ask. I’ve decided otherwise, though. My most important work happens in the moment, not just asking, but also listening. And then, if needed, adjusting what I planned to ask next based on the responses of the students in my care. And so the journey will always continue …

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Posted by on November 15, 2016 in Geometry, Rigid Motions

 

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#NCSM14 Art of Questioning: Leading Learners to Level Up #LL2LU

What if we empower and embolden our learners to ask the questions they need to ask by improving the way we communicate and assess?

Great teachers lead us just far enough down a path so we can challenge for ourselves. They provide us just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out the solution to the world, makes me want to step to the next higher level.  Great teachers somehow make us want to ask the questions that they want us to answer, overcome the challenge that they, because they are our teacher, believe we need to overcome. (Lichtman, 20 pag.)

On Monday, April 7, 2014, Jennifer Wilson (@jwilson828) and Jill Gough (@jgough) presented at the National Council of Supervisors of Mathematics Conference in New Orleans.

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Jill started with a personal story (you’re letting her shoot…) about actionable feedback and then gave the quick 4-minute Ignite talk on the foundational ideas supporting the Leading Learners to Level Up  philosophy.

Our hope was that many of our 130 participants would help us ideate to craft leveled learning progressions for implementing the Common Core State Standards Mathematical Practices.  Jennifer prompted participants to consider how we might building understanding and confidence with I can make sense of problems and persevere in solving them. After giving time for each participant to think, she prompted them to collaborate to describe how to coach learners to reach this target.  Jennifer shared our idea of how we might help learners grow in this practice.

Level 4:
I can find a second or third solution and describe how the pathways to these solutions relate.

Level 3:
I can make sense of problems and persevere in solving them.

Level 2:
I can ask questions to clarify the problem, and I can keep working when things aren’t going well and try again.

Level 1:
I can show at least one attempt to investigate or solve the task.

 Participants then went right to work writing an essential learning – Level 3 – I can… statement and the learning progression around this essential learning. Artifacts of this work are captured on the #LL2LU Flickr page.

Here are the additional resources we shared:

How might we coach our learners into asking more questions? Not just any question – targeted questions.  What if we coach and develop the skill of questioning self-talk?

Interrogative self-talk, the researchers say, “may inspire thoughts about autonomous or intrinsically motivated reasons to purse a goal.”  As ample research has demonstrated, people are more likely to act, and to perform well, when the motivations come from intrinsic choices rather than from extrinsic pressures.  Declarative self-talk risks bypassing one’s motivations.  Questioning self-talk elicits the reasons for doing something and reminds people that many of those reasons come from within. (Pink, 103 pag.)

[Cross-posted on Experiments in Learning by Doing]

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Lichtman, Grant, and Sunzi. The Falconer: What We Wish We Had Learned in School. New York: IUniverse, 2008. Print.

Pink, Daniel H. To Sell Is Human: The Surprising Truth about Moving Others. New York: Riverhead, 2012. Print.

 
 

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