Guest Blog: A Principal's Perspective on Number Talks

This week we are proud to introduce our first guest blogger for the 2013-2014 school year, Principal Mark Koller, from Pleasant Hill Elementary! Principal Koller and his staff are working hard to transform math instruction and they know that it begins with action steps and trying a few things different. Let's learn from this principal as he begins his journey with Number Talks...

There are many benefits to being a campus administrator. You get a sweet walkie-talkie, maybe an extra nugget or two in the cafeteria, and most importantly, the joy of working with hundreds of students on a daily basis. I love my job, but as an administrator, I do miss the interaction, academic conversations and relationships built in the classroom setting that thousands of teachers across our district experience each day. Luckily for me, my staff allows me to pop in from time to time and teach.

Recently, I was able to work with my fourth grade team facilitating Number Talks in six different classrooms on six consecutive days. If you’ve read this blog before, you are probably very familiar with the basics of Number Talks. We were fortunate enough to have our math curriculum department on campus this week, and I also had the fortune of hearing from them in my district admin meeting. The point that hit home with me, and what I tried to model in my lessons this week, was the three pronged approach to math:

1: Make Sense of the Math

2: Do the Math

3: Use the Math

According to Cathy L. Seeley, author of Faster Isn’t Smarter, students must have a “conceptual understanding,” while utilizing “facts, skills, and procedures,” when problem solving. (Seeley, 2009) This to me, reiterated the make sense of, do, and use the math approach.  Equipped with this information, I felt ready to get into the classroom and work with the students.

I started my Number Talks journey in Mrs. Lukes’ class. The students and I discussed 27x5. As with every Number Talk, I ask if anyone had a way to solve that problem. Hands went up or really hands went to their chest and they started gesturing to me in a sort of Number Talk sign language that took a second to decipher. Each student held up the number of ways they could solve the problem.

• The first student I called on started to talk to me about friendly numbers and why it’s easier to count in ones, 2’s, 5’s, and 10’s She encouraged me not to look at the problem as 27x5,  but more as 20, 5, and 2 multiplied by 5. This way I could literally count by 20 five times, 5 five times and 2 five times. I was super excited. I could hear Yoda saying, “Conceptual Understanding this one has.” (Star Wars reference)
• A second student made the point that multiplication was repeated addition and I should just add 27+27+27+27+27 to get to our eventually goal of 135. I was pumped.
• A third student said to just multiply the numbers using the traditional algorithm to solve it. When I asked this student to walk me through this, he stumbled on some steps. While participating in a Number Talk all answers are valued and validated. The conversation with the students is the basis of the mini lesson. This particular student was on the right track but just was not sure how to move the numbers around in the algorithm to bring him to ultimate success, and could not explain the reasoning behind it. My advice to him and the student in the second class I worked with that wanted to write out 27 dots, five times and then count up all the dots was similar; When choosing the best strategy it is important to pick one that you understand and will ultimately bring you reasonable and efficient success. I found myself reiterating this point over and over in all six classes: make sure you can make sense of what you are doing first.

When asked how you came up with your strategy, a student’s answer shouldn’t be my teacher showed me. It should be based on the numbers and how they can manipulate their thinking with them. Algorithms are great in some instances. They should be used as a tool for doing the math only after we can make sense of it. Reasonable, efficient strategies are ones in which we are not setting ourselves up for failure before we even start. Putting 27 dots on the paper five times in a row is a recipe for miscounting and frustration. They may start there, but encourage the progression from dots, to tally marks, to numbers, and then finally the friendly numbers that will help them succeed in an efficient manner.

Encourage your students to look for the friendly numbers that the first student I encountered encouraged me to do. Think in numbers that are easy to manipulate and don’t settle for 13 to be 13. Let it be a 10 and a 3 or two fives and three ones.

Bridging the conversations from the Number Talk to the application or the “Use the Math” portion of the classroom is the key for ultimate learning target success and the recipe for cooking up mathematical thinkers. I look forward to revisiting these classrooms and others in the coming weeks and Tweeting out the evidence of great Number Talks and math conversations. You can follow me, @KollerTX, on Twitter.

Guest Blog: Number Talks in a 3rd Grade Classroom

Magen Schott, 3rd grade teacher at Knowles Elementary, is our guest blogger this week! She has been using number talks with her students, so we asked her if she would share her thoughts on the topic. Thank you Magen, for sharing your learning and inspiring others through your experiences.

"Since beginning Number Talks in my classroom, my kids are able to have great conversations about their mental computations. It's easy to have a conversation in Language Arts class about the main idea of the book, the author's purpose, etc.  Before reading Number Talks, we never had REAL conversations in Math about numbers.  It has been amazing to listen to my kids discuss numbers in this way.  Students have learned to reason with numbers, and their mental math ability has greatly increased.  Our classroom is a "safe" place for the kids to be wrong, and they are open to admitting their mistakes.  They all learn from each other, and most have begun to try out and adopt different strategies that others are using.  I feel that they think about numbers differently now-- that numbers can be taken apart and combined with other numbers to make new numbers.  They have great conversations about manipulating numbers to make the problem easier and organizing numbers into groups of thousands, hundreds, tens and ones."


Below is a impromptu video recorded during a recent school improvement visit.  Watch Magen's class in action!

Comment below how you use number talks in your classroom...

Number Talks

I was worried about my children not understanding Number Talks, but it was amazing how quickly they wrapped their brains around different mental strategies.

Christi Muto

3rd Grade, Parkside Elementary

Number Talks are classroom conversations around purposefully crafted computation problems solved mentally. What a great way to "warm-up" students' brains, but more than that, they are a fun way to build number relationships.

Key Components of Number Talks

1. Classroom environment and community

• Number talks build a cohesive math community. It is so important that this is a risk-free environment.  Designate a place in your room where the students sit altogether on the floor. Have a place to write because in Number Talks the teacher does the recording!

2. Classroom Discussion

• Since the computation is done mentally, provide plenty of time. Use a signal such as thumbs up on their chest to show they have the answer. Students are given the opportunity to share their strategies and justifications with their peers. The benefits are students clarify their own thinking, test other strategies to see if they are logical, apply number relationships, and build a repertoire of efficient strategies.

3.  The Teacher's Role

• Since the heart of Number Talks is classroom conversations, the teacher becomes the facilitator. The teacher writes down all the students' answers. Then the students can "justify" their answers by sharing their strategies. While the student is explaining a strategy the teacher is recording the strategy on the board. What a great way to model recording strategies!
• Teacher poses questions to the students to lead the conversation. By changing the question from "What answer did you get?" to "How did you solve this problem?" the teacher is able to understand how the students are making sense of mathematics.
• Don't be afraid to share incorrect solutions. Wrong answers can lead to great classroom discussion and point out misconceptions a student may have.

4. The Role of Mental Math

• Number Talks help the students focus on number relationships and use these relationships to solve problems. When students approach problems without paper and pencil, they are encouraged to rely on what they know and understand about the numbers and how they are interrelated.

5. Purposeful Computation Problems

• Careful planning before a number talk is necessary to design the problem that is "just right." The learning target should determine the numbers and operations that are chosen.

Here is what Leander teachers are saying about Number Talks:

I begin class several times a week with number talks. This is a great way to get kids thinking about math concepts and not just memorizing "how the teacher said to do it". It also models how to communicate your math thinking. I see students using the same symbols that I modeled sometimes in their problem solving. We have a common format for communicating. By having the students defend their answers, it also helps them understand "justifying" when communicating solutions. Number talks are a great way to start a lesson.

JoJo Fentress 

2nd grade, Naumann Elementary

I use them almost everyday! We talk about numbers (odd/even, what comes before after on the number line, how many more/less to get to 5 or 10, different ways to represent a number - numeral, tallies, doubles, an octopus for 8, triangle for 3, twins for 2 and anything else we can thing of that relates to the number) and I use the dot cards. The kids love the dot cards!  One day I had a Watch Dog in my class during number talks. He owns his own computer gaming software company and is a really smart guy. He came over to me later and told me how impressed he was with the dot cards and what we were doing with them - especially since it was a kindergarten class. I have a pretty high math class overall, so I am also including partial number sentences when the kids tell me how they saw the dots. So for the number 8 we had things like:

8

5+3

3+3+2

4+2+2

6+2

2+1+5

I also have all the kids put up fingers as the person tells us how he saw the dots. That way they are actively participating and making the number. The biggest success is that kids don't just think of 8 as 8 and counting out 8 objects - they understand that it can be represented different ways and can be taken apart and put together many different ways.   

I also talked about the dot cards with parents at our parent teacher conferences. I wanted them to understand what we are doing with them. I had one mom tell me that they were what her second grader needed because she was struggling with her math facts. I told her that when her second grader was in kindergarten we did not have them.  :o(

Does it sound like I like number talks? You bet! It's always one of the most fun and engaging times of our day.

Colleen Welliver

Kindergarten

Steiner Ranch Elementary

After doing Number Talks with my students, one of my students came in the next day and asked me very excitedly, "Can we do "Math Speaks" again?

Ann Hutton

1st Grade, Mason Elementary

You can learn more about Number Talks in the book:
Number Talks: Helping Children Build Mental Math and Computation Strategies by Sherry Parrish

What are your thoughts about Number Talks? Please share! Post your comments below.