Overview

Session Focus

In this session you will watch, read, and think about how to support math talk as students work alone, in partners, small groups and with the whole class.

Math talk is central to students’ mathematical learning. They communicate their thinking and listen to others as they share their thinking – in pairs, small groups or with the whole class. The teacher carefully plans activities grounded in mathematical situations, elicits different approaches (strategies) to solutions and the use of representations to find a solution, demonstrate thinking or uncover common mistakes or misconceptions. Small group and whole class discussions are focused on key mathematical ideas that will move students’ thinking, reasoning and the ability to communicate their reasoning forward.

Getting Started: Establishing a Community for Productive Talk

In Session 1 the focus was on ways to set up the physical classroom and establish a safe learning community. We now concentrate on aspects that will result in productive math talk: interactive discussions where students engage in sharing their ideas and reasoning and actively listen to and make connections as others share their thinking.

Setting Productive Talk Norms and Expectations

Students need support as they engage in math talk. This can be accomplished by planning time during a lesson for the class to discuss, model and reflect on…

  • what productive math talk looks like and sounds like when students work in pairs, small groups and as a whole group.
  • ways to actively listen and add to others’ ideas
  • how to respectfully disagree with a solution and justify why
  • reflective questions and statements that focus on the mathematics while playing a game or sharing a strategy

Reflective learners assimilate new learning, relate it to what they already know, adapt it for their own purposes, and translate thought into action. Over time, they develop their creativity, their ability to think critically about information and ideas, and their metacognitive ability (that is, their ability to think about their own thinking).”

Effective Pedagogy, NZ Curriculum p. 34


Read: Instructional Practices For Productive Math Talk

Reflection Questions

From the Field

As teachers and students engage together in each other’s mathematical ideas, they create not only opportunities to enrich their mathematical understanding, but they also create opportunities to learn how to learn in ways that are generative. Teachers learn about the content, about the development of student thinking, about their students as mathematics learners and people, and about how to support their students. The students, while learning mathematical content, learn how to listen to another, how to ask a question that moves the mathematics forward, and how to position their ideas in relation to others’ ideas. The interactions among the teacher and students support students to learn to persevere as they communicate with each other and productively struggle to understand and articulate each other’s ideas.” p.145

Franke, M., Turrou, A.C., Webb, N., Ing, M, Wong, J., Shim, N, Fernandez, C. Student engagement in each other’s mathematical ideas: The role of teacher invitation and support moves. Elementary School Journal, p. 145, September 2015

Readings

Cases

Additional Resources

Activity 1: Discussing Mathematical Ideas

In this activity, you will watch, read, and think about how to support discourse and math talk in the classroom. You will see students talking and teachers facilitating math talk.

Read: Discussing Mathematical Ideas

Gilberto's Stickers

Solve the following problem.

Gilberto had 81 stickers.

Then he bought some more and now he has 312 stickers.

How many did he buy?

If you thought about this problem as addition, try using subtraction to solve it. If you thought about it as subtraction, use addition to solve it.

Video

Next you will view students solving the Gilberto problem. Click on the link below and scroll down the page to the first video link.

Use your notebook to make notes about what and who you heard talking in this clip, and what that means for you in your classroom/role.


Children’s Mathematics: Engaging with each other’s ideas


Revisit the video with a focus on the talk moves that you see the teacher making.

Record what you noticed about how the teacher facilitated the discussion in your notebook.

Activity 2: Math Talk Cases

In this activity you will read 5 cases written by teachers at different grade levels. They share what they do in their classroom to support students’ math talk. You will respond to questions for each case in the Math Talk Case Forum

Notebook

Record your responses to the questions located at the end of each case in your notebook.

From the Field

Communication is an essential part of mathematics and mathematics education. It is a way of sharing ideas and clarifying understanding. Through communication, ideas become objects of reflection, refinement, discussion and amendment. The communication process also helps build meaning and permanence for ideas and make them public. When students are challenged to think and reason about mathematics to communicate the results of their thinking to others orally and in writing, they learn to be clear and convincing. Listening to others’ explanations gives students opportunities to develop their own understandings.”

National Council of Teachers of Mathematics [NCTM} 2000, 60

Activity 3: Whole Group Discussions

classroom

In this activity you will consider key components in planning productive discussions, and watch Kindergarten, first and fifth grade teachers facilitate a whole group discussion. You will read and listen to authors Elham Kazemi and Allison Hintz share whole group discussion structures that target different learning goals.

In her book My Kids Can, Judy Storeygard says making math explicit is

classroom

to make visible the assumptions and processes involved in problem solving that lead to successful solution strategies. Teachers who do this kind of explicit teaching create a learning environment where students learn about themselves as learners and develop strategies for success.”

(Assera, 2006; Judy Storeygard (2009) My Kids Can, Heinemann. p. 1).

Watch each of the following classroom videos two times.

  • The first time you watch, focus on the students.
  • The second time, focus on the teacher.

Record your observations about the students and teacher for each video clip in your notebook.

  • What did you notice about the students during the discussion?
  • List what the teacher did to make math explicit to the students.

Is a Book a Square? – Kindergarten

Watch as this Kindergarten teacher facilitates a discussion about the attributes of a square.

Record your observations about the students and teacher for each video clip in your notebook.

Today’s Number – 1st Grade

This 1st grade class is doing a routine called Today’s Number. The students have written several expressions that equal 16 in their notebooks. In this clip you will watch the students take turns sharing their expressions. Notice how the teacher facilitates the discussion.

Defining a Triangle – 5th Grade

A classroom culture based student mathematical talk encourages students to express their uncertainties and confusions.

Finding a balance between giving information and listening to a student’s thinking can be challenging.”

Talking Math Video, Supporting Classroom Discourse. Heinemann. 1993

In this clip you will watch a discussion about triangle attributes. One student shares and explains why she does not think one of the shapes is a triangle. Once she shares, it’s obvious others are also uncertain if some of the figures are triangles. Notice how the teacher facilitates this discussion.

Triangle Video

Michaela and her classmates know the basic definition of a triangle but are still developing a definition that includes all kinds of triangles, especially scalene triangles. Their experiences with different types of triangles and how they can be positioned are limited.

The second paragraph in the following quote highlights the difference between knowing and understanding a concept or term.

It is important to note that, in mathematics, there are some things that can only be told. Social conventions such as the name of a six-sided shape, which numerals represent which quantities (5 is the symbol for this many: *****), or what the plus (+) and equals (=) sign stand for, cannot be "discovered." We as a society agree upon these conventions. In order for students to learn that there are 12 inches in a foot, or the fact that a quarter equals 25¢, someone must tell them.

It is also important to note that knowing the name of, say, a quarter, does not mean that one understands that it is worth 25¢ that is equivalent to 25 pennies (or 2 dimes and a nickel, or a dime and 3 nickels); that 4 of them make a dollar, etc.”

This note appeared in an Ask an Author Essay on the CESAME site, Northeastern University and the Educational Alliance, Brown University.

Sam and Charlie

Think about your Sam or Charlie in your journal – how are you supporting their math talk?

From the Field

Intentional Talk: How to Structure and Lead Productive Mathematical Discussions.

Whole class discussions need to be purposeful and productive. In their book, Intentional Talk: How to Structure and Lead Productive Mathematical Discussions, Kazemi and Hintz have identified six discussions structures to target different learning needs.


Listen as they describe the different discussion types: Open Strategy Share, Compare and Connect; Why? Let’s Justify, What’s the Best and Why? Define and Clarify, Troubleshoot and Revise.

Leading Different Kinds of Mathematical Discussions


Discussion

In this session you have had a look into several classrooms as students worked and communicated their thinking. Share the following…

  • 3 things you learned about productive discussions,
  • 2 instructional moves you plan to implement, and
  • 1 question you are wondering about

Go to the Forum

Notebook

Complete the Session 2 Notebook page using the indicated prompts.

In the final field of your notebook, reflect on the key take-aways from this session for your own learning and record ideas that you will implement to support math learning.

Key Learnings

  • Productive mathematical discussions need to be structured around a goal
  • Whole group discussions are most successful when the strategies or work being discussed are scaffolded so all students have entry points and challenges
  • Independent group work is most effective when the groups are well formed
  • Discussions provide students opportunities to:
    • articulate their mathematical ideas
    • share different approaches to solving a problem
    • identify and investigate what they don’t understand
    • analyze why a solution works or how it is flawed
    • pose conjectures and identify evidence to support them
    • collaborate to build ideas or solve problems
    • develop mathematical language
    • use representations to describe mathematical relationships
    • compare and connect students’ various ideas, representations, and solutions
    • learn to consider and question each other’s ideas