Number Concept, Number Sense & Numeracy

In my last blog post, I posted a video of Dave Willard explaining that taking the time to focus on mastery of number sense made grade level concepts more accessible. However, it occurs to me that it might not be clear what "number sense" is. We have various terms that we may throw around: number concept, number sense, numeracy. But what do these terms really mean? And how do they relate to mastering grade level concepts? Let's unpack these terms a bit...

Coverage vs. Mastery: Slowing Down with Dave Willard

A couple of weeks back, we had the opportunity to come together around math instruction at East Montpelier Elementary School for clinical rounds with Mahesh Sharma.  Mahesh worked with a group of fourth grade students who are taught math by Anne Carter and Dave Willard.  After working with the students, Mahesh remarked how well they did.  As I watched the class, I was seated next to a fifth grade teacher who was also favorably impressed.  Dave and Anne spent a little time with us afterwards reflecting on the changes that they made to their math instruction this year.  These changes were inspired by the training they received together last summer at "Lab School" - a week long course focusing on math instruction that was taught by Mahesh. 

Dave was adventurous enough to agree to let me capture some of his thoughts and ideas on the video embedded above (if you can't see the video, here is a link).  He's very articulate (even under duress), so be sure to watch Dave discuss how he changed from a "coverage" mindset to a "mastery" mindset this year.  And he feels that this change has made his students stronger math learners. 

Calais Unplugged

I spent this past week in lovely Calais. While we weren't literally unplugged, connectivity issues lent a bit of a "post-apocalyptic" feel to the first half of the week (minus the mayhem - everyone was making the best of it).  No Google Drive access, no internet, no network, no printing, no cell phone coverage, etc...  

Since my essential tools for working as I travel from school to school are my Chromebook, iPhone and a set of manipulatives, this was a challenge.  It forced us to go "old school," and highlighted the power of good manipulatives - especially when there's no power!

By the end of the week, all systems (with the exception of cell service) were back up and running, and there is a lot of good stuff to share out...

Tech Assisted Communication and Application of Division

When I left EMES, fifth grade students were working to get to the communications level on long division (blog post: Math Coaching at EMES: The Sequel).  As you would expect, students were in different places with some ready to communicate and apply and others needing more conceptual work.

Tech Assisted Communication

Students have been using videos to practice the communication piece and document their learning as they became ready.  Fearlessly, one teacher used a cell phone to record the videos and enlisted the media specialist/technology guru to upload it to Teachertube.

Here is one student's video.  Kindly, she was willing to share it with all of us.  I love it for so many reasons, but especially because of how proud of herself she looks.  If you can't see the video below, click on this link: http://bit.ly/1GrotF5.

Meanwhile, what to do with the students who have the communication piece down???

Math Coaching at EMES: The Sequel

Ellen Shedd's freshly renovated room at EMES is to die for.

A cancelation left me with an open week, so we carved out some time to work with the fifth grade teachers at EMES since our last attempt at a coaching week was foiled by snowfall and programming conflicts.  I had a blast (love those fifth graders!).

A couple of things I really love about EMES: the "Acts of Kindness" announcements and the gorgeous classrooms (see left).

Focus

We focused entirely on fifth grade this time.  As readers may recall a couple of weeks back, I spent a couple of days at EMES and the focus of the fifth grade was division (Division, Order of Operations and Ugly Fraction Problem... post).

This time, our goal was to move students from the intuitive to concrete/pictorial to abstract/symbolic understanding of division using the standard algorithm efficiently.  We had three days (Monday, Wednesday and Friday) to spend.  For each of the three days that I was there, our schedule was the same:

7:45 - 9:00 -     I was available for planning/debriefing.  
9:00 - 10:00 -   I worked in one fifth grade class.
10:00 - 10:30 - The teacher and I debriefed.
10:30 - 12:45 - I was available for meetings.
12:45 - 1:45 -   I worked in the other fifth grade class.
1:45 - 2:15 -     The teacher and I debriefed.

The focus of our collaborative time was looking at the evidence of student understanding collected using formative assessments to decide how to mold our instruction to improve understanding.

Math Coaching at U-32 and Dealing with Apathy for Deep Math

I was back at U-32 this week, which made me feel nostalgic.  Much has changed in middle school math from last year to now: heterogeneous grouping, math on core, a few new babies, a new schedule...  but I am appreciative that our administrators and superstar representatives on the scheduling committee (that's right, CG!) have made it so that the middle level math teachers still have common planning time.  We were able to pull together a coaching schedule that involved planning, modeling, debriefing, data analysis, and more planning. All of this on a (somewhat) half-time coaching schedule!

Focus

The prior week, the middle school teachers and I sat down on at our Thursday math huddle to map out our week of math coaching.  After batting around a few ideas, we decided to focus on seventh grade content and instruction (with our next week of math coaching focusing on eighth grade content).  The content would be operations on fractions starting with multiplication.  The modeling would involve using the "Square 1" concrete area of a rectangle.  The focus of our collaboration would be using formative assessment to inform instruction because we know that this is something we all need to do better.

Division, Order of Operations and an Ugly Fraction Model! Math Coaching at EMES and Beyond

Well... A snow day on Monday, in-service on Friday and Fitness on Thursday gave us only two days to focus on math coaching this week at East Montpelier.  So, we did the best we could with the time we had.

Goals

Fifth grade teachers, Robin and Ellen S. were looking to work on teaching long division using the area of a rectangle model so that they can move onto Divisibility, Least Common Multiple and Greatest Common Factor.  Our math coaching work this fall focused on models for multiplication and using the area of a rectangle to model the partial product method and the standard algorithm for multiplication.