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Showing posts from August, 2012

Mathematical Realizations

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NOTE: S stands for students, it was not just one voice speaking but many different voices



Me: Look at the the two tables, one with a fixed perimeter and the other with a fixed area.  What do you notice?

S: The numbers on the right table are changing.  There is 9 in between, and then 7, and then 5, and then 3, and then 1.

S: Yeah, it is like a pattern.  But then the other side is ummm (calculating) 34, 10, 4, and 2 in between, so there is no pattern.

S: I see something weird.

M: Is it okay we change the subject and look at N's weird thing?

S: Yes.

M: Go ahead please.

S:  when the area is 36, the perimeter is 24, on the left table, and when the area is 24 the perimeter is 36 on the right one.  They are flipped.

Ss: Cool.  Why is that Mr. D?

M: Well, what do you think?  Look hard at the chart, you may see something special about those two shapes.

S:  Oh!  They are squares!  The others are rectangles and they don't flip.

S:  And look at this, in the area table, the square is the smallest numb…

Collectivity in the Math Classroom

A presentation for our research proposal.  Looking forward to getting started!


Markers of collectivity research from dwyerteacher

The Learning Curve

I'm pretty adept with technology, but kids amaze me.  Our school recently purchased about 20 iPads to use in the elementary school level.  So, from time to time, I have a 1:1 iPad class.  A couple of them are equipped with iMovie.  I recently started a project where the kids are using the Trailer templates on iMovie to make a trailer about the story of their lives.

iMovie Trailer Storyboard

Once we started filming, I sat the class down and hooked the iPad up to the TV to give a short demo on how to use the basics in iMovie.  A couple of them said they already knew how, they use it at home.  The others brushed my tutorial aside and said they would play with it and figure it out.  So, I let them go, and I helped as we went.

By the end of the second day of shooting, I would say that the majority of the kids in the class had surpassed me, and were teaching me new tricks and shortcuts.  I felt like my parents must have felt when I helped them figure out how to send a link through Skype.

Th…

Dancing with Systems

I love this.  I love it so much.  I cannot tell you how much this one short piece of writing has influenced me.  I can't remember where I read it, or who recommended it to me, or even when it was.  It was a while ago.  Before I had even played with the idea of becoming a teacher.  It send my mind down avenues I didn't know existed, and introduced me to ideas that are now very much a part of who I am.

http://www.sustainer.org/pubs/Dancing.html (click on the link for the full article)

The Dance

1. Get the beat.
2. Listen to the wisdom of the system.
3. Expose your mental models to the open air.
4. Stay humble. Stay a learner.
5. Honor and protect information.
6. Locate responsibility in the system.
7. Make feedback policies for feedback systems.
8. Pay attention to what is important, not just what is quantifiable.
9. Go for the good of the whole.
10. Expand time horizons.
11. Expand thought horizons.
12. Expand the boundary of caring.
13. Celebrate complexity.
14. Hold fast to the goal of goodn…

Teacher Inquiry vs. Student Inquiry

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So, I've got this great unit planned.  I thought of an engaging provocation to hook the learners.  It worked.  They are loving it and they are following every step of the way.  It is engaging, fun, and full of opportunities for critical thinking, art exploration, and differing perspectives.  Along the way, I infused the unit with technology.  They are blogging, making Keynote presentations, and working with GoogleSketch.  I have scheduled in some reflection and meta-cognitive time at regular intervals.  They are putting their work into e-portfolios, and connecting with other students around the world.  I work my way through the initial points of the unit, going through my lines of inquiry one at a time, going back to check understanding, and moving forward when I feel they are ready.  I have structured the unit to scaffold the learners to the final summit, the understanding of the big idea.
But, it was my inquiry.  I planned it all out.  I chose the direction.  I chose the topics. …

Listening

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Part of my personal focus for the upcoming school year is to improve my listening as a teacher.  As part of my summer studies, I was introduced to a taxonomy of listening written by Brent Davis.  His book applies it mostly to the mathematics classroom, but I think it is easily transferred to the all aspects of teaching, learning, and knowing.  I wrote a paper on the taxonomy that was a brief summary of his ideas geared towards the math class, but I would like to rewrite it here and expand on some thoughts to broaden the idea to encompass all of a teachers listening practices.

There are three levels in the listening taxonomy, and each level in nested within the next:

Evaluative Listening

The purpose of listening at this level is to assess what is being studied.  In other words, to check for right or wrong answers, or to find something that the teacher is trying to correct.  We do this all the time in a class.  Can anyone tell me what this is called?  Who can tell me what 6x7 equals?  In t…

Listening in the Math Class

A paper I wrote this summer. Would love feedback!

Listening to the Trajectory of the Lesson