PROMOTING SUCCESS IN MIDDLE AND HIGH SCHOOL MATHEMATICS FOR ENGLISH LANGUAGE LEARNERSDR. L INDA GRIFF IN , LEWIS & CLARK COLLEGE, PORTLAND, OREGON

LGRIFF IN@LCLARK.EDU

NWM CONFERENCE: OCTOBER 11 , 2014

CONTENT OBJECTIVESLearn what research says about high quality mathematics

instruction for ELLsIdentify CCSS-M resources that reflect research-recommended

practicesDetermine ways you can support ELL students and math teachers

to improve outcomes for ELLs.

LANGUAGE OBJECTIVESDiscuss new learning using appropriate mathematical and

pedagogical vocabularyWrite a personal action step resulting from the presentation

Building backgroundChat Stations*In groups of 3-4, rotate through the four chat stations posted around the room.Stop at each station and discuss the prompt.Rotate when timer sounds.Be ready to share your group’s ideas.

*Source: Jennifer Gonzalez, Cult of Pedagogy

http://www.cultofpedagogy.com/chat-stations/

Addressing Head & Heart & Hand

Equity issues math teachers need to understand

HeadMath teachers need to understand the critical equity role mathematics education plays

“Mathematics is the gatekeeper to higher education…Because ELLs are not achieving at the same levels in math as their native English-speaking counterparts, many are at risk of having the gate to higher education closed to them.”

—Bresser, et al (2009)

“If we fail to provide the tools for ELL students to gain math literacy, they will be left with ever narrowing access to the democracy that defines this country.”

—Sarah A. Roberts (2009)

Position Statement: Teaching Mathematics to English Language Learners

Mathematics teachers must attend to all students, including those who speak a first language other than English or have related cultural differences, and ensure that all have access and opportunities to learn mathematics and to reveal what they know. Every student’s cultural and linguistic heritage should be respected and celebrated for the diversity that it contributes to the learning environment. Expanded learning opportunities and instructional accommodations should be available to English language learners (ELLs) who need them to develop mathematical understanding and proficiency.

COMMON CORE STATE STANDARDSNew ambitious goals for all studentsStandards for Mathematical Practice require language skills Increased language demands in new mathematics curricula

What else? What other equity issues exist in your school for ELLs and mathematics?

Perspectives math teachers need to feel

HeartMath teachers need to build empathy for ELL students

GREAT DIVERSITY IN ELL POPULATION

Diversity exists across many characteristics◦ Native languages◦ Levels of English language development◦ Prior life experiences◦ Prior schooling and formal education experiences◦ Interest in and prior success with mathematics◦ Personalities and learning preferences

It is the teacher’s role continually explore new methods to engage all ELLs to meet the same high standards set for all students.

LANGUAGE ACQUISITION ELLs move through different stages as they acquire English proficiency and at all stages need comprehensible input.

LANGUAGE USED AT SCHOOLBASIC INTERPERSONAL COMMUNICATION SKILLS (BICS)

Language used for social interactions

Informal language about day-to-day events

Requires vocabulary to communicate about people, places, and events

Primarily verbal, present tense, active voice

COGNITIVE ACADEMIC LANGUAGE PROFICIENCY (CALP)

Language used for acquiring knowledge

Formal language about specific academic subjects

Requires vocabulary to communicate about abstract and complex ideas

Verbal and written, other tenses, passive voice

RELATIVE COMMUNICATION DEMANDS

COGNITIVE LOAD

Undemanding Demanding

CONTEXT

Reduced

Rich

Gestures

Peer Conversations

Small group discussion about math

Scaffolded and structured learning tasks

Phone conversation

Text messaging

Read and understand word problem

Gain information through lecture

LANGUAGE DIVERSITY IS A RESOURCE “Students’ cultural and linguistic differences in the mathematics community should be viewed as intellectual resources rather than deficits and should be used in the classroom to connect prior knowledge and to create a community whose members value one another’s ways of engaging in mathematics.”

Ramirez & Celdedn-Pattichis in Beyond Good Teaching: Advancing Mathematics Education for ELLs

From Chat Station #2What do you think ELL students wish they could tell their math teachers?

WHAT HS ELLS WISH TEACHERS KNEWMISTAKES TEACHERS MAKE

1. Saving us embarrassment by not calling on us.

2. Always grouping us together.

3. Avoiding conflict by ignoring students who tease us.

4. Giving us assignments that are identical to everyone else.

5. Assuming that when we don’t raise our hands we don’t need help.

6. Assuming the help we need is always translation.

HOW THIS HURTS US

1. This makes us feel invisible and unvalued in your class.

2. This prevents us from learning from and with all of our classmates.

3. We can’t ignore the teasing. We need someone in authority to address it.

4. We need language accommodations to help us meet the learning targets.

5. We may be too shy or uncomfortable to raise our hands. We rely on you to initiate assistance.

6. We need the same help as everyone else—an example, more explanation, a definition.

Research-based practices math teachers need to use

HandsMath teachers need tools and resources

T-Chart PredictionsEffective practices I’ve seen/used in

math classResearch-based practices

(will be revealed on the next slides)

TEACHERS PROVIDE LANGUAGE SUPPORTS

Use multiple modes of mathematical communication Develop linguistically sensitive mathematics discourse practices

“Students must learn to speak the language of mathematics and participate in practices that are unique to the mathematics classroom. In many cases, this means that teachers will need to model these practices for students until they can be full participants.”

—Roberts (2009)

Require student-to-student talkThink – pair – share

Multiple representations (diagrams, drawings, gestures, technology, objects)

Jigsaw tasks

Give 1-Get 1 brainstorming

Purposeful grouping of students

Chat stations

Support Vocabulary Development•Use graphic organizers such as the Frayer model

Support Vocabulary Development• Personal glossaries in English and/or first language

Term Definition Example/diagram

Inequality

la desigualdad (Spanish)

Like an equation, but no equal sign (<, >)

4x – 5 > 15

Vertex

Lugood (Somali)

Corner of a figure or angle

Record

Ghi lại (Vietnamese)

Write down. Tally marks for data collection.

|||| ||||

Support Vocabulary Development

Online math glossaries in multiple languages

http://www.glencoe.com/apps/eGlossary612/landing.php http://my.hrw.com/math06_07/nsmedia/tools/glossary/msm/glossary.html

Anticipate Potentially Confusing Language

Clarify polysemous words in math◦ E.g: table, right, similar, rational, difference, root, domain, power

Point out mathematical homophones◦ Sum vs some; hundreds vs hundredths; by vs buy

Be aware of cultural variations

3,000 3.000

4.56 4,56

Mediate Language Demands

Framework continued

Source: Oliveira, Luciana. (2012). “The Language Demands of Word Problems for English Language Learners.”

Consider Five Language DomainsReading Writing Speaking Listening Representing

Class survey results

Newspaper excerpt (text and graph)

Task directions posted on doc camera

Other students’ presentation posters

Responses to newspaper article

Summary statements from class data

Poster annotations

Summarize newspaper article (partner)

Graph interpretations (partner)

Respond to teacher questions (whole class)

Present poster with partner (whole class)

Teacher questions about newspaper article

Task directions

Partner responses

Other students’ presentations

Poster showing survey responses (tally marks and graph)

Gestures during presentation

Source: Aguirrre & Bunch (2012)

TEACHERS PROVIDE VISUAL MODELS

Make use of technology to support mathematical learning Encourage the use of models as tools for thinking and communicating mathematically

“Mathematical tools and mathematical modeling provide a resource for ELLs to engage in mathematics and communicate their mathematical understanding and are essential in developing a community that enhances discourse.”

—Ramirez (2012)

Use Graphing Tools◦ Source: NCTM’s Illuminations site◦ Example: Function Matching

Use Manipulatives◦ Source: National Library of Virtual Manipulatives◦ Example: Algebra Balance Scales-Negatives

Use Tutorials◦ Khan Academy videos in English and 18 other languages◦ Example: Ukranian

TEACHERS USE HANDS-ON ACTIVITIESEmpower learners by engaging them with the content

Promote mathematical understanding of the problem context and the solution

“It is both possible and important to engage ELLs at all levels of language proficiency in mathematical work that challenges them on a regular basis to reason mathematically and solve problems.”

—Driscoll, Heck, & Malzahn (2012)

Example: Barbie Bungee Jump◦ Lesson: NCTM’s Illuminations◦ Video: Teaching Channel

Example: The Shape of Things◦ Lesson: Inside Mathematics◦ Video: Inside Mathematics

Example: Setting Up Sprinklers◦ Lesson: Illustrative Mathematics

TEACHERS PROVIDE SCAFFOLDINGGraphic organizersThink-write-pair-share Intentional partneringThink aloud by teacher; by studentsReciprocal learningSummarizing

TEACHERS VARY ASSIGNMENTS Provide options that reduce the language demands while maintaining the content demands◦ Sentence frames for responses

◦ The main idea of today’s lesson was _______________.◦ These two ___________ have the same ______________.◦ It’s important to remember ________ when solving ______________.

◦ Flexibility with respect to ◦ Due dates◦ Length of assignment◦ Ways to demonstrate knowledge

SummaryEffective practices I’ve seen/used in

math class Research-based practices

Provide language supports

Provide visual models

Use hands-on activities

Provide scaffolding

Vary assignments

Model Lesson Plan: Interpreting Graphs1. G UIDE D IN T E R PR E TAT ION

2. R E AD IN G & DE M ON ST RAT IN G IN FOUR VO IC E S

3. C R E AT E – E XCHAN G E – ASSE SS

4. SUM M AR IZ IN G W HAT YOU K N OW

1. GUIDED INTERPRETATIONPreview what students will need to know about line graphs.

Describe key features of a graph

Describe 1 point on the graph.

Tem

per

atu

re

Time of Day

2. READING & DEMONSTRATING IN FOUR VOICESEach student is given one of four “voices” that represent different portions of the graph.

As a group, students determine which voice matches which part of the graph and record their observations.

Tem

per

atu

re

Time of Day

This graph shows the relationship between the time of day and the temperature in Portland, Oregon in October.

• By 9 p.m. the temperature has returned to 40 degrees.

• In the next two hours, the temperature increased quickly to 70 degrees.

• At 8 a.m. the temperature was 40 degrees Fahrenheit and it slowly increased to 50 degrees by 10 a.m.

• THE TEMPERATURE STAYED AT 70 DEGREES UNTIL 5 P.M. AND SLOWLY DECREASED UNTIL 7 P.M.

3. CREATE – EXCHANGE – ASSESS Students groups are given a novel graph and asked to create 4 new “voices.”

Groups exchange graphs/voices and are again asked to match voice with graph.

Groups give feedback to one another to help improve voices.

Atm

osp

her

ic C

O2(

pp

m)

Year

1960 1970 1980 1990 2000 2010

4. SUMMARIZING WHAT YOU KNOW The final piece is to specifically teach students the language of summarizing.

Use one last graph. Use sentence frames: “This graph represents the relationship between ___ and ___.” “As ___ increases, ___ decreases.”

Use short exit slips, or dedicate more time to writing summary paragraphs. But always have students take the time to determine what they have learned.

NOW WHAT? PERSONAL ACTION STEPS

Give 1—Get 1 sharing

CONTENT OBJECTIVESLearn what research says about high quality mathematics

instruction for ELLsIdentify CCSS-M resources that reflect research-recommended

practicesDetermine ways you can support ELL students and math teachers

to improve outcomes for ELLs.

LANGUAGE OBJECTIVESDiscuss new learning using appropriate mathematical and

pedagogical vocabularyWrite a personal action step resulting from the presentation

Books and articles•Carroll, C., S. Cremer, et al. (2009). Making mathematics accessible to English learners: A guidebook for teachers, grades 6-12. WestEd.

•Celedon-Pattichis, S., N. Ramirez. (2012). Beyond good teaching: Advancing mathematics education for ELLs. NCTM.

•Deussen, T., E. Autio, et al. (2008) What teachers should know about instruction for English language learners. Education Nortwest. Available for download: http://educationnorthwest.org/resource/what-teachers-should-know-about-instruction-english-language-learners

•Echevarria, J., M. Vogt, et al. (2010). The SIOP model for teaching mathematics to English learners. Pearson.

Books and articles•Hansen-Thomas, H. (2009). English Language Learners and Math. Charlotte, NC, Information Age Publishing.

•Roberts, S. A. (2009). "Supporting English language learners' development of mathematical literacy." Democracy & Education, 18(3): 29-36.

•Waddell, L. R. (2014). “Using Culturally Ambitious Teaching Practices to Support Urban Mathematics Teaching and Learning.” Journal of Praxis in Multicultural Education, 8(2), 2.

Websites featured in this presentationCult of Pedagogy◦ http://www.cultofpedagogy.com/

NCTM◦ http://illuminations.nctm.org

National Library of Virtual Manipulatives◦ http://nlvm.usu.edu/en/nav/vlibrary.html

Khan Academy—list of language options◦ http://khanacademy.desk.com/customer/portal/articles/329337-is-khan-academy-available-i

n-other-languages-

Websites featured in this presentation

Inside Mathematicsohttp://insidemathematics.org/

Illustrative Mathematicsohttp://www.illustrativemathematics.org/

Online multilingual glossariesohttp://www.glencoe.com/apps/eGlossary612/grade.phpohttp://my.hrw.com/math06_07/nsmedia/tools/glossary/msm/glossary.html

The Teaching Channelo https://www.teachingchannel.org/

Other helpful websites Mathematics for English Language Learners Project

◦ http://www.tsusmell.org/resources/mell-resources.htm

TODOS: Mathematics for ALL◦ http://www.todos-math.org/

Center for the Mathematics Education of Latinos/as◦ http://math.arizona.edu/~cemela/english/Supporting ELLs in Mathematics◦ http://ell.stanford.edu/teaching_resources/math