Lesson Study Fishbowl - Ed Camp @ U32

This blogpost accompanies an Ed Camp on March 15, 2017 at U-32. The session is designed to introduce participants to the basics of lesson study and give them an opportunity to consider how the model could be used to facilitate collaboration within their own disciplines and practices.

Lesson study is not just for math. Anyone interested in seeing a job embedded professional development model for fostering high depth teacher collaboration around student learning should consider attending a session.

There will be two Ed Camp sessions (the first from 2:15 - 3:15 and the second from 3:15 - 4:15). Interested participants should plan to attend just one of the two sessions.

Session participants will use this blogpost to embark on a self-guided tour of a lesson study planning session for Algebra 1. You will need an electronic device (preferably a laptop or chromebook).
The tour itinerary will include:

• Part 1: Laying the Foundation - The tour begins with some background information about the Algebra 1 lesson study and lesson study in general. Participants will complete this in their own physical space BEFORE observing the planning session. 
• Part 2: Observing the Planning Session - After completing Part 1, observe the planning session in room 28 (Cathy Guiffre's room in the middle school). 
• Part 3: Reflection & Closure - After completing Part 2, participants will spend some time reflecting and complete a Google Forms closure card. 

Decimal Madness - Anatomy of a Lesson Study

Last week, a group of teachers from three schools within our supervisory union came together to participate in a lesson study at Calais Elementary School.  In this blogpost, I share that experience with you addressing:

• What is lesson study?  Why is it valuable professional development?
• What happened during our fifth grade lesson study at Calais?
• How to get started with lesson study?

To L.A.: I Promise to Persevere

We started this week in my educational community with the sudden, gutting loss of our beloved colleague and friend, Laure Angel.  It's impossible to find adequate words to describe Laure's impact.  She was absolutely unique. A combination of warmth and positivity and spunk and intellect and pure energy.  She was an adventurer.  She was the go-to gal, if I was looking for someone with enough spark to start a fire and enough fuel to keep it going.  And I'm sure that I'm not alone in that...

Those who know me well know that I've been working on a doctoral program at UVM and that at times I wonder why I bother.  My area of focus is understanding teachers' experiences integrating math with other subject areas.  A few years ago, Laure asked me if I could chaperone the Hunger Mountain hike that accompanies the seventh grade elevation study.  I had been unable to attend (my job is grant funded and it couldn't be justified), but we agreed that it would be great if in the future, math was being integrated to the extent that I could justify going.  Since then, Laure and I have had many more discussions about integrating math with her subject area (which was Social Studies) in the middle school.

Last year, Laure invited me into her classroom to observe an integrated lesson that she and the Language Arts teacher developed and were teaching together.  I take so many pictures in my job - recording things I see, things I want to act on, things I want to share.  That day, I took some pictures of the whiteboard, students working and also one of Laure giving me a wink and a big grin as I was leaving the room.

When I found out that Laure died, I remembered that picture.  It had stuck in my mind.  At the time, I remember remarking how natural she looked winking with a smile whereas I can only wink with a completely straight face.  I wondered if that was some indicator of a difference in our dispositions.  Was this something I should work on?

On Monday, I scrolled through my phone to look for that picture only to find that it was gone.  Like everyone else, from time to time I have to cull my collection to create more storage space for videos and other pictures.  I deleted the picture of Laure, but I saved the picture of her whiteboard included here.

And strangely it feels just as quintessentially "Laure" as the other picture did.  It reminds me that the best way to honor the memory of this beautiful person is not to dwell, but instead to continue on in spite of struggle.  I'll keep working on my degree.  I'll keep working on supporting teachers and teams on math instruction and integration.  I'll keep working on learning how to wink with a smile on my face.  I'll continue to ask myself, "What would Laure do?"  And then, I'll do it.

DI to support PBL - Dabbling and Diving at U-32

This post accompanies an Ed Camp on Wednesday, February 8 @ U-32.

Participant's choice:

Session 1: Dabble

 Links for Dabblers:

• Danielson Proficiency Scale.
• Sample Assessment: Grade 8 October Math Benchmark Assessment

Session 2: Dive

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Combining Multiple Pathways and Layered Curriculum

Links for Divers:

• LFHC task assessment and revision organizer
• Reading on Layering Curriculum 
• Example of Layered Science Curriculum

Mixing it up - CES/EMES Collaborative Staff Meeting

See the Prezi below to accompany our collaborative staff meeting at East Montpelier Elementary School on January 25, 2017.

Fourth Dimension 101 for Three Dimensional Beings

One of my favorite books of all time is Flatland: A Romance of Many Dimensions published in 1884 by Edwin Abbot.  It's nerdy and cheeky and thought provoking, or at least it was for me when I first read it as an undergraduate.  Abbott was making a commentary on the social hierarchy in Victorian England, but he used the idea of spatial dimensions to do it.  Different social classes reside in different dimensions: Lineland is one dimensional, Flatland is two dimensional, and Sphereland is three dimensional.  One of the main themes is that perception depends on perspective - a central tenet in critical theory (when applied to social sciences) and relativity (when applied to theoretical physics).  It was an idea ahead of its time.

Abbott begins his narrative from the perspective of a two-dimensional being (A Square).  The dimension in which a character resides determines perspective.  For example, the two-dimensional being watching a sphere pass through their plane would perceive it as a line appearing suddenly, increasing in length (quickly and then slowly), and then decreasing in length (slowly and then quickly) before disappearing altogether.  Whereas, a three-dimensional being would perceive the same event quite differently.

Imagine how confusing the conversation between these the two beings would be.  Which perspective is "true?"  Both?  Neither?  Place yourself as a mediator between the two.  How would you get them to understand one another?  What language would you use?  What visual models?  What experiences would they need?  What dispositions would they need?  Math Practice 3 - Construct viable arguments and critique the reasoning of others comes to mind...  The interchange of perspectives between the two would stretch the perception of both beings.

How does this connect to teaching and learning?  How often have you asked a student a question and been completely confused by their response?  I have come to understand that students always respond in a way that makes sense - to them.  I can't think of it as me being right and them being wrong.  I am right from the standpoint of my own perspective.  In order to teach them my perspective, I need to be open.  I need to understand their perspective first.  I need to know how do they see it?  What sense are they making of it?  What experiences are they drawing from?  How do I provide them with opportunities to widen their perspective?  I've come to realize that simply asking, What do you see? and then following up with How do you know? is often a great, low floor, high ceiling starting point.

Just for kicks, ask your students (whatever their age) for their perspective on mathematics sometime.  What is math all about?  I've done this many times with students at various grade levels.  Most often they say that math is about answering questions involving numbers and equations.  They might mention the importance of efficiency, too.  They might mention the importance of "right" and "wrong."  They tend to focus in on the quantitative, closed-ended aspects of math rather than seeing creative and exploratory aspects of math.  Math is about discovering, describing, generalizing, and explaining patterns in structure, quantity, space, and change.  Efficiency is an important perspective, but it's not the only perspective.

There is a myriad of dimensions to mathematics (literally), each offering a unique perspective.  Dimensions are (and have always been) elemental to visualizing and conceptualizing math.  By exploring dimensionality, we can make concepts and patterns concrete and then extend from what we can experience to the realm of abstract ideas.  Dimensions provide us with a set of tools (hand tools, perhaps) that we can use to build understanding and communicate perspective.

So, what could the fourth dimension look like?  Is there only one answer?  What do you see?

Want more?

Here's a video about Flatland that I like:

Here is a blogpost that outlines lesson that centers around a discussion of dimensions.

A Peek in the Classroom - Stacey's Multi-dimensional Class

One of the things I love the most about my job is having opportunities to watch others teaching.  When we have done lesson studies in WCSU, it is one of the most valuable things teachers take away from that experience... the opportunity to see another teacher in action.

I am so, so, so grateful to Stacey Rupp (5th and 6th grade teacher at Calais Elementary) for being willing to allow me to share a peek in her fifth grade math classroom with you.  Rather than making one long video (which would make my iphone gag while uploading to youtube), I created a playlist of the videos starting with my introduction video (the first video below, the whole playlist is linked here).

Watch Stacey tackle:

• A classroom management strategy to get kids to stop playing with those darn Cuisenaire rods when they're supposed to be learning math
• Explaining dimensions
• Efficient movement breaks
• Using learning targets and ongoing formative assessment 

The first two videos give you an overview of what you will see, giving you the context for the lesson that I observed on Friday, December 16, 2016.