teaching math to english learners

1. English Language Learners
in the Mathematics
Classroom

2. Rocío Benedicto
New Mexico State University MC2 Field Specialist
Email: rojustus@nmsu.edu

3. Did you know?
 There are sixty-six native
languages, other than English,
spoken by students in some
school districts.

4. Language Diversity
 Three in four English Language Learners’ first language is
Spanish.
 Other languages spoken by public school children include
Vietnamese, Hmong, Cantonese, Korean, Haitian, Creole,
Arabic, Russian, Tagalog, Navajo, Khmer, Mandarin,
Portuguese, Urdu, Serbo-Croatian, Lao, Japanese,
Punjabi, Armenian, Polish, French and Hindi.
Crawford, James (2004). Educating English Learners: Language Diversity
in the Classroom. Los Angeles, CA: Bilingual Education Services.

5. Newcomers Today
 30.1% Mexico
 27.3% from Asia
 23% from other Latin American countries
 13.1% Europe
 2.2% North America (Canada, Greenland, etc.)
 0.6% Oceania
(Migration Policy Institute, 2008 found at
www.migrationinformation.org/datahub/state.ctm?IOD=US)

6. Hispanics/Latinos in the
United States
 The United States has the second largest Spanish
speaking population in the world.
 More than 53 million Hispanics/Latinos in the
U.S.(Pew Hispanic Center, 2010).
 Come from every Spanish speaking nation in the world.
 The majority of Hispanics in the United Sates (66%)
identify as Mexican, Mexican-American or Chicano
(2006).
 The majority of Hispanics/Latinos live in 5 states.

7. 7
States with the greatest population
of Hispanics/Latinos (PEW, 2008)
State Population 2008 Population 2000
California 13,434,896 10,928,470
Texas 8,815,582 6,653,338
Florida 3,846,267 2,673,654
New York 3,232,360 2,854,991
Arizona 1,964,625 1,292,152
Fuente: U.S. Census Bureau, Estimados demográficos, Julio 1, 2006

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12. Distribution of
Hispanics/Latinos by age
and gender
Distribution of population by gender
Age (years) Masculine % de Hispanics Femenine % de Hispanics
< 18 years of age 7,845,751 17.3 7,486,235 16.5
> 18 years of age 15,506,157 34.4 14,437 31.8
Distribution of population under 18 years of age
< 5 years of age 2,506,434 5.5 2,388,003 5.3
5 to 9 years of age 2,111,113 4.7 2,041,303 4.5
10 to 14 years of age 2,038,884 4.4 1,941,531 4.3
15 to 19 years of age 1,982,738 4.4 1,846,811 4.1

13. Hispanics/Latinos in U.S. Schools (K-12)
 The number of Hispanic/Latino students has doubled in the last 15
years.
 There are approximately 10 million Hispanic/Latino students in the
K-12.
 One in five public school students in the United States is
Hispanic/Latino.
 By 2040, the U.S. Census Bureau has projected that there will be
more Hispanic/Latino children in U.S. schools than non-
Hispanic/Latino children.

14. Use of the Spanish
Language
 By youth under the age of 18
 U.S. Born – approximately 70% speak Spanish in
their homes
 Foreign born– more than 90% speak Spanish at
home

15. Reflection
Let’s pause for 10 minutes and take some time to reflect on what this
information means for our K-12 mathematics classrooms.
Each of you has a different colored paper in front of you. On that
piece of paper write down
1) 2 things that you have learned, &
2) 1 question that you have
Find the person who has the same colored paper as you and discuss
your thoughts.

16. BREAK
PLEASE BE BACK IN 10
MINUTES

17. Share out discussion

18. What has been the response
to linguistic diversity in the
U.S. K-12 classroom?

19. Objectives of Bilingual Education
 Not allow students to fall behind in academics
because of lack of command of English.
 Gradually learn English as a second language.
 Ease the transition from the native language to
English through subjects.
 Offer more opportunity for academic success through
ease of transition into English.

20. Models Of Bilingual Education
 English immersion
 Transitional bilingual education
 Maintenance bilingual education
 Two-way bilingual education – Dual Language
Immersion
 English as a second language (ESL)

21. Immersion
 Instruction is entirely in English.
 All subject content and communication is
conducted in English.
 There is no instructional support for native
language.

22. Transitional and Maintenance models
 Instruction for some subjects is in the
students’ native language but a certain
amount of each day is spent on
developing English skills.
 Classes are made up of students who
share the same native language.

23. One-way or Two-Way Immersion
 Instruction is given in two languages.
 Teachers usually team teach.
 This approach is also called dual
language immersion.

24. English as a Second Language (ESL)
 May be the same as immersion but also may include
some support to individuals in their native tongue.
 Typically classes are comprised of students who
speak different languages but are not fluent in
English.
 Students may attend classes for only a period a day,
to work strictly on English skills, or attend for a full
day and focus both on academics and English.

25. Arguments Against Bilingual Education
 Keeps students in a cycle of native
language dependency.
 Costly
 Ineffective compared to the amount
of money invested
 Is not systematized
 Massachusetts 2002 mid-year
referendum Question 2
 Arizona Proposition 203 – similar
to California proposition.
Implemented fall 2001.
 California Proposition 227 –
approved in 1998 by California
voters to basically eliminate
bilingual education. Most LEP
students are now in immersion
programs.*

26. Reflection
 How does Moises’ (the boy in the movie) resemble students in the
schools in which you are teaching/working?
 How do you and the teachers in your schools address the needs of
students such as Moises?

27. Comprehensible Input
How is mathematics understood by English Language Learners?

28. Language Acquisition -
General
 Everyone agrees that human beings are born with
the ability to learn language (to speak)
 We use language to communicate.
 2 schools of thought of how we learn language
 Behaviorist – we learn language through modeling.
 Innatist – we are born with a mechanism that
monitors grammar (the structure of language).

29. Krashen SLA Hypotheses
 The Natural Order Hypothesis - 'we acquire the rules of language in
a predictable order'
 The Acquisition/ Learning Hypothesis - 'adults have two distinctive
ways of developing competences in second languages ..
acquisition, that is by using language for real communication ...
learning .. "knowing about" language' (Krashen & Terrell 1983)
 The Monitor Hypothesis - 'conscious learning ... can only be used
as a Monitor or an editor' (Krashen & Terrell 1983)
 The Affective Filter Hypothesis - 'a mental block, caused by
affective factors ... that prevents input from reaching the language
acquisition device' (Krashen, 1985, p.100)
 The Input Hypothesis - 'humans acquire language in only one way -
by understanding messages or by receiving "comprehensible
input"’ *

30. Input Hypothesis

31. BICS & CALP
 BICS – Basic Interpersonal Communication Skills
 Sometimes referred to as playground communication.
 Immigrant and non-immigrant children learn this type of
communication first.
 Communication is informal.
 CALP – Cognitive Academic Language Proficiency
 Formal language used in academic and professional
environments.
 This type of communication is learned through modeling by an
adult.
 Is not often used outside of the classroom or professional
environment.
 Source: Cummins, J. (1979). Cognitive/Academic language proficiency, linguistic interdependence,
the optimum age question and some other matters. Working Paper on Bilingualism, 19, 121-129.

32. Relative Communicative
Demands
 Source: Carr, J. , Sexton, U. & Lagunoff. R. (2007). Making Science Accessible to
English Learners: A Guidebook for Teachers. San Francisco, CA: WestEd.

33. 5 Levels of English
Language Development
 Beginning
 Early Intermediate
 Intermediate
 Early Advanced
 Advanced
(Refer to the Handout ELD stages for discussion)

34. Academic Language
Skills for the Math
Classroom
 Listen with Comprehension
 Use Academic Vocabulary
 Ask and Answer Questions
 Communicate Critical Thinking
(refer to handout for discussion)

35. Lexicon of Mathematics
 The terms that are used by mathematicians and math learners
use to talk about mathematics.
 Content specific
 Uses of language are specific to mathematics
quadratic, function, algebraic, geometric, sine, cosine
 Words that have a specific meaning when used in the math
classroom
Positive, negative, about, rational, irrational, infinity, imaginary
(refer to handout for discussion)

36. 6 Steps for Teaching
Vocabulary
 Identify words all students need to know
 Identify words English Learners need to know
 Select the highest-priority words
 Choose key words for a day’s lesson
 Build from informal to formal understanding
 Plan many opportunities to apply key words

37. Word Walls , Sentence Frames, Graphic
Organizers and Classroom Setup
 Word Walls * .
 Sentence Frames*
 Graphic Organizer * .
 Classroom Setup

38. Now it’s your turn to play
 There are several problems on the table
 Read the problem and solve (if you want to)
 How would you scaffold this problem for
understanding?
 Write down your strategies
 Find a partner and discuss your strategies
 Write down both of your strategies on a large paper
and place on the wall for group discussion