Teaching Place Value: Keep Calm and Transmogrify!

Earlier this week, I received the following email from a colleague:

I am looking to teach place value and its pattern (multiply by ten every time you move to the left, divide as you move to the right)... I need to make it hands on and am not sure how to do it, as you can only show from ones to tens to hundreds. Beyond that it's too big... 

I immediately thought of a slight of hand that I have used with my students to teach place value:  the Transmogrifier invented by Calvin (A.K.A. Bill Watterson).  It was a "machine" that Calvin invented that could vary the appearance of a thing, without altering its relationship with other things.  For example, it could change Calvin into a bug, but the bug would still interact with the world as Calvin would.  In other words, the Transmogrifier made Calvin's appearance variable.

Here is a video I made to explain how I have used this idea to teach place value:

I might also play them a video like this so they get an idea of the real magnitude we're trying to convey:

So remember...

And here's the link if you want to buy extra 1000 cubes.  Or you and/or your group can try this flat pattern and have them build the 10 by 10 by 10 cubes.

Any thoughts?

Math Mindsets

Over April vacation in 2011, I read a book called Mindset: The New Psychology of Success by Stanford professor and developmental psychologist Carol Dweck.  It shook my foundation.  I re-examined my teaching, my parenting and my self identity.  Probably many of you are familiar with the book which (in a nutshell) states that:

• Intelligence is not fixed, and the brain is strengthened through mistakes and challenges.
• Our self beliefs affect the way our brains work.
• It is possible to change our self beliefs (and therefore make our brains work better).

When I returned to my classroom after vacation, I put all of my plans on hold.  Fostering growth mindset became my first priority.  I developed this lesson for my seventh grade students: Ellen's Mindset Lesson.  My stated instructional goal was this:

The most important thing for me to teach you is that you are capable of learning math at deep, deep levels if you open yourself to mistakes and challenges. 

A Math Idea Worth Checking Out

I've been meaning to post this for a while, ever since I was visiting Heather Robitaille's fifth grade classroom last fall at Rumney.  As an ongoing math thread in her class, Heather has her students use checkbooks use to track various debit and credits that she devises for them.  In her own words, here's how she works it:

I give the students deposits each day and throw done withdrawals in there as well.  For example, students have to rent their chair...  If I rent it to them for $3.75 a day, then how much would they be charged for the week?  Some students decide to do a daily withdrawal, while others pay the sum up front for the week.  At the end of the week students have to have a certain balance.  If their balance is off, then they go back and find their mistake and correct it just like you and I would have to do.  I really try to make this very realistic for the kids. Adding and subtracting decimals with real life skill.

Math Steering Update: Making Sense of Mastery

Greetings, math nerds!  I hope you have all had a fabulous summer... Last spring, on the WCSU Math Coaching Blog, I left off with a discussion of mastery and number concept.  Obviously, we want mastery, but what does it mean?  What does it look like?  How do we teach for it?  The math non-negotiables give us a sense of what will be "covered," but to focus on mastery, we need more...


This summer the WCSU Math Steering Committee had the opportunity to spend a few days working collaboratively on a document that (we hope!) will be an excellent resource supporting WCSU math instruction.  We worked together on the format and content for kindergarten and first grade.  I will be working with individual Math Steering folks to fill in other grade levels as soon as possible starting with 5th and 6th grade (because much of the work was done last year as a focus of math coaching, but just needs to be curated).

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...