Book Study Wednesday: Chapters 7 & 8

This week we decided to wrap up the book study in and of itself and use our final week next Wednesday to finish designing a Number Sense kit.  The study group that also meets in person is going to put together a kit that teachers can use to remediate some important concepts within the broad spectrum of what we call number sense.
Using the Learning Trajectory on page 9 as a guide, the team is going to pull together a series of leveled activities to help with subitizing.  In addition to materials, we want to include a teacher's guide.
Stay tuned for next week's post!  It'll include a freebie or two for you!  For now I hope you'll read below and join the conversation.

Discussion Questions
Q1-  Consider Shumway’s discussion about mistakes in the classroom:
“Through the course of the year, as we build a supportive community of learners…” (Shumway, p. 130)
In what ways do I, as the teacher, support an environment that encourages mistakes?

Q2- What does student reflection look like in my classroom? What implications does holding discussions have on written explanations?

Q3-  “Formative assessment are ongoing, in-the-moment, dynamic processes that provide the teacher information during instruction.  They are assessments for learning, because teachers use them to make instructional decisions and plan the next steps for student learning (Chappius and Chappius 2007/2008; Tomlinson 2007/2008).” (Shumway, page 137)

How does this definition fit with your idea of formative assessments?  Can formative assessments be paperless? How would you keep track of and organize information collected from formative assessments?

Book Study Wednesday : Chapter 6 Calendar & Data Routines

I apologize for the tardy post.  This week really caught up with me and then ran me right over and kept going!  Anyone else know what I'm talking about?  Well, let's get on with it anyhow!  Welcome back!
 
Chapter 6 was pretty brief in comparison to the previous chapters  Basically it was broken down into calendar and data.  Both types of routines, as with all the previous routines in this book, encourage math chatter among students and that is my favorite part.  Many educators are afraid of math talk and I can tell you from experience that talking is the most valuable part of learning.  How many times a day do I bounce ideas off of a co-worker or friend?  Constantly!!  I think out loud all the time as a way of problem-solving and making observations.  And so do students.

Talking about math during number sense routines gives students the opportunity to converse in a way that many may not be used to in the home.  Working in a Title I school, many students do not have the vocabulary and background knowledge that their same age peers do. Discussing ideas in class is life ring for those who are struggling.  These little number sense routines are social opportunities to bridge the learning gaps!

Click here for a little freebie! Some great discussion task cards for 1st and 2nd and easily modified for Kindergarten.
 
Discussion Questions:


Q1 - How is your calendar routine different from the way Shumway presented it in Chapter 6?  How is it the same?

Q2 - What mathematical concepts are you currently focused on and how are the number sense routines supporting them?

Book Study Wednesday - Chapter 5 Playing with Quantities

Last week I met with my first grade team.  There is a district wide assessment approaching and we've all been a little apprehensive about how the students will do.  So we spent some time discussing number sense routines, specifically routines that allowed students to play with numbers.  I shared with them the following experience.

I spent some time going through chapter 5 and chose "Ways to Make a Number" since one of the items in our standards (and coming up on the assessment) required students to think flexibly about a number.  I had a wonderful teacher volunteer to let me come in and try this routine with her class.  We did "Ways to Make 17".  I chose 17 because I wanted to see what the students did with a teen number, to see if they'd draw out the ten.  I was pleasantly surprised by most.  One little girl in particular wrote the following:

I asked her about the last equation.  It was clear from her number bond that she knew the fact family.  I asked her if her last number sentence was equal to 17.  I gave her a chance to revisit her thoughts while I visited other groups.  Later, when I returned, she has modified her answer to read 10 + 7 =17.  

After 1st grade returned to their classrooms, I received a message from one of the teachers (the same teacher I had visited in the above story). She had decided to use the last 20 minutes of her day using "Ways to Make a Number".  She presented the with "Ways to Make 55".   Here are some of their responses.

Students use manipulatives to explore 55.

Students made a list of their discoveries.

My take-aways from this my experience and hers were as follows:

1 - This didn't take as long as I thought it would.  The second time this class did this routine, they did it in the last 15 minutes of the day...WITH manipulatives! Because this teacher has manipulatives available to her kids all the time, it shaved minutes off of this routine because the kids simply pulled from the buckets in the middle of their table and clean up went just as quickly.

2 - Kids love to use these manipulatives!  It is ENGAGING!

3 -  The students came up with far more responses than I imagined that they would.  They were CAPABLE of doing this, they just need the chance to show it!  Paper and pencil should wait.  

Discussion Questions:
Q1 -What have been your biggest take aways this week as you work through routines with your classes?

Q2 - What are some obstacles that you are currently facing and how you overcome them?

Book Study Wednesday: Chapter 4 Counting Routines

          Welcome back to Book Study Wednesday! This week we're discussing Chapter 4: Counting Routines and Understanding the Place Value System.
 

Short post this week! I've got a video of "Count Around the Class" as it was presented to an upper elementary class. I chose a 5th grade class because I wanted to show the versatility of this routine. Below I've included some links to resources that I found using number routines in middle school as well. 

As it was stated earlier in the book, number sense routines provide opportunities for students to build on existing number sense and helps students make connections to big ideas in mathematics (Shumway, 2011, p17). This can happen even later than 3rd grade and, quite frankly, many students need this continued support long after elementary school!

I have to say that I LOVE the Organic Number line. It was my favorite routine in chapter 4. I'm not currently in my own classroom but if and when I ever am again, I am going to develop this with my students. What a great way to track continued growth of student understanding throughout the year! How amazing to see coherence between concepts such as time and fractions! Exciting stuff, I tell ya!

Discussion Questions:
Q1 - Name one thing you will start and/or continue doing after reading this chapter.
Q2 - Name one thing you will stop doing after reading this far in the book.
Q3 - Choose a routine from chapter 4 and list 2-3 questions you could ask your students of different levels.

Additional Resources:

http://mathspot.net/2013/11/08/count-around-the-circle-with-fractions/

http://investigations.terc.edu/library/curric-math/qa-1ed/counting_around.cfm

Book Study Wednesday - Chapter 3 Visual Routines

Being that I am a visual learner, I like to see how things are done prior to trying them out myself.  Thanks to the leaps and bounds technology has made in the last few years, I can do just that.  So this week I've put together a collection of videos that demonstrate most of the routines we read about in Chapter 3.  Discuss away!

Quick Images (Using Dot configurations)
http://yhoo.it/20dDQsh

Shumway mentions Van de Walle's book, Elementary and Middle School Mathematics, on page 52.  After Googling his name, I found this video slide show and it moves pretty quickly through a series of dot configurations. There are plenty more where that came from! My first thoughts were of fluency, after the students know the routine well, and perhaps even for individual or small group choral practice. It's a great example of how a Quick Image routine can be used for enrichment as well. 
 
Quick Images (Using Ten Frames)
https://www.teachingchannel.org/videos/visualizing-number-combinations

I must admit that my favorite part of this video clip was how the teacher reacted to the student who called out his insight.  When she changed her board around, he noticed that she did not add or subtract magnets so it must still be eight.  I love her reaction and must remember to do the same the next time I am in a kindergarten classroom.  

Rekenrek Demo
https://www.youtube.com/watch?v=JBEKOb7tWEY

There has been much discussion surrounding rekenreks recently since the majority of us haven't personally used them.  This is a great (and brief) demo of the math concepts rekenreks can reinforce. 

I noticed in a few other videos I browsed that the teacher was allowing the students to sketch what was seen on a white board or paper.  Then the students were given a second quick look to double check.  The idea of double checking their thinking appealed to me because as teachers, we're always trying to do that and this was an easy way to work that into a classroom routine.  

The other observation I made both during the reading of the chapter and watching the videos was the amount of time the students were allowed to discuss their observations.  This cannot be overstated.  Children must, must, must have a chance to discuss their ideas and learn how to listen to someone else's ideas well.  It takes time and practice but I know adults who are still learning how to listen so....

Discussion Questions:
Q1  What have your considered adding to your classroom to give your students that much needed "multiple exposures" component?

Q2  What have you already started in your classroom to build number sense?

Book Study Wednesday - Number Sense Routines (Ch. 2)

Today I had the pleasure of working in two 1st grade classrooms.  I always love working in first grade because those 6 year old kids love having a guest in the room and it makes me feel like a celebrity!  If you're ever having a down day, go visit first grade.

Last week during our face to face meeting, we decided to write about one student and identify where in the Number Sense trajectory he/she might be.  The following is my description.

Nevaeh
I was in working with a small group on "Ways to Make a Number" (page 83).  I asked the students to think of all the possible ways to make the number 14.  I gave them white boards, markers, and two minutes.  One child wrote a whole fact family that included 10, 4, and 14. Another student simply wrote '14' and Nevaeh's board was left blank.  I realized that the students were in very different places.  I dismissed the student who wrote the fact family so I could focus on the the students who seemed to be having the most trouble and I dove in with an example.  I wrote, "10 + 4 = 14".  I also drew a ten frame to support this number sentence.  The little guys just seemed stuck and I noticed that each time we drew a picture, Nevaeh was counting every single dot one at a time.  I decided to stop the routine because even with the scaffolded support of ten frames, Nevaeh was still having trouble.  I decided to dismiss the other child and do some more probing with her to find out just where she might be in the Number Sense Trajectory (page 9).  
I started by drawing a ten frame and filled it with 10 dots.  I asked her to tell me how many.  She correctly counted them one by one until she reached 10.  I erased one and asked her to identify the new number and instead of simply counting back from 10 one time, she started counting one by one again.  I kept probing until I found that she could correctly subitize numbers up to 6.  Once I showed her a number larger than 6, she began counting one by one.  

Discussion Questions:
Q1 - What type of subitizing was Nevaeh demonstrating?  

Q2 - Thinking about the next step, what routine would you use with Neveah next?

Book Study Wednesday - Number Sense Routines Chapter 1

Welcome back to Book Study Wednesdays!  We shifted from Fridays because, let's face it, no one wanted to do much after work on a Friday!  So each week for the next eight Wednesdays, there will be a blog post discussing Jessica Shumway's "Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3".

  I would LOVE to include discussion questions from readers so we can gather perspectives from all around the globe.  If you'd like to submit a question, please email them to me at momentum79@yahoo.com.  

Next up: Chapter 1

When you think about it, all children have a sense of numbers.  If I gave one child 10 M&Ms and another child 2 M&Ms, you can bet the child with two candies would have some very strong feelings about it!  Number sense is demonstrated very early on and Shumway puts it like this on page 11:

     "Before children even come to school, their intuitive sense of number begins to develop.  They are able to recognize amounts of one, two, and three without counting (Sarama and Clements, 2009).  They develop a sense of more and less.  Early on, young children come into contact with a variety of situations that involved quantities and to problem solve."

Then they get to school and we beat it out of them with a textbook.  Sit here quietly, write this, test on Friday. Boom.

Shumway goes on to discuss how children need multiple chances to see situations differently and to discover that there are MANY different ways to reach a solution and I couldn't agree with her more!  Students needs to discuss ideas, even at a young age, even for 10 seconds, but they need to work out their thoughts.  It is one of those things we need to TEACH children how to do because for many of them, it is hard to wait for someone else to finish talking!  

Number sense routines can help teacher in six major ways (see figure 1.3 on page 10):

• language
• big ideas
• skills
• tools
• models 
• strategies

As you work through routines with your class, the students start to see the strategies others are using to  work through mathematical situations.  They also begin to incorporate the vocabulary that a teacher models within these routines.  These routines are so simple yet pack an academic punch.  Who knew number sense incorporated so much! 

I can't wait to read on so I can try some of them!  In fact, I'll be modeling some of the routines and posting videos.  I know sometimes it helps me to watch someone else do it first. So those will come in later weeks!

So let's get started with the discussion! 

Discussion Questions

(for Hernando County Employees, please answer in the Comments and respond to at least one other person to receive in-service credit.  Everyone else, it's free game!)

What was your definition of number sense prior to reading chapter 1? How has it changed (if at all)?

What number sense routines are you currently using and what concepts are you targeting by using those particular routines? 

What, if anything, surprised or intrigued you as you read through chapter 1?