Overview

Session Focus

In this session you will:

  • Goal 1.
  • Goal 2.
  • Goal 3.
  • Goal 4.
  • …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

Video

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.

The students in this clip have solved and shared their strategies on the whiteboard. Watch as they try to make sense of strategies. Notice how they are engaging with each other’s ideas.

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.

On occasion, you may find that certain applications or websites in this course may work differently in different browsers. We recommend that you become familiar with how to use an alternate web browser, in addition to the one that is included on the computer you primarily use (often Internet Explorer for PCs, and Safari for Macs).

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 each case’s questions 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

Math Learning in the Classroom

In this final Orientation activity we share our beliefs about teaching and learning mathematics and the classrooms in which these happen. You will reflect on your personal elementary school math learning experiences and how they influence your teaching.

The goal of all math teaching and learning is to promote a deep understanding of mathematics and develop mathematically proficient students who can think, reason, model and solve problems.

Karen Economopoulos
NCSM 2013

Supporting the range of learners in math class involves

Teachers

  • … teachers need to deepen their own knowledge of mathematics, pedagogy and student learning
  • … teachers need to have a clear understanding of their mathematical goals within their grade level and maintain a clear, focused, and coherent agenda for mathematics teaching
  • … teachers understand that to differentiate learning, student ideas need to be front and center

Students

  • … students have mathematical ideas
  • … students build on the ideas they already have and learn about new mathematics they have never encountered in an environment that focuses on sense making

Learning Environment

  • … mathematical practices, such as reasoning, perseverance, and communicating about mathematical ideas, are integral to the learning
  • … the classroom environment allows all students to share ideas and listen to and learn from each other
  • … mathematics classrooms need to be filled with rich math tasks that include space for learning as well as space for struggle and growth
  • … mistakes, unrefined strategies and ‘kid language’ are all part of the learning process
  • … teachers and students have a growth mindset

Personal Math Learning Experiences

Reflect back on your own elementary school math learning experiences.
Focus on the role of your teachers, you as a student and the learning environment.

In what ways have those experiences influenced how you support your students’ math learning?

Click here to share your experiences. Be sure to check back to what your fellow participants have shared. [forum or notebook? not clear what is needed “ETLO Link to Personal Math Learning Experience Forum”]

Discussion

Watch the tutorial Posting and Replying to Messages in the Moodle Discussion Board (Transcript) [needs update for moodle 2.6]. Then introduce yourself to your online colleagues by creating a new thread in the discussion board. Give your thread a descriptive title and include the following:

  • Your name, your role in your school, and your motivation for taking this course;
  • Two or three facts about yourself so that we can get to know you better; and
  • A photo of yourself (optional).

After you post and respond to some of your colleagues’ introductions, be sure to check back often to continue the conversations.

Go to the Forum

Notebook

Personal Math Learning Experiences

Reflect back on your own elementary school math learning experiences.
Focus on the role of your teachers, you as a student and the learning environment.

In what ways have those experiences influenced how you support your students’ math learning?

Be sure to check back to what your fellow participants have shared.