Does "automaticity" = timed tests?

Bring up timed tests for math facts at a dinner party or on a soccer sideline and you're likely to start a debate.  There are those who feel that timed tests put the focus on rote learning which is obsolete in this day and age in which we can rely on calculators and computers for these calculations.  Others laud the timed tests as they are seen as taking us back to the basics in a good way.

Last year, my own third grade daughter was time tested each week.  On Fridays, she was given a table of ten facts to complete within 20 seconds.  She "passed" by completing the test correctly on time for two weeks in a row.  Then, she would move on to a new set of facts.  As I lamented in my "Coverage vs. Mastery" blog post, I feel that this practice emphasized speed over depth for her.  She memorized to pass, but I was not impressed by the depth of her understanding (granted, I'm a hard case).  The timed tests had a much more demoralizing effect on a friend's son who would make himself physically ill on Thursday nights anticipating these tests the next morning.

Sorting Out the Messages

Recently, I went with a group of folks from WCSU to a training facilitated by Loree Silvis called PNOA* and Common Core.  Sitting in this workshop, I encountered ideas that pulled with my current practice and others that pulled away from my current practice.  As a result, I experienced some internal conflict.

I find that I often feel this way when I attend workshops and receive different messages about math instruction, curriculum and assessment.  It takes me some time and thought to sort it out, and I know that I am not unique in this regard.  Recently, I have had conversations with teachers that highlight the pervasiveness of this feeling.  Teachers perceive mixed messages about what to teach and how to teach it.  The messages come from a variety of sources, and teachers feel pulled in different directions.  They want focus, clarity, and communication.  

To address this, Jen Miller-Arsenault, Bill Kimball and I are collaborating with the goal of unpacking and reconciling some of the conflict and to provide WCSU teachers with a consistent message about math curriculum, instruction and assessment.

We will address the mixed messages in separate posts that are linked below.  For the in-service on October 13, we will spend some time "browsing" the posts.  To honor your individuality, we'll use this menu differentiation strategy (that I've used with homework and practice activities in class).


Main Dishes (Read and comment on each of these posts.):

• WCSU Math Non-negotiables vs. the Common Core States' Standards
• Untangling Assessments: What are they all for?

Side Dishes (Read and comment on at least one of these posts.)

• Math practices vs. Habits of Mind vs. Positive Math Classroom Norms
• Is it okay to use a textbook?
• Why am I attending this PD?  I don't teach math.

Desserts (Yummy, but optional.  You can put these in your doggie bag for later, if you want.)

• Loree and Mahesh don't completely mesh...
• Does "automaticity" = timed tests?
• How to do a Low Floor High Ceiling makeover...

If you have another mixed message you'd like addressed, please write it in as comment below on this post or send me an email (edorsey@u32.org).  



*"PNOA" stands for Primary Number and Operations Assessment.  It is an interview format assessment that was developed by a team of Vermont educators as a multipurpose tool for grades k-2.

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...