Number Talks
Quick Images
Routine: Quick Images
Subitizing seeing groups of numbers without counting
Multiple ways to add numbers (commutative and associative properties)
• Groups of (i.e. multiplication)
• Making friendly numbers to add
• Using doubles
• Making tens (using ten frame cards)
• Beginning of the year can be used to teach students how to turn and talk and how to use words to describe their thinking
How did you know that?
How did you see it? •
What did you see? •
Did anyone see it a different way? Teacher holds up card for 2 to 3 seconds. Teacher asks student to hold up thumb on their chest when they have an answer. Teacher then has students share answers. Teacher can record their thinking as they share
Subitizing seeing groups of numbers without counting
Multiple ways to add numbers (commutative and associative properties)
• Groups of (i.e. multiplication)
• Making friendly numbers to add
• Using doubles
• Making tens (using ten frame cards)
• Beginning of the year can be used to teach students how to turn and talk and how to use words to describe their thinking
How did you know that?
How did you see it? •
What did you see? •
Did anyone see it a different way? Teacher holds up card for 2 to 3 seconds. Teacher asks student to hold up thumb on their chest when they have an answer. Teacher then has students share answers. Teacher can record their thinking as they share
Number Strings
4 x 25 =
6 x 25 =
12 x 25 =
Children develop stronger number sense if allowed to explore strategies when computing, instead of being tied down to rigid procedures such as algorithms.
The goal is for children not to be bound to a rigid procedure such as an algorithm that is used regardless of the problem, but rather, to look to the numbers to decide which strategy to use.
Dibrienza, J. & Gary Shevell, (1998). Number Strings: Developing Computational Efficiency in a Constructivist Classroom.
6 x 25 =
12 x 25 =
Children develop stronger number sense if allowed to explore strategies when computing, instead of being tied down to rigid procedures such as algorithms.
The goal is for children not to be bound to a rigid procedure such as an algorithm that is used regardless of the problem, but rather, to look to the numbers to decide which strategy to use.
Dibrienza, J. & Gary Shevell, (1998). Number Strings: Developing Computational Efficiency in a Constructivist Classroom.
Planning a lesson....
Ground Rules for Respectful Talk and Equitable Participation
First and foremost the teacher must establish ground rules for respectful and courteous talk. You will not be able to use successfully the talk moves described previously unless you have established a classroom culture in which students listen to one another with respect. If students are afraid that their ideas will be ridiculed, they will not talk freely, no matter what inducements you offer. They must feel that their classroom is a safe place to express their thoughts. Therefore, your first steps in creating the conditions for productive classroom talk must involve setting up some clear ground rules for interaction.
The ground rules must center on each student’s obligation to treat one another with respect. No name-calling or derogatory noises or remarks are ever allowed. There must be clear consequences for violation of these rules.
You may need to remind students of these rules every day until they become a routine part of your classroom culture.
As you establish the conditions for respectful and courteous talk, you will also need to set the conditions for full participation: all students must have the opportunity to engage in productive talk about mathematics. This means that you must make sure of three things:
- that every student is listening to what others say,
- that every student can hear what others say, and
- that every student may participate by speaking out at some point.
As part of your ground rules for respectful and courteous talk, you no doubt will have put in place a rule that obligates students to listen attentively as others talk. This is respectful behavior, but just as important, it is pragmatic behavior. It enables students to participate in the ongoing talk. If they do not know what was just said, they cannot possibly build on it
Principle 1. Establish and maintain a respectful, supportive environment.
- A big part of the preparation for using talk in mathematics involves putting in place classroom norms that will ensure a safe and supportive place for people to talk about their thinking
- Neither students nor teachers will engage in productive talk about mathematics if they are afraid that they will be laughed at, “dissed,” or somehow made to feel stupid.
- Emphasize the positive aspects of respectful discourse—the good thinking and learning that can emerge in a civil and supportive environment
- Make clear to students that this respectful discourse is not optional, and that there are sanctions for failing to maintain the norms of respect that you set up.
- Students are obligated to try very hard to make their thinking available to others and communicate their thoughts as clearly as they can.
- They don’t give up as easily, and they begin to pursue the consequences of their own ideas and those of others.
Principle 2. Focus talk on the mathematics.
As you establish norms for respectful discourse, you should simultaneously make sure that classroom talk is focused on the mathematical content and reasoning that is relevant to the lesson.
- Be sure to tell students that the role of talk in math class is to help them understand the mathematics they are studying, and that a thorough and solid understanding for everyone is the goal.
- To make sure that you and the students maintain this focus, you need to prepare lessons carefully, considering ahead of time how the mathematical topics and procedures might play out in the classroom talk.
- A focus on talk can strengthen not just your students’ understanding, but your own as well.
Principle 3. Provide for equitable participation in classroom talk.
All students can benefit from the kinds of discourse practices we are describing, not just those who are actively speaking, but also those who are listening. Yet it’s important to think carefully about equitable participation. This has two aspects: how to make it possible for all students to participate actively in the talk from time to time, and how to make certain that all students are listening actively all of the time.
- If a student rarely has an opportunity to talk, that student does not have full access to participation.
- If a student can participate in the talk but is not listened to seriously, again, there is a problem with equitable participation.
- If a student does not listen, that student does not have access to participation.
One of the core obligations of teaching is to provide equal access to learning for all students. However, in every css there are challenges to achieving this goal. Some students are eager to discuss mathematics and feel confident doing so. Others, however, may seem diffident, reluctant to participate, even resentful of being asked to talk out loud. Still others may seem not to understand, or may understand so well that you fear they will be bored as others talk. Dealing with the variety of personalities, knowledge, and attitudes that one finds in any classroom is always a challenge. While this challenge will not disappear when you use talk in your classroom, carefully orchestrated talk may help.
The traditional method of calling on students (whether or not they have raised their hands) gives the teacher maximum control of who talks in the conversation.
Some teachers augment this with a variety of methods of assigning turns. For example, some teachers institute a “gender rule” for taking turns, in which boys and girls alternate. In a class where girls don’t participate as actively as boys, or vice versa, this rule supports girls (or boys) by making every other turn in the talk an opening for them.
Some teachers allow a student to nominate the next speaker after he or she has finished speaking. This can be useful when there are one or two students who tend to monopolize the floor. Some teachers institute a reward system whereby students receive points for volunteering a question or an explanation. (There should be a limit to the number of points that can be gained this way, as otherwise the monopolizers will be encouraged.) Each classroom and school has its own set of norms for taking turns, but we encourage you to think creatively about this important aspect of setting up the conditions for equal participation in productive talk.
Here is an example of some ground rules for talk used in a successful New Zealand classroom: