CCRS Quarterly Meeting # 1 CCRS Quarterly Meeting # 1 Promoting Discourse in the Mathematics Classroom

CCRS Quarterly Meeting # 1CCRS Quarterly Meeting # 1

Promoting Discourse in the Mathematics Classroom

http://alex.state.al.us/ccrs/

Alabama Quality Teaching Standards (AQTS)

Standard 1: Content Knowledge

Standard 2: Teaching and Learning

Standard 3: Literacy

Standard 4: Diversity

Standard 5: Professionalism

As professionals, we should take ownership of our professional

growth and continued improvement

Year One Reflection

• What have you changed about your practice in response to implementing the College-and Career-Ready Math Standards ?

• What are two priorities related to implementation of the CCRS Math you have identified for 2013-2014?

• How has incorporating the College-and-Career-Ready Math Standards into your classroom culture caused your students to learn and behave differently?

The discourse of a classroom – the ways of representing, thinking, talking, agreeing and disagreeing – is central to what students learn about mathematics as a domain of human inquiry with characteristic ways of knowing.

NCTM 2000

Outcomes

Participants will:

•Discuss and define student discourse

Discourse

What is Discourse?

• How do you define student discourse?

• How does discourse encourage reasoning and sense making in your classroom?

Unlocking Engagement Through Mathematical

Discourse

Making the Case for Meaningful Discourse

“Mathematics is not about remembering and applying a set of procedures but about developing understanding and explaining the processes used to arrive at solutions – the Mathematical Practices in action.”

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Making the Case for Meaningful Discourse: Standards for Mathematical Practice

• Standard 1: Explain the meaning and structure of a problem and restate it in their words

• Standard 2: Explain their mathematical thinking

• Standard 3: Habitually ask “why” – Question and problem-pose– Develop questioning

strategies ...– Justify their conclusions,

communicate them to others and respond to the arguments of others

– Listen to the reasoning of others

– Compare arguments

• Standard 4: Communicate their model and analyze the models of their peers

• Standard 6: Communicate their understanding of mathematics to others

– Use clear definitions and state the meaning of the symbols they choose

• Standard 7: ...describe a pattern orally...

– Apply and discuss properties

Possesses the knowledge and skills needed to enroll and succeed in credit-bearing, first-year courses at a two- or four-year college, trade school, technical school, without

the need for remediation.

HOW IS A PREPARED GRADUATE DEFINED? Possesses the

ability to apply core academic skills to real-world situations through collaboration with peers in problem solving, precision, and punctuality in delivery of a product, and has a desire to be a life-long learner.14

Purposeful Discourse

• Through mathematical discourse in the classroom, teachers “empower their students to engage in , understand and own the mathematics they study.”

(Eisenman, Promoting Purposeful Discourse, 2009)

Outcomes

Participants will:

•Discuss and define student discourse

Exit Activity

LUNCH

Outcomes

Participants will:

•Identify advantages of planning lessons that focus on facilitating carefully constructed student engaged discourse.

•Describe practices that teachers can learn in order to facilitate discourse more effectively.

Through the LensUse the handout to make notes as you watch the video.

Observation LensStandard for Mathematical Practice

that was Supported

Teacher’s Questions

Student Discussions

Classroom Culture

Envision a Discourse RichMath Class

• How does teacher best practice produce student math practices?

• What are you going to do to produce student discourse in your classroom?

Figure 5.5 Teacher and Student Roles in Classroom DiscourseTeacher’s Role Student’s Role

Poses questions and tasks that elicit, engage, and challenge each student’s thinking.

Listen to, respond to, and question the teacher and one another.

Listens carefully to student’s ideas. Use a variety of tools to reason, make connections, solve problems, and communicate.

Asks students to clarify and justify their ideas orally and in writing.

Initiate problems and questions.

Decides which of the ideas students bring up to pursue in depth.

Make conjectures and present problems.

Decides when and how to attach math notation or language to students’ ideas.

Explore examples and counterexamples to investigate conjectures.

Decide when to provide information, when to clarify an issue, when to model, when to lead, and when to let different students struggle with a problem.

Try to convince themselves and one another of the validity of particular representations, solutions, conjectures, and answers.

Monitors student participation in discussions and decides when and how to encourage each student to participate.

Rely on mathematical evidence and argument to determine validity.

Source: Adapted from information in Professional Standards for Teaching Mathematics, by the National Council of Teachers of Mathematics, 1991, Reston, VA; Author.

Kenney, Hancewicz, Heuer, Metsisto, Tuttle(2005).

What are the practices that will promote student discourse?

Five Practices for Orchestrating Productive Mathematical

Discussions•

0. Setting Goals and Selecting Tasks

1. Anticipating (e.g., Fernandez & Yoshida, 2004; Schoenfeld, 1998)

2. Monitoring (e.g., Hodge & Cobb, 2003; Nelson, 2001; Shifter, 2001)

3. Selecting (e.g., Lampert, 2001; Stigler & Hiebert, 1999)

4. Sequencing (e.g., Schoenfeld, 1998)

5. Connecting (e.g., Ball, 2001; Brendehur & Frykholm, 2000)

The Five Practices (+)

Purpose of the Five Practices

To make student-centered instruction more manageable by moderating the degree of improvisation required by the teacher during a discussion.

Thinking Through a Lesson Protocol (TTLP) Planning Template

Leaves and Caterpillar Task

A fourth-grade class needs 5 leaves each day to feed its 2 caterpillars. How many leaves would they need each day for 12 caterpillars?

Use drawings, words, or numbers to show how you got your answer.

• Solve the task in as many ways as you can, and consider other approaches that you think students might use to solve it.

• Identify errors or misconceptions that you would expect to emerge as students work on this task.

Mathematical Goal

I want students to:

• recognize that the relationship between caterpillars and leaves is multiplicative.

Students might:

• make tables showing the relationship of leaves to caterpillars

• draw pictures

• write explanations

• count by 1’s or 5’s

• use unit rate

• use scaling up

• multiply

Mathematical Discourse

“Teachers need to develop a range of ways of interacting with and engaging students as they work on tasks and share their thinking with other students. This includes having a repertoire of specific kinds of questions that can push students’ thinking toward core mathematical ideas as well as methods for holding students accountable to rigorous, discipline-based norms for communicating their thinking and reasoning.”

(Smith and Stein, 2011)

Why These Five Practices Are Likely to Help

• Provides teachers with more control

• Over the content that is discussed

• Over teaching moves: not everything improvisation

• Provides teachers with more time

• To diagnose students’ thinking

• To plan questions and other instructional moves

• Provides a reliable process for teachers to gradually

improve their lessons over time

Outcomes

Participants will:

•Identify advantages of planning lessons that focus on facilitating carefully constructed student engaged discourse.

•Describe practices that teachers can learn in order to facilitate discourse more effectively.

Resources Related to the Five Practices

Kenney, J.M., Hancewicz, E., Heuer, L., Metsisto, D., Tuttle, C. (2005). Literacy Strategies for Improving Mathematics Instruction. Alexandria, VA: Association for Supervision and Curriculum Development.

Smith, M. S., & Stein, M. K. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teachers of Mathematics and Thousand Oaks, CA: Corwin Press.

Smith, M.S., Hughes, E.K., & Engle, R.A., & Stein, M.K. (2009). Orchestrating discussions. Mathematics Teaching in the Middle School, 14 (9), 549-556.