Bridging Math PracticesWelcome back!June 24, 2014

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Bridging Math PracticesJune 24, 2014

Pedagogy Day 2: Connecting Classroom Discourse & Student Reasoning

Objectives• Content Objectives: We will …

– grapple with connections of student reasoning to mathematical practices and classroom discourse

• Language Objectives: We will …– increase understanding & application of classroom

discourse approaches (e.g., “funneling & focusing”)

– use everyday and academic language to support content & language objectives

• CCCSM MP 3 – Construct viable arguments and critique the reasoning of others. Begins, “Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments …”

How do mathematical practices relate to student

reasoning?

CCSSM MP3 Strategic Communication needed …• CCCSM MP 1 – Make sense of problems and persevere in

solving them. Begins, “Mathematically proficient students start by explaining to themselves the meaning of a problem …”

• CCCSM MP 3 – Construct viable arguments and critique the reasoning of others. Begins, “Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments …”

• CCCSM MP 6 – Attend to Precision. Begins, “Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning…”

• How do our approaches to math classroom discourse impact student reasoning & conceptual understanding?

Mathematical Discourse to Promote Student Reasoning

Two DialoguesExcerpt #1:

Brownies ProblemTeacher: Ms. Carter

Excerpt #2:Simplifying FractionsTeacher: Ms. Reardon

• Please read the dialogues & jot down notes.• What do you notice? How do teacher questions (&

other verbal moves) impact student reasoning? • We will discuss these in a few minutes.

2112

= ?

Two Dialogues

• Please share some of your observations ...

Considering other approaches to classroom

discourse…We will reconsider these dialogues as we discuss approaches to math classroom discourse …

For example, you may have heard of Talk Moves

Revoicing: (Teacher) restating students’ ideas

Repeating: Asking students to restate someone else’s reasoning

Reasoning: Asking students to apply their reasoning to someone else’s

Adding On: Prompting students for further participation.

Waiting: Using wait time. (Chapin, O'Connor & Anderson, 2009) See handout for

more info

Funneling & FocusingWays of approaching classroom discourse…

Herbel-Eisenmann, B. A. & Breyfogle, M. L. (2005). Questioning our patterns of questioning. Mathematics teaching in the middle school, 10(9), 484-489.

Funneling & Focusing • Funneling: When teacher asks a series of

questions that guide the students to a procedure or to a desired end.

• Focusing: A focusing-interaction patterns requires the teacher to listen to students’ responses and guide them based on what the students are thinking rather than how the teacher would solve the problem.

Herbel-Eisenmann, B. A. & Breyfogle, M. L. (2005).

Funneling & Focusing • As we read/listen to example dialogues, notice

the teachers’ approaches related to classroom discourse …

• See article in your binder

Funneling & Focusing• Think back to the dialogue from Ms. Carter’s

and Ms. Reardon’s classrooms• How might these relate to funneling &

focusing?

Shifting talk in a math classroom

• Revisit Ms. Reardon’s class.• Ms. Reardon heard you talking about

funneling & focusing. She asked if you could give her some suggestions on shifting her practice away from funneling more toward focusing. Ms. Reardon recorded some classroom talk for you to consider…

• (see previous handout)

Helping Ms. Reardon

• Work with a partner (or two).• Choose one or more of Ms. Reardon’s verbal

moves and re-write to include focusing questions/verbal moves (rather than funneling questions/verbal moves)

• Keep your ideas in mind as we move forward …

Question worded using students’ phrasing

Notes representing students’ ideas

(These include correct ideas as well as misconceptions. Also, the number of “talk idea” sections used will vary according to the lesson, student contributions, and teacher’s

decisions about how to group ideas.)

Summary of the mathematically valid conclusion agreed upon by the class

We Understand

Think

Talk Idea Talk IdeaTalk Idea

From Casa, T. (2013). Capturing Thinking on the Talk Frame. Teaching Children Mathematics. 19(8), 516-523.

Talk Frame Mini-Lesson

Watch for discourse approaches and tools during this mini-lesson … as well as

the implementation of the routine

Recall from yesterday: A pedagogy of mathematical reasoning

New question(s)

Generate ideas

Elicit and Publicize ideas

Press on and develop ideas collaboratively

Solidify and/or refine new meanings

Talk Frame Mini Lesson

• Teachers working with grades 2-5 (including coaches) stay here

• Teachers working with grades 6-high school go with Megan to Gentry 101

Talk Frame: Your Turn

• You will work in a group of 4 (same as your protocol group) to develop ideas for a talk frame mini-lesson (~20 min. to plan)

• Tomorrow you will then teach/share this idea with another group (~20 min. for each group to teach/share)

• See details in your handouts.