Choral Counting: So Much More than Counting

When you hear the word “counting” your mind quickly goes to primary age students. You see the kindergarten students counting, the 1st grade students counting, but what about 6th graders?

Our school is trying to target students’ needs by having tw,o 30 minute target times (RTI), to help move students forward.  My Tier 3 group needs a lot of work with number sense and they had been asking me to work with fractions, so I decided to do some Choral Counting with them. (The next day I did choral counting with my whole class. I love things that all students learn something from.) I thought it would be a great way for them to work with fractions, while also engaging students in SMP 3.

To be fair, we have done a lot of work this year with patterns: number patterns with the 100s chart, Pascal’s triangle, the multiplication chart, visual patterns and growth, and structural patterns in equations. Actually, we look for patterns everywhere…in the books we are reading, social studies, science, and across disciplines…we are becoming pattern seekers. This was completely evident during a choral counting lesson that I did with fractions.  Patterns and relationships are so important to learning.

We started off…” We are going to count by 2/3 starting at 0.” I had planned how I would record the pattern and thought about what relationships the students might notice: patterns in a column, the denominator remains the same, the numerator is changing by 2 (I wanted to start easy, to build success and ease their working memory so that they could really focus on the relationships.) We started counting. (I was nervous that this was going to be too easy for them.) Hmmm…they were getting stuck in a few places and then I was reminded how important counting is. We are working on fractions, but at the same time we are reviewing multiplication facts, skip counting, and number sense in general. We then had 3 rows completed and I stopped. “What do you notice?”

“We are skip counting by 2.”

“Turn to your math partner. Do you agree or disagree with that statement?”

We then discussed this as a class. Many students agreed and then we got into the discussion of the numerator and denominator. Whoa! Misconceptions have surfaced!

Then a student stated, “We are not counting by 2s, we are counting by 2/3.”

“No, we are adding by 2s. See,” and a student points to the numbers in the numerator.

“If we are counting by 2s, then we should be able to add 2 to the previous number to get the next number. That doesn’t work.”

Ahhh…we have an argument going on. Great! So, I ask the students to sit with their partner and prove or disprove that we are adding by 2.

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After some drawings and equations the students come to the realization that we were not counting by 2, but we were counting by 2/3. Though, they all agreed that the numerator is changing by 2.

Then a student said, “I noticed that if you look diagonally down toward the right, the numbers are increasing by 14/3 .” I asked “Is that true for every diagonal?” We tested it out? Yes. “But, why does that work I asked?” Again the students turned to their partners and discussed.

“Well, we are counting by 2/3 and so from 2/3 to 16/3 we keep adding 2/3. That adds up to 14/3.

I write what she said… 2/3+ 2/3 + 2/3 +2/3 + 2/3 + 2/3 + 2/3= 14/3

“Actually if you just multiplied the fraction by the number of times that is much faster,” a student shouts out. Ahhh, yes now we were connecting their previous knowledge about addition and multiplication with whole numbers to fractions.


We continue to look for patterns and notice the relationship down the column, moving diagonally from right to left. We talked about adding and multiplying fractions and then also subtracting fractions if we moved backwards.

Then I placed some boxes in some areas below the 3 rows and asked students to determine which numbers would go into those boxes? They used all the patterns we discussed earlier to determine which number fit and critiqued each other’s reasoning and pointed out more efficient ways.

What I love about choral counting is that it surfaces some misconceptions, allows us to discuss operations, vocabulary, and relationships between numbers. It is not threatening. Every child feels successful and we can really work on justifying their thinking and critiquing the reasoning of others.

Lastly, it is so important how I record students thinking. I have been thinking about this a lot and color has become my best friend. The best statement at the end of our counting session as we looked at the finished board.

“We all know what we were doing, but if someone walked in right now, they would have no idea what all those circles and lines were. But, it looks so cool.”

It looks cool to me too because it reminds me of the rich discussion we just had.

Making connections and looking for patterns. It is so much more than fractions and counting. It is learning how to make sense of the concepts we are exploring.


The Tug-of-War between Program/Textbooks and Student Learning

I have always hated the focus on programs or textbooks.  When a district adopts a new program we are told, “You need to do the program to fidelity”. What does that mean? Shouldn’t we be meeting students where they are and guiding students in the learning process? How can a single program be the right path for every student? I hate the term “fidelity to the program”! What about fidelity to individual students’ learning?

I recently had a meeting with the 6th grade teachers in my district and we had to discuss 1 of 4 topics: program assessment, program pacing and planning, differentiation, and program technology. I am not sure why we were doing this? What outcome was expected? But, It was through this discussion that I noticed people, myself included, allowing the program (in this case the textbook) to make their instructional decisions instead of they, the teachers, making the instructional decisions based on their students’ needs. And, when they did, there was an underlying sense of guilt of not following the program or of doing something wrong. That frustrates me to no end. What it comes down to is people want to follow directions and do what is right. But, my question is what is more right? Is it to follow the program or to follow students’ needs? (That was rhetorical. 🙂 ) We need to remind ourselves that we must do right by our students and not the program.

This made me reflect on content understanding, content standards understanding, and student readiness understanding. This is what we need to focus on because the people that understand content and standards deeply, have a much greater ability to differentiate and meet students’ needs. I can see where students need to be and a path of how I can get students there. In my conversations with others, they have indicated they don’t see the goal. They don’t see the path. This is a vital piece.

Created by Jason Zimba

The past two years in our district when I was a TOSA, we were really focusing on this: learning the CCSS for math, and we were deepening our content knowledge in math as we learned about Number Talks and mathematical reasoning with CGI. We were scratching the surface. (Maybe I left too soon, but maybe being thrown back into the classroom was the best thing. Only time will tell. ) People were struggling and they were overwhelmed with the planning of math. At times there was too much struggle, and thus the district decided to adopt math texts, both with good qualities. Both have some strong mathematics.

I am now back in the classroom after supporting teachers through that process and we have a newly adopted program. I am now hearing teachers battling with “following the program”. It is clear that their gut is telling them what their students need and instead of addressing those needs, they are “following the program”. Teachers, or the majority of teachers, have dropped Number Talks even though they noticed the benefits and the power they had for student learning. I spoke with one teacher yesterday, “I miss Number Talks,” she said. “They (students) got so much out of them.” My response?

“Do them! Take something out that you don’t feel is as impactful and do a Number Talk in its place.”

But, I can’t judge. I catch myself doing the same thing. Number talks changed the way I saw math and taught math when I was first introduced to them 3 years ago. CGI was then the next catalyst for me…focusing on students’ mathematical thinking and using what they know to move their learning forward. But, how many Number Talks have I myself done this year?  A few, but not as many as I should have. Have we done a lot of great math? Yes! Have we done some things just because I wanted to stay on pace with my team? Ughhhhhh….I have to admit it. Yes. Am I teaching in a sequence I don’t agree with? Yes.

There is this underlying pressure to stay on track with a program, but I know my students better than the program, and need to do what they need, not what the program is telling me they need. I feel conflicted. I want to teach with the sequence I came up with two years ago. I want to teach and move with my students. I can do this. I have the knowledge to do this. But, I am suppose to follow the same textbook and chapter tests as everyone else. So, I follow the pacing, I use components of the textbook (the really good problems) and I open up some of the other problems. I work with my students’ needs and do alternate math work two days a week and I differentiate with open problems and needs based grouping at times too. But, I can do better. I will keep working.

Differentiation is hard. But, it is especially hard if you do not know the content in depth or you do not know the progression of learning students need to take. Having studied math education in depth over the last few years (I am not an expert), I know the progression of mathematics learning (always more for me to learn), I have things in the back of my pocket (always more that I can learn) that I can pull out when we are discussing a concept that allow me to take a step back or a step forward when needed. But, I know that is not the same with others. I compare it to my science teaching this year.

I have only the most surface level understanding of cells: cell structures, their functions, and what the progression of learning is. Thus, I really struggle with leading a discussion on it. I don’t know what questions to pose, what are prerequisite skills, really how far my 6th graders are suppose to go in the topic, and all of that makes it really hard to teach.  I have been researching cells, watching videos, doing what I can, studying NGSS, but I am only minute ahead, not even a day ahead of my students. I then run out of time to plan the best way to help my students acquire the information and use it. I have done some good things, such as our inquiry about the hydrogen peroxide and chicken liver and potato, but I didn’t follow up with the depth that I know I should have.

I will be moving on to a unit on currents soon, and I will have a program for that. It will be interesting to use a program in a content area I am not strong in. Will it be the key to allowing me to support my students effectively? Will it be a vessel for my own learning? How many of my own instructional practices will I use instead of the program’s recommendation? Will I just follow it or will I break from it when I sense the needs of my students?

The tension is great. It is easy to know what the research says. It is easy to say what to do. But, doing it is a whole other level. I will get there. I will keep exploring, reflecting, and ultimately find the right balance.

This past week, I set a goal to know my students more and focus on them. What I found was I did a much better job of “teaching”. I wasn’t as worried about making sure I was teaching everything, but I really tried to make sure that they were carrying more of the cognitive load than I was. I decided it was more important for them to process and think and have the time to do that, than completing everything that I felt we needed to complete.

As I have said many times over and over again…it is not about all the skills, facts, pieces of knowledge, but it is about the learning process and the critical thinking skills; the practices of learning that are most important. I just have to keep reminding myself about this and focusing on what my students need, not trying to do it all.

How do you make sure you are meeting your student’s needs and not just following a program?

The tension is great.

…a cause for reflection

I had had recently been reintroduced to the word technocrat. It’s interesting as it came up in a few different conversations and readings. I wasn’t sure of its exact definition, so I looked it up…MjTUyWVHrnTjzRKv0OC3aWqPA5masDkzxu_5548iJXk

It was an interesting word for me. I believe whole heartedly that teaching and leading is so much more than being a technocrat. Then I started reflecting…Crap!

I only wish it was this cold!


Have I been too focused on the technical components of teaching? Am I not paying enough attention to the little humans sitting in my classroom and the bigger humans that they go home to? (There are parents I have not even met or talked to once during the past month and a half. I need to make some calls.)

Am I spending enough time building relationships with my students, laughing with them, developing an understanding of their cultures and their desires? I know I want to. I know I am trying. I know it is important to me. I know it is a goal that I have. But, am I executing this? Or are the technical components of the job taking over?

So,  relationship building is important, but the reason I need to do this is for the ultimate goal of developing my students’ processing skills to be independent learners.

How do I forget the pressures (inner and outer) of achievement that cause panic and stress and focus on my students and growing their brains?

I know my students need to connect with me. I know I want to connect with them.  I see them wanting to come in and hang out before school, recess, and lunch time. Then I hear the words, “Go play!” escape out of my mouth. I want to hang. I want to play. But, I am just full!

I am spending every waking minute creating lessons, trying to keep up with providing feedback (I am so terribly behind on this), and planning a rich curriculum to make sure that I am addressing all the complex standards that my students are required to learn this year. I am full!

ihave a team of grade level teachers that I am suppose to meet with. We have a staff meeting once a week that I must attend.  My introverted self is in need of space. I am full!

And while I am spending the bulk of my time on the planning, meeting, and technical thinking, I am still so far behind where I need to be. I am full!

But, my students need to connect with me. We started the year building academic mindsets and understanding why we are in school. We started the year getting to know one another. We are doing great things, but it is never enough. What would happen if I create space: space for me, space for them, space for us? 

And then I remembered Zaretta Hammond referring to this in her book, Culturally Responsive Teaching and the Brain. (I know…I think I have mentioned this book in almost every blog post. It is kind of stalkerish, but it is so so relevant and important. Especially in today’s society.)


I have seen myself in the top two categories. By goal, the stay in the top left. What do I need to do? Can I forget about some of the technocratic minutia this week and focus on us and our humanistic needs? How can I give them access to me during recess, lunch, or before school without taking away the much needed alone time that I need? How can I give them the support to develop the processing skills they need to be active and competent learners?

Can we make our reflection time sacred, instead of finishing up social studies, or science during that time? Yes! That will be my goal this week. I will not go backwards, but I will start where we are.

  1. I will provide instructive feedback in the right dose. (I am overwhelmed by it because I am not providing the right dosage to my students.)
  2. I will not skip our two afternoon meetings on Tuesday and Friday to discuss how the class is going and develop next steps for our learning.
  3. I will open the classroom during two lunch breaks for students to hang out so we can connect and I can make sure I understand their needs.
  4. I will make my students hold the cognitive load in my class and not me, by having them inquire and develop the questions that lead our study.
  5. I will give students time on Wednesday for personal reflection and goal setting.
  6. We will connect our study on cells back to the brain and what our brain needs in order to learn.

Let’s see how the week feels after a little more “personal warmth” and a little less “professional distance”.

****Update**** Well, it has been a work in progress. I have successfully met(and still working on) goals 1, 4, 5 and 6. I definitely need to make more effort on 2, 3. Work in progress.

How do you find balance between the technical sides of teaching and the time to build trust and relationships with students that we all know are vital components to success?