The word routine is defined as a sequence of actions that are regularly followed so that they become a habit. In the classroom routines are often thought of as classroom management procedures that support students in making more effect use of classroom time and to transition more efficiently from one activity to another. Classroom routines such as how to sharpen your pencil, clean up your materials, come in from recess etc. are explicitly taught, and practiced early on in the school year. As these routines become habits they help the classroom community run more smoothly, save valuable learning time, and create a predicable, safe space for learners and learning.
Routines can also be powerful tools for mathematical thinking and reasoning. “Like the management routines, these “mathematical thinking routines” also have a predictable set of actions that students learn and then practice repeatedly until they are second nature.” (Kelemanik, Lucennta, and Creighton, 2016, p.18) Number talks are one such reasoning routine. As you use Number Talks in your classroom you establish a routine of actions which the students come to expect and become familiar with. These actions form a habit and in so doing free up cognitive energy so that the brain can focus not on the routine but on the mathematics.
Think of a routine as a container. The container does not change, it is a constant, it is solid, it is reliable. You can count on the container to hold what you need it to hold. When the container is well established for students their cognitive energy can shift from focusing on the container to focusing on the contents in the container. This is the power of an established and predictable Number Talk routine.
The routine of a Number Talks has 5 main steps that students come to expect. During a Number Talk they will:
View a problem/ task.
Think and solve it.
Share their answer.
Defend their solution.
Compare and connect their reasoning to the reasoning of others.
The benefits of adding this promising practice to your instructional routines are numerous. Besides building more confident mathematicians, Number Talks increase students number sense as they require students to become more flexible and strategic thinkers. Number Talks also, increase students ability to articulate their thinking and refine their mathematical communication skills. As we work to increase our students computational fluency Number Talks have become one of THE most promising practices we can add to your professional repertoire.
If you would like to learn more about other Routines for Reasoning check out these books:
My current role as an Acting Math Coordinator provides me with opportunities to talk with many people about one of my passions…teaching and learning mathematics. Through conversations I learn from and with others, I clarify my thinking, and I uncover ways that I can offer my support. Over the past few months in this role I have found myself asked the same questions repeatedly by parents, by teachers, and by administrators. Each conversation is another opportunity to learn, so I thought I would bring the conversation here…to my blog, a place where we can take the conversation beyond the walls of the schools, and beyond the one on one setting. It is my hope that by doing this I can invite more ideas and perspectives in and learn with and from you all. So here goes…I am going to share with you my most common questions and the responses I most often give. I do this not to share the “right” answer but to invite your thinking and perspective into the response.
Why does the “new math” not require kids to know the basic facts?
Our current Saskatchewan Mathematics Curriculumdoes require that students learn the basic facts. In grade 1, grade 2 and grade 3 curriculum outcomes exist specifically for addition and subtraction. In grades 3, 4 and 5 outcomes for multiplication and division are listed. In almost all of these outcomes the process of Mental Math and Estimation is explicitly highlighted as an integral part of the understanding.
According to our curriculum “Mental mathematics is a combination of cognitive strategies that enhance flexible thinking and number sense. It is calculating mentally and reasoning about the relative size of quantities without the use of external memory aids. Mental mathematics enables students to determine answers and propose strategies without paper and pencil. It improves computational fluency and problem solving by developing efficiency, accuracy, and flexibility.”
Demonstrating understanding of addition, subtraction, multiplication, and division through mental mathematics requires that students learn the basic facts to the degree that they can calculate mentally efficiently, accurately and flexibly.
Why are students not retaining the basic facts?
To this I often respond…it depends. It depends on the student, their specific learning needs, their learning styles and their previous experiences. The answers to this question can be as varied as the number of students we teach every day.
However, I do have two working hypotheses as to why some students are having a harder time retaining the facts. My first hypothesis is that they need to continue to develop and strengthen their Number Sense. Number Sense is the foundation for mental mathematics and enhances a student’s ability to flexibly compute. As students learn their basic facts they move along a continuum from counting to reasoning to mastery. The intermediate stage of reasoning or “using what you know to figure out what you don’t know” is fueled by Number Sense. Without a developed sense of number is can be very difficult for students to reason strategically through the operations.
My second hypothesis is that students have not had enough time to practice. Every student is different, and as such every student requires different amounts of practice to move along the continuum. As teachers, we need to ensure we provide opportunities for students to practice their basic facts in ways that are targeted to their current needs, engaging, and regular. For many students it is not simply enough to practice these skills only during the month or two where they are working through the Operations Unit. Often they need regular, targeted, repeated, and short practice times that span the entire school year and beyond.
Should we help students become automatic with their math facts first then focus on Number Sense?
We should focus on them both at the same time. Strong Number Sense supports reasoning and reasoning leads to mastery. Without Number Sense we run the risk of having students memorize sequences of numbers that have no real meaning to them. Without meaning these sequences of numbers can not be effectively called upon to solve problems, communicate understandings, make connections, and logically reason through mathematical situations.
At the same time, if we do not allow students to practice their basic facts we run the risk of them not having the time they need to master them. This mastery allows basic computation to move into long term memory which in turn frees up working memory for increasingly sophisticated mathematics.
How do we support English Language Learners in our classrooms?
Once again to this question I often say… it depends. Again, each and every student is unique and bring with them specific learning needs, learning styles, and previous experiences. As teachers we need to get to know our students and their learning needs to really understand how best to support them.
That being said, I often find that students who are just learning English require support in learning and understanding the English language being used in the mathematics classroom. Supports for language development can include:
providing time for students to engage in conversations as part of a supportive community of young mathematicians.
using a Math Wall in the classroom that allows students to link the English words used to a symbol or picture of what it is.
creating Anchor Charts with students that allow them to connect the words to symbols
reading mathematics picture books that allow students to
hear mathematics being spoken and connected to visuals.
How can I help my child with math at home?
This question is complex as so much of it depends on the child and what their interests and needs are. There simply is no one size fits all response. However, I do have some ideas…each of which I think requires a blog post of their own to adequately describe and share. Some quick responses might be:
Play– find games that you can play with your child that invite them to use math. Common games can involve cards and dice that require computation…but be on the look out for opportunities to use math in other ways too. Games that require logical reasoning and problem solving are also mathematics and can help your child see math as more than just computation.
Talk– find ways to talk about mathematics as it exists in your world. Look for examples of math in grocery stores, as you are driving in the car, on television, and in your kitchen. If you find yourself using or seeing math share that with your child and start a conversation. These conversations can help them see that math is alive in our world and is useful.
Value– if you value mathematics so will your child. Share with your child that math is a valuable and important subject for them to learn AND that you will support them along their learning journey.
So there you have it. Some common questions and my common responses. Now I would like to invite you into the conversation. What do you think? What are your common questions? What would you add to, or change in my responses?
I look forward to learning with you as we all work to support teaching and learning in mathematics.