Wow where do I start?
Ok so I didn’t come up with this idea out of nowhere. I was reading this awesome book–> Number Sense Routines by Jessice Shumway and I had this awesome class of students who were lacking in number sense. They were also a class of students who were very used to being unsuccessful in math and most of them did not enjoy interacting with mathematics. After reading through chapter 4 (Counting Routines) I thought my high schoolers would be much more receptive to sitting in a circle and counting than using visual routines (Chapter 3). So I decided to try it. If you are going to dive in and try this I HIGHLY recommend reading chapter 1 and Chapter 4 (if you can read the whole thing, please do). Chapter 1 discusses what number sense is and talks about subitizing, unitizing and lots of specific skills that most math teachers never thought of. My definition of number sense was almost verbatim described in Chapter 1 of this book! In a nutshell, its a great book for any math teacher even though the book states K-3 grades.
Moving on to WHY? I came up with this idea. You can read about it here (THE BLAME GAME) and read through my #TMC13 presentation here. In a nutshell, I am unable to live with myself if I allow students to graduate high school (pass my class) without having mental math strategies. It is equivalent to allowing a student to graduate from high school without being able to read. I refuse to be part of this movement anymore.
So I start this idea with my high school class of 12 students who’s only relationship with mathematics was very negative. To be completely honest, these students’ relationship with school was very negative and they were kind of ready to give up on school all together.
Counting circles in general seem on the surface like a routine that is just done 10 mins a day however it is much more than that. They help start a culture change in your classroom. They give students the opportunity to own math, to be successful in math, to “create” and share their strategies, to make mistakes and learn from them. They are asked to verbally describe their mathematical thinking not just write it like we have always asked kids to do. You will find that students are NOT used to these kinds of activities in math. Learning a new way to feel and be in math class (at least if you are doing these in gr 4-12) is not a FUN process for students. They are scared! School has trained them, for s0 long, to conform to learning as a feeling of success and ease at all times. For anyone that has actually LEARNED anything this is very far from the truth. The learning process is messy, ugly, scary, tiresome, filled with failure, extremely hard and you normally pick up scrapes and bruises along the way. So when you start counting circles in your classroom it is extremely important to start slow. Start with something students will be successful with: Gr 3-5 start with counting by tens starting on either a decade or non-decade number, Gr 6-8 start with counting by tens on a non-decade number, Gr 9-12 start with counting by tens on a non-decade number. (These recommendations all depend on where your students are, do not start with these if you know they will be unsuccessful)
When I started this with my class I started with counting up by 1s. Yup I know what you might be thinking…”Why 1s? That is too EASY?” YOU. ARE. EXACTLY RIGHT! My students were so hesitant to do math that I had to start with 1s. I had to build their trust with me and the trust within themselves. Everyone can count by ones so I knew that my students would have NO excuse not to be able to participate. I also wanted to change their mindset about mathematics and the relationship they have had with mathematics (extremely negative). So I needed a hook. I need to show them that they CAN DO math, that they aren’t unsuccessful ALL THE TIME. This is where you start the culture change in your classroom! You are giving them the opportunity to change the mindset have had about themselves for years!
So you’ve decided what you are going to count by and what you are going to start at….Now what?! YOU COUNT IN A CIRCLE! I normally ask for volunteers (“who’s wants to start for us today?”) and we start there and I decide to go counterclockwise or clockwise. Depending on the number of students my classroom (I have done it in as big of a classroom as 30 5th graders) I normally go one time around the whole circle and sometimes more. It really depends. When I am starting the routine and want them to get used to the routine I make sure that the focus of the counting circle is not on the math but more on feeling successful (hence the choice of starting easy) and the way the routine functions. So students count around the circle and I’m paying attention to what they are saying, how much time it is taking them to answer, any fingers being used to count or any other type of non-verbal clues students are showing me as to how hard the adding is for them or strategies they are using to find their answer. In addition to this pay attention piece, I am writing their answers on the number line as we go around the circle.
This is an important visual piece to counting circles that makes it attainable to all. Also it allows me as a teacher to hear any mistakes students might be making with place value or verbal descriptions of numbers. It also gives students who don’t have a lot of mental math strategies to use the number line to look for patterns to help them with another aspect of the counting circle: Stop and guess (I will get to this shortly)
As students are counting I am writing the numbers they said on the number line and I am also pay attention and making note of any common errors I see. As a teacher you already know some hard transitions for students to make while counting. For example:
- Counting up (or down) by 10s on a non-decade number common error happens when counting to the next place value unit and also the teen numbers (i.e. 97, 107, 117,..)
- Counting up or down by tenths common error happens when counting to the next place value unit (9 tenths and one more tenth makes the next whole number not 11 tenths)
The basic errors that happen can all be pretty much pinpointed to place value unit changes. As you do more and more counting circles you will see common errors and will be able to anticipate errors so you have an idea of what you want to ask in the stop and guess part.
While we are talking about errors another part of the counting circle is that I (THE TEACHER) DOES NOT correct ANYONE! If a students says an answer I write it up and I DO NOT EVEN HESITATE!! I keep counting, I keep on moving along. I wait to see if any students will speak up or if there are lots of whispers happening after a couple other people have said their numbers. If a students says something I make sure that the way they say it to other students is using what a colleague of mine calls “synergizing” language. For example: “Can you please check your answer?” “I want you to check your answer” The key to this is that students are NOT being talked to negatively. You do not want to hear “that is WRONG!” This ties back into the culture change in your classroom you want students to feel safe and comfortable to make mistakes and learn from them instead of them being reprimanded and feeling stupid for making those mistakes.
After you count around the circle, see some common errors, now is the time to stop at someone. This is where my paying attention part allows me to decide where I should stop. I normally stop on a number that students made errors on or in the past I have seen students make errors on or if I want to see IF they are going to make a common error. When I stop at that student I write his/her name under the number and then I choose how many people down the circle they have to guess. For example: “What number is Ashley going to say?” <–Ashley might be 6 people down the circle from the person I stop at or 7 people or whatever you decide based on what you see students struggling with previous) In the example below, we stopped at Kauhi and I asked them “When you figure out what number Megan is going to say, put your thumb up.”
Now we be patient and wait. We give kids as much time as possible. I have done this in a class of 30 fifth graders and I will wait and expect them to also wait patiently while everyone is able to come up with an answer. If someone doesn’t put their thumb up we continue to wait until they are ready or at least pretend they are ready.
Now comes the fun part! NUMBER TALKS!
I have students share ALL their answers. EVEN the ridiculous ones! I can’t stress enough how important this is…ALL ANSWERS!! Take them all! The wording I use “What answers do we have?” “Are these all the answers? The number you were thinking about in your head is on the board?”
After I take all answers from any students I ask for volunteers to share HOW they got their answer. This piece I am not going to describe because it is basically a number talk and you can find lost of info on the internet about number talks but I have also added my video of jotting down one of my students strategies. I normally try to take around 3 DIFFERENT strategies and I make sure to put the students answer, their name and to write ONLY WHAT THEY TELL ME VERBALLY! NO ADDING TEACHER THINKING IN!! VERY IMPORTANT HERE!! We are asking kids to be verbally specific about math and I want them to learn that their words are not specific enough or maybe they are but I write exactly what they say. I often here “you know what I meant” and I tell them “I am only writing what I hear you say” This forces my students to think about the way to verbalize their mathematical thinking (addressing SMP 2, 3, 6). After they have shared sometimes I have to verify the answer so I will start where we stopped and continue to the person we were guessing and confirm what is the correct answer. This normally only has to be done in the first half of the year because after they get accustomed to the routine they are critically thinking about answers and are able to catch their own mistakes more often and don’t need the validity piece. After the number talk is over the counting circle is over.
Once this routine gets used regularly and gets built into your classroom it should take no longer than 10 mins. I normally only do one circle a day, everyday for 8-10 mins. That is basically it. I have added one more video for an example and I still working on more videos to show the various ways counting circles change based on classroom and students. There is no one set way to really do it. I am kind of outlined a good start here but there have been lots of days that I ask different questions: “What mistake do you see in today’s counting circle?” “Who is going to say (certain number?” etc. I am in the process of starting a website that will have a post a day for a counting circle progression. I am hoping to get that started by next school year. Sorry for the delay and thank you for being patient. For now I have compiled a album of pictures that I have taken for some important reason of my counting circles throughout the 3 years I have been doing them. Feel free to ask me on twitter (@wahedahbug) or via email (email@example.com) if you would like a description about the picture or if you want to chat more about counting circles.
I am briefly going to just list some of the math “things” that counting circles address without really going into them:
- Problem solving
- Standards for Mathematical Practice: 2, 3, 5, 6, 7, 8
- Linear equations
- Mental math strategies
- Multiple strategies for 4 basic operations in all different number rings (whole numbers, integers, rationals, etc.)
- Adding polynomials
- Formative Instruction
- Self confidence (in relation to mathematics)
- Igniting math interest
- Skill practice
- Classroom Routines
- So much more that I will be updating continually
Here is a good overall video of how counting circles works in my classroom. Please note that this video is with a class that needs a lot of support with counting circles so I don’t normally help as much but because I need to adjust to what my students need I have to give more support for this class of students.