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:
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?
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?
