mathlanguageroutines presentation nabe 2019 1€¦ · 1. stronger and clearer each time 2. collect...

www.corelearn.com© 2018 Consortium on Reaching Excellence in Education, Inc.

Implementing

Mathematical Language Routines

from Simple Adaptations to Focused Activities

NABE 2019

Dean BallardDirector of Mathematics

2www.corelearn.com

© 2018 Consortium on Reaching Excellence in Education, Inc.

Presenter

Dean BallardDirector of Mathematics, CORE

[email protected]

www.corelearn.com

Booth 321

mailto:[email protected]

http://www.corelearn.com/

www.corelearn.com33www.corelearn.com


Revisions to presentation

• Include sentence frames someplace

• In handout, include handout showing the Guess My Graph (Every graph tells a story) page with samples of graphs so folks can see the idea.



Essential Questions for Today

• What are Math Language Routines and why are they important?

• How can Math Language Routines be used in classrooms?



Math Language Routines

A 'math language routine' refers to a structured but

adaptable format for amplifying, assessing, and

developing students' language. . . . These routines can

be adapted and incorporated across lessons in each

unit to fit the mathematical work wherever there are

productive opportunities to support students in using

and improving their English and disciplinary language.

Zwiers et al., 2017

Understanding Language/ Stanford Center

for Assessment, Learning, and Equity

Zwiers, Dieckmann, Ruherford-Quach, Daro, Skarin, Weiss, & Malamut



Math Language Routines (MLRs)

1. Stronger and Clearer Each Time

2. Collect and Display

3. Critique, Correct, and Clarify

4. Information Gap

5. Co-Craft Questions and Problems

6. Three Reads

7. Compare and Connect

8. Discussion Supports



– Five Proficiency Strands in Mathematics – Eight Math Practice Standards

• Conceptual understanding

• Strategic competence

• Adaptive reasoning

• Productive disposition

• Procedural fluency

National Research Council 2001

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



Don’t Let This Happen in Your Math Class



Amplify not Simplify

Teachers can foster students’

sense-making by amplifying

rather than simplifying, or

watering down, their own use

of disciplinary language.

Zwiers et al. 2017

What does amplify vs. simplify mean to you?

Describe an example of simplifying the use of language

rather than promoting correct use of academic or

mathematical language. (see Handout p. 3)



Common Misconceptions

• Mathematical language proficiency means using

only formal definitions and vocabulary.

• Developing the language of the discipline requires

continuous “time-outs” from the content, and multiple

detours to “math language” mini-lessons.

• Students will learn the English language and

disciplinary language by merely being immersed in

them over time, with little additional support.



Focus on the Math

Research shows that ELs, even as they are

learning English, can participate in discussions

where they grapple with important mathematical

content. Instruction for this population should

not emphasize low-level language skills over

opportunities to actively communicate about

mathematical ideas.

Moschkovich, 2012



Commit to Develop Student Agency with Language

A commitment to help students develop their own

command of the “mathematical register” is therefore not

an additional burden on teachers, but already embedded

in a commitment to supporting students to become

powerful mathematical thinkers and ‘do-ers’. Lee, Quinn & Valdes, 2013

Teachers can adapt and respond more effectively to

what students are saying and doing as they develop

disciplinary language and content understanding

concurrently.Zwiers et al., 2017



Four Foundations for MLRs

1. Support sense-making

2. Optimize output

3. Cultivate conversation

4. Maximize linguistic and cognitive meta-awareness



Let’s Dive Into the MLRs

Stronger and Clearer Each Time

Collect and Display

Critique, Correct, and Clarify

Information Gap

Co-Craft Questions and Problems

Three Reads

Compare and Connect

Discussion Supports



MLR #1: Stronger and Clearer Each Time

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).

Examples:

• Amplify vs. Simplify

• “Test error analysis” activity

• State Park problem



PARCC Grade 4 – "State Park" (2013)

The perimeter of the rectangular state park shown is 42 miles.

A ranger estimates that there are 9

deer in each square mile of the park.

If this estimate is correct, how many

total deer are in the park? Explain

your answer using numbers,

symbols, and words.

I added 8 + 8. Then I subtracted 16 from 42. Then I divided

this by two. Then I multiplied 8 times 13 to get 104. Then I

multiplied 104 by 9 to get 936.

I need to know how many square miles are in the park.

Since the perimeter is 42 miles I subtracted 16 to get the top

and the bottom. These sides are equal, so I divided by two

to get the length. 42 – 16 = 26 26 / 2 = 13

To get the area of the rectangle I have to multiply length x

width, so I did 8 x 13 to get 104 sq. miles.

Since there are 9 deer in each square mile, I multiplied

9 x 104 = 936 deer.



MLR #2: Collect and Display

Purpose: To capture students’ oral words and phrases

into a stable, collective reference.

Examples

• Collect, focus, assign and use vocabulary while

working on a problem.

• Notice and Wonder – Show an image and ask

students “What do you notice?” and “What do you wonder?”

• Number Talks – Discuss, collect (selective sharing)

and discuss again solution methods.



Collect, focus, assign and use vocabularywhile working on a problem. (see Handout p. 4)

What mathematical language or vocabulary

is related directly to the following problem?

Solve:

6(3x – 5) = 3(x + 5)

Variable Coefficient Constant

Expression

Equation

Inverse operation

Do same thing to both sides of the equation

Distributive property

3(x + 5) = 3x + 15



What do you notice? What do you wonder?

Photo from Juan Oliphant

https://www.instagram.com/p/BssxmtOhva1/

Ocean Ramsey with Great White Shark



Number Talks

How are these numbers the same and how

are they different?

10 1 0.1 1/5

A five- to fifteen-minutes classroom

conversation around purposefully crafted

problems that are solved mentally.(Parrish and Dominick 2016)



MLR #3: Critique, Correct, and Clarify

Purpose: To give students a piece of mathematical

writing that is not their own to analyze, reflect on, and

develop.

Example:

• My Favorite ‘No’

https://www.teachingchannel.org/video/class-warm-

up-routine

from Lea Alcala



“My Favorite ‘No’”

Lea Alcala (on Teaching Channel)



MLR #4: Information Gap

Purpose: To create a need for students to communicate

(Gibbons, 2002).

Examples:

• Guess My Graph

• Information Gap Cards

• Guess My Polygon (yes/no questions)



Guess My Polygon

1 2 3 4

5 6 7 8

9 10 11 12

Two players compete in the game using the polygon chart.

– Player 1 will pick a polygon from the chart but does not tell player 2

which polygon he/she chooses.

– Player 2 asks yes/no questions to figure out which polygon player 1

chose. The goal is to be able to know within 4–5 questions.

(See

Handout

pp. 5-6)



MLR #5: Co-Craft Questions and Problems

Purpose: To allow students to get inside of a context

before feeling pressure to produce answers, to create

space for students to produce the language of

mathematical questions themselves, and to provide

opportunities for students to analyze how different mathematical forms can represent different situations.

Examples:

• Guess My Graph (Every Graph Tells a Story)

• Matching equations to word problems



MLR #6: Three Reads (See Handout p. 7)

Purpose: To ensure that students know what they are

being asked to do, create opportunities for students to

reflect on the ways mathematical questions are presented,

and equip students with tools used to negotiate meaning

(Kelemanik, Lucenta & Creighton, 2016).

Example:

• Three Reads with different numbers.

• Three Reads with missing numbers.



Three Reads – Examples

A phone originally sells for $245. It is now on sale for

1/5 off the original price. April has a coupon for an extra

10% off the sale price. To the nearest dollar, how much

less than the original price will April pay for the phone?

from Ready Math Grade 7 Lesson 16

Marcos has $17 altogether. He has some money in his

pocket and $12 in his hand. How much money does he

have in his pocket?

Pocket Money

Cell Phone Deal



Three Reads – Board the Roller Coaster

Jackson needs to be 1 ¾ inches taller in order to ride

the roller coaster. Since he can’t wait, he puts on a pair

of boots that adds 1 1/6 inches to his height and slips

an insole inside the boot that adds half as much as the

boot does to his height. Will this make Jackson appear

tall enough to ride the roller coaster?

Adapted from Eureka Math Grade 5 Module 3 (2016)

five

three



MLR #7: Compare and Connect

Purpose: To foster students’ meta-awareness as they

identify, compare, and contrast different mathematical

approaches, representations, concepts, examples, and

language

Examples:

• Number Talks

• Solve problems in more than one way and

compare with another student

• Which One Doesn’t Belong (www.wodb.ca)



Which One Doesn’t Belong

wodb.ca(See Handout p. 8)

Shapes Numbers Graphs



Which One Doesn’t Belongwodb.ca



MLR #8: Discussion Supports

Purpose: To support rich and inclusive discussions

about mathematical ideas, representations, contexts,

and strategies (Chapin, O’Connor, & Anderson, 2009).

Examples:

• MLRs #1-7

• No pencil test

• Partner test or assignment

• Discourse techniques



Techniques for Discussion Support

Questioning Strategies

• Collaborate on problem solving

• Compare/contrast

• Explain/justify/prove

• Discuss disagreements

• Investigate “What Ifs”

• Test student conjectures

• Analyze errors

• Predict

• Connect ideas/concepts

• Why does this make sense?

Managing Techniques

• Clear directions

• Wait time

• Revoice

• Restate

• Revise

• Add on

• Pair share

• Think-write-pair-share

• Snowball

• Group chart



Implementing Mathematical Language Routines

1. Stronger and Clearer Each Time

2. Collect and Display

3. Critique, Correct, and Clarify

4. Information Gap

5. Co-Craft Questions and Problems

6. Three Reads

7. Compare and Connect

8. Discussion Supports



Let’s Connect!

Dean Ballard

[email protected]

www.corelearn.com

@COREInc

If you’d like CORE to come to your

school to provide instructional

coaching and other professional

learning services, please get in

touch.

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