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1 © Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org 1 © Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org Vanessa Cerrahoglu Orange County Office of Education Sadie Estrella Illustrative Mathematics Craig Schneider, PhD Santa Barbara Unified School District Mathematical Language Routines Developing Students’ Voices and Sense Making
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Page 1: Illustrative Mathematics | K-12 Math - Mathematical Language … · 2020. 10. 21. · © Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org 2 Let’s get to know

1© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org 1© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Vanessa CerrahogluOrange County

Office of Education

Sadie EstrellaIllustrative

Mathematics

Craig Schneider, PhDSanta Barbara

Unified School District

Mathematical Language RoutinesDeveloping Students’ Voices and Sense Making

Page 2: Illustrative Mathematics | K-12 Math - Mathematical Language … · 2020. 10. 21. · © Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org 2 Let’s get to know

2© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Let’s get to know each other!Who teaches or works with teachers…● PK - 2?

● 3 - 5?

● 6 - 8?

● 9 - 12?

● Post secondary?

Why are you here?

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3© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Learning Goals

➢ Understand that learning mathematics is a language-demanding activity for all students

➢ Understand how MLRs support mathematics sense-making and language development

➢ Engage in and prepare MLRs

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4© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

A company claims that their new bottle holds 25% more laundry soap. If their original container held 53 fluid ounces of soap, how much does the new container hold?

Let’s Do Math

Handout 1Source: Illustrative Mathematics 6-8 Math (Grade 7 Unit 4, Lesson 7, Cool Down)

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Language demands?

Prompts:

● How did you use language to engage in this task?

● How did you make your thinking visible?

A company claims that their new bottle holds 25% more laundry soap. If their original container held 53 fluid ounces of soap, how much does the new container hold?

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6© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

(Adapted from Aguirre & Bunch, 2012)

Mathematical Language DemandsIt matters for all students

REPRESENTING

LISTENING SPEAKING

WRITINGREADING

CONVERSING

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7© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

UL/SCALE: Mathematical Language Routines

1. Stronger and Clearer Each Time

2. Collect and Display

3. Clarify, Critique, Correct

4. Information Gap

5. Co-Craft Questions

6. Three Reads

7. Compare and Connect

8. Discussion Supports

MLRs are structured but adaptable formats

for amplifying, assessing, and

developing students' language.

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8© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

What are instructional routines?

“Instructional routines are specific

and repeatable designs for learning

that support both the teacher and

students in the classroom.”

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9© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Let’s Do a Mathematical Language Routine

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10© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Mathematical Language Routine:Clarify, Critique, Correct

PROMPT partners to:● Clarify: Describe what the

author did● Critique: Analyze the author’s

reasoning● Correct: Improve the

responseHandout 2

A company claims that their new bottle holds 25% more laundry soap. If their original container held 60 fluid ounces of soap, how much does the new container hold?

Modified 7th Grade Task

Incomplete Response

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11© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Clarify, Critique, CorrectPartners Clarify (1 minute)● “I notice … “ “What do you notice?”● “I wonder…” “What do you wonder?”

Handout 2

Individuals Correct (2 minutes)● “I can build onto this response by …”● “What else could I do/show?”

Partners Critique (2 minutes)

● “This reasoning is strong because …”

● “What might make this reasoning stronger is …”

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Clarify

“We noticed … “ “We wondered…”

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Critique

“This reasoning is strong because …”

“What might make this reasoning stronger is …”

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14© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Initial Draft

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Revised Response

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16© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Unpack the Routine

How does “Clarify, Critique, Correct”

● support language demands of the task?

● support development of mathematical understanding?

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17© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

In this routine:

● What is the teacher doing?

● What are students doing?

Handout 3

Unpack the Routine

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Purpose: To give students a piece of mathematical writing that is not their own to analyze, reflect on, and develop. The intent is to prompt student reflection with an incorrect or incomplete written argument, and for students to improve upon the written work by clarifying thinking, offering critique and then correcting the initial response.

Mathematical Language Routine: Clarify, Critique, Correct

Handout 4

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Clarify, Critique, Correct

Handout 4

1. PRESENT a partial or broken argument, explanation, or solution method.

2. PROMPT partners to:Clarify: the reasoning in the initial responseCritique: Analyze the response in light of partner’s own understanding of the problemCorrect: Partners work collaboratively / individually to improve the initial response

3. SHARE: Partners share out their drafts of an improved response and refine as needed during whole group discussion.

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20© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

1. Support sense-making

2. Optimize output

3. Cultivate conversation

4. Maximize linguistic and cognitive meta-awareness

A Partnership

Design PrinciplesTo Promote

Mathematical LanguageUse and Development

in Curriculum and Instruction

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21© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Connecting to the UL/SCALE Guiding Principles

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22© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Students are Engaged in Mathematical Language Development When...

Extending discourse

Discussing complex problems

Giving explanations

Constructing arguments

Making conjectures

Reading complex sentences

Stating assumptions

Using vocabulary in context

MATH LANGUAGE

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23© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Routines in the Mathematics Lessons Support Students’...

MathematicalSenseMaking

Mathematical Language

Development

Simultaneously

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24© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

A Double Challenge for English Learners

“(The English learner must) learn how to effectively

employ a new language in an academic setting, while

learning through that language the knowledge and

skills in multiple disciplines.”

(UL/SCALE 2014)

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Let’s Do Another Mathematical Language

Routine

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What do you notice? What do you wonder?

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Pick 2 equations. Describe how the two equations are related

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What do you notice? What do you wonder?

1

2

3

4

Mathematical Routine:Stronger and Clearer Each Time

1. Pre-write2. Think time3. Pair share4. Repeat with new partners5. Revise pre-write

Handout 5

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29© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Pick 2 equations. Describe how the two equations are related.

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30© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Initial Draft

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31© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Revised Response

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32© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Unpack the Routine

How does “Stronger and Clearer Each Time”

● support language demands of the task?

● support development of mathematical understanding?

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33© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Unpack the Routine

In this routine:

● What is the teacher doing?

● What are students doing?

Handout 3

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34© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Purpose: To provide a structured and interactive opportunity for students to revise and refine both their ideas and their verbal and written output (Zwiers, 2014). Pairs borrow and use the language, ideas, and justifications each time. Responses become:● Stronger (often longer) with better justifications and examples,● Clearer with more precise terms and linked, organized,

complete sentences.

Mathematical Language Routine: Stronger and Clearer Each Time

Handout 6

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Language Routines in General

After experiencing both routines:● How is learning mathematics a language

demanding activity for all students?

● How do these routines support mathematical sense making and language development simultaneously?

● How do these routines empower students?

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Let’s Prepare a Mathematical Language Routine

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37© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Implementing Mathematical Language Routines

Which of these routines will I try with my students?● 3 Reads

● Clarify, Critique, Correct

● Stronger and Clearer Each Time

I want to try ____ because...

Handout 7

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38© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Implementing Mathematical Language Routines

As you prepare to develop your own students’ voices and sense making, what are some things you might consider as you prepare to facilitate the routine with your students?

Handout 7

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Consider Students’ (and your) Cognitive Load

X

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40© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

UL/SCALE: Mathematical Language Routines

1. Stronger and Clearer Each Time

2. Collect and Display

3. Clarify, Critique, Correct

4. Information Gap

5. Co-Craft Questions

6. Three Reads

7. Compare and Connect

8. Discussion Supports

MLRs are structured but adaptable

formats for amplifying, assessing,

and developing students' language.

Page 41: Illustrative Mathematics | K-12 Math - Mathematical Language … · 2020. 10. 21. · © Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org 2 Let’s get to know

Available for fall implementation

Available Version 3.1415 available for fall

implementation including Spanish translations and EL supports for teachers

Coming July 2021

Visit illustrativemathematics.org to learn more.

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THANK YOU@IllustrateMath

#LearnWithIM

Illustrative Mathematics

© Illustrative Mathematics 2019 #LearnWithIM illustrativemathematics.org

Vanessa CerrahogluOrange County Office of Education

[email protected]

For Exploring Mathematical Language Routines

Sadie EstrellaIllustrative Mathematics

[email protected]

Craig Schneider, PhDSanta Barbara Unified

[email protected]


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