I hope you’ve been following along with our Summer 2014 Double Book Study so far.  If not, here are the links to get caught up before you scroll down and see what I have to say about Number Releationships; Multiplication and Proportional Reasoning
Okay, all caught up?  Good… let’s rock and roll then!
Mathematics is all about relationships!  And when we ask our students questions about these relationships we begin a pathway of curiosity for our students.  Students don’t inately HATE math…. they learn to hate math.  We, as teachers, have a responsibility to ask the questions that help keep our kiddos curious.  Curiousity is the key to engagement and the key to NOT hating math….
One of my favorite parts of this book is that they not only give you amazing content rich questions to ask your kiddos, they also give you the black line master activities that they use in their questioning examples.  Seriously – they give you almost everything you need to go back to your classroom and begin working to build your students’ curiosity!
5 Number Relationships & 6 Multiplication and Proportional Reasoning
Both chapters are broken into two parts 5th/6th grade and 7th/8th grade.  Both sections of CH 5 give very specific examples on how to work with number theory.  (I only wish I had learned this way when I was in elementary / middle school).  Both sections of CH 6 give very specific examples on how to develop a deeper conceptual understanding of multiplication and division.
“We need to listen very carefully to the mathematical talk of our students to support their correct use of the terminology” (Schuster, 17).
Schuster really hits the nail on the head with this statement!  Our biggest role as a teacher needs to be that of a facilitator. We need to choose tasks that are student appropriate and centered that allow students to discuss their thinking AND allow us to step back and help facililate the discussion.  We need to be comfortable enough in our roles to allow students to take center stage!  In doing so, we need to
“carefully craft questions that probe the depth of the children’s understanding, which may be initially fragile…” (Schuster, 18).
Schuster subtly makes a point that many tend to forget.  Jumping into the world of student-centered tasks with rich math talk is NOT an overnight victory.  Setting up a classroom that is ready for this type of learning takes time AND takes patience.
I love all the connections that are being made in this book.  Shuster takes the time to not only present great content rich questions but also takes the time to connect the the number theory to geometric and graphical reasoning.
“Although procedural competency is an important goal in the teaching of multiplication and division, the questions… are designed to promote and establish further conceptual understanding and knowledge of these operations…” (Schuster, 31).
I recently saw a video at a conference about a girl named Sasha.  Sasha clearly understood HOW to rotely divide but once probed for further understanding it was very clear that she had no idea what division meant, how to see if her answer was reasonable, or what connection any of this had with place value.  On the surface Sasha “knew” what she was doing and more than likely would pass any standardized test you gave her… but she had no connection to why anything worked and was just going through the motions.  Sasha was probably going to be one of those students who would accelerate through math and eventually will hit a wall where just working through the motions would no longer help her.  Sasha clearly had not sat in a classroom with ‘carefully crafted questions’.  We had a long discussion about Sasha and how we as educators are failing her.  (I’m still looking for the video, but am not sure that it is on the internet… if I find it, I’ll post it!)
Okay, enough from me… let’s get some discussion going!
Reflection:
Can you see yourself using any of the activities in these sections?  Which one(s), why?
What questions are you still not comfortable letting students explore on their own?
How are you already using ‘carefully crafted questions’ in your classroom?  If you are not, what’s holding you back?
What parts of this section made you reflect on your own teaching practices?
Do you know any “Sasha’s?”

1. I definitely plan to implement the array activity this fall. What a terrific tool for my visual learners!

I began asking my students more thoughtful math questions last year, but found there were times they couldn’t answer. I know now that it’s probably because I didn’t set up the question correctly. I am looking forward to changing that!

I have had “Sasha’s” in my class: math calculations came easily, but you could tell it was “surface” knowledge. I am excited about helping my students develop a more comprehensive relationship with math and an ability to see the connections.

2. Very interesting. A lot of good information. Thanks for sharing. Since we switched to Common Core 2 years ago I have been using teams in my room. I am definitely a facilitator and plan to improve on that role this year with my questioning. And my big goal for this year is to help the students improve in their academic discourse with a focus on academic vocabulary, verbalizing their reasoning and being precise.