Catching up in Math: The Case of Newly-Arrived Cambodian Students in a Texas Intermediate School

1
Catching up in Math The Case of Newly-Arrived
Cambodian Students in a Texas Intermediate School

• Wayne E. Wright
• University of Texas, San Antonio

National Association for the Education and
Advancement of Cambodian, Laotian, and Vietnamese
Americans May 2006, Washington DC
2
Challenges faced by newly arrived non-Spanish
speaking ELL Students

• Few bilingual programs in languages other than
  Spanish
• Less likely to have teachers or staff who speak
  their native languages
• Most placed in English-only classrooms
• Sheltered English Immersion
• Mainstream classrooms
• With ESL
• Without ESL

3
ELL students in the United States

• 5,000,000 ELLs nationwide
• Over 80 of ELLs are Spanish-Speaking
• Texas
• 94 of ELLs are Spanish-speaking
• 37,000 ELLs speak languages other than Spanish
• Represent over 100 different language groups
• More than the total ELL population in 30 out of
  the 50 states
• More than the total ELL populations of Delaware,
  Kentucky, Maine, Mississippi, New Hampshire,
  South Carolina, South Dakota, Utah, and West
  Virginia combined

4
The Challenge of Catching Up

• Research has repeatedly shown that ESL students
  usually require at least 5 years of exposure to
  academic English to catch up to native-speaker
  norms. In addition to internalizing increasingly
  complex academic language, ESL students must
  catch up to a moving target. Every year,
  native-speakers are making large gains in their
  reading and writing abilities and in their
  knowledge of vocabulary. In order to catch up to
  grade norms within 6 years, ESL students must
  make 15 months gain in every 10-month school
  year. (Cummins, 2003)

5
No Child Left Behind (NCLB)and Texas Mandates
for ELLs

• ELLs must take the states high-stakes test
• Texas Assessment of Knowledge and Skills (TAKS)
• Students may be assessed in their native language
  for up to the first five years
• Most states only have tests in English
• Some states also have Spanish
• Few states have tests in any other languages
• Overwhelming majority of Non-Spanish ELLs take
  the same English-only test as their
  English-fluent peers

6
Testing Accommodations for ELLs

• Newly arrived ELLs may be exempted from the
  English reading test the first year
• But, newly arrived ELLs must take the states
  math test
• ELL must be provided with reasonable
  accommodations
• Texas Linguistically Accommodated Test (LAT)
  Math
• Set of procedures for test administration, rather
  than a different test
• Reality
• Little research on how ELL students can be
  accommodated
• Thus newly arrived non-Spanish speaking ELLs are
  required to take (and expected to pass) the same
  test as English-fluent students with little to no
  accommodations

7
Research Question

• How reasonable is the expectation that newly
  arrived non-Spanish-speaking ELLs can catch up to
  their peers in grade-level math instruction
  sufficient to pass the TAKS Math test in English?

8
Case of Two Newly-Arrived ELL students from
Cambodia

• Two sisters (Nitha and Bora) placed in 5th grade
  at a suburban intermediate school in the San
  Antonio, TX area
• Students came from poor village in Cambodia
  (Takeo Province)
• Girls and their father sponsored to the U.S. by
  relatives
• Students arrived in October 2004
• (more than 2 months after beginning of school
  year)
• Spoke no English whatsoever at time of arrival
• Placed in mainstream classroom
• 3 other ELL students in the classroom, but with
  intermediate to advanced proficiency in English
• Expected to take and pass the TAKS Math test in
  English less than 6 months later

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Site Description

• Rodgers Intermediate School
• Medium sized school district
• 13 schools serving 7,636 K-12 students
• Fast growing suburb on out-skirts of San Antonio
• 590 students in grades 5 and 6
• White (58), Hispanic (29), African American
  (10), Asian-Pacific Islanders (2)
• Middle-class neighborhood
• Only 31 free and reduced lunch (compared to 53
  state-wide average)
• ELLs less than 1
• Academically Acceptable rating for 2004-2005
  school year

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Participant Description

• Nitha and Bora
• Lived with aunt and uncle who sponsored them
• Spacious two-story home
• Far cry from thatched hut with no electricity or
  running water they lived in in Cambodia
• Both girls attended school in their village and
  were top students in their class
• Nitha had completed 6th grade
• Bora had completed 4th grade
• Both had strong Khmer literacy skills and basic
  arithmetic skills
• Neither learned English before arrival to U.S.
• Both are highly intelligent, are fast learners,
  and showed a great deal of courage and enthusiasm
  in adjusting to the strange customs, language,
  and food in America.

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Math Instruction for ELLs

• The Math Myth
• Math is easy for ELLs because its mostly numbers
• Reality
• Research shows that math instruction and math
  tests have a very high language demand which pose
  great difficult for ELLs
• AZ and TX Many ELLs score lower on Math test
  than Reading and Writing tests
• The Language of Math
• Different than regular spoken and written English
• For ELLs, Math is a third-language

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Language of Math

• Words specific to math
• Divisor, Dividend, denominator, quotient
• Common words with have different meanings in math
• Table, column, row, equal
• Complex phrases
• Least common multiple, greatest common
  denominator, negative exponent
• Syntax of math is not left-to-right
• The square of the sum of A and B ? (AB)2

13
Math Texts

• Conceptually packed
• Have high density
• Require left-to-right as well as up-and-down eye
  movement
• Must be read more slowly than natural language
  texts
• Often require multiple readings
• Use numerous symbolic devices such as charts and
  graphs

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Other Math Challenges for Newly-Arrived ELLS

• Math instruction in their home countries
• May have learned different algorithyms for
  problem solving
• May use different mathematical notation
• (e.g., 5,234,232.56 would be written as
  5.234.232,56 in Cambodia)
• Lack of vocabulary and syntax knowledge
• ELLs dont know the meaning of many of the words
  or cant understand due to complex syntax
• High correlation between reading and math test
• Students who read well often do well on math
  tests. Poor readers do poorly on math tests

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Other Math Challenges for Newly-Arrived ELLS

• Math learning must be acrued
• Must learn and master simpler concepts before you
  can learn more complex concepts
• e.g., must learn to add, subtract and multiply
  before long division
• Opportunity to learn
• How much math did students learn in their home
  country?
• Some learn more than U.S. Students
• Others learn much less
• Thus, already behind U.S. peers as soon as they
  arrive

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Education and Math Instruction in Cambodia

• Cambodian Education System
• Still recovering from genocide and 2 decades of
  war
• Khmer Rouge Period 1975-1979
• Schools shut down
• Teachers and other educated Cambodians
  systematically executed
• Many other died of disease or starvation
• Many of the survivors fled as refugees and later
  resettled in Western countries
• Few educators remained left to help rebuild
  school system

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Education and Math Instruction in Cambodia

• Despite enormous problems, education has greatly
  improved in Cambodia over the past decade
• However
• Many schools lack water, electricity, bathrooms,
  or even walls and roofs
• Average class size 40 to 60 students
• Most students attend only half day
• High drop out rates, even among elementary
  students
• Especially female students
• Many elementary teachers have less than a high
  school diploma
• 69 of elementary teachers in Takeo province did
  not graduate from high school
• Lack of educational materials and supplies
• Only one basic text book per grade per subject
• Small, short, poor quality paperback books
  printed on cheap paper
• In many schools, only teacher has a copy of the
  book
• In some schools, teachers do not have a book

18
Education and Math Instruction in Cambodia

• Math Instruction in Cambodia
• Covers mostly basic arithmetic and problem
  solving
• Math instruction in Cambodia is far below math
  concepts taught in equivalent grade-levels in the
  U.S.
• Even without the language barrier, Nitha and Bora
  were already academically far behind their
  classroom peers in Texas in math instruction
• Combined with the language barrier, catching up
  to their grade-level peers was a major challenge

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Assistance for Nitha and Bora

• Classroom teacher
• Differentiated instruction
• Tried to provide work and activities of similar
  content but at much lower grade level
• Obtained and allowed girls to use bilingual
  Khmer-English dictionaries
• Encouraged them to write translations of words on
  their school work
• Work on classroom computer
• ESL Teacher
• Girls received daily pull-out ESL instruction
  from experienced teacher 3 to 5 days a week, 45
  minutes to an hour each day
• Focused on vocabulary development and basic
  reading

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Assistance for Nitha and Bora

• Individualized instruction with a
  paraprofessional
• An aide to the school counselor worked with Nitha
  and Bora for an 1 to 1½ hours a day
• Classroom teacher prepared activities and lessons
• Aide provided additional lessons and activities
  developed on her own
• Oral language heaven
• Computer Lab
• Extra time in computer lab
• Compass Learning Software
• Self-paced Reading and Math programs

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Assistance for Nitha and Bora

• Khmer Primary Language Support Assistance and
  Tutoring
• Provided by a community volunteer
• Professor from local university who speaks Khmer
• Once a week, 1 hour
• Classroom teacher (and sometimes ESL teacher)
  would prepare lessons
• Cover lessons which teachers and aide found too
  difficult to teach in English
• Cover issues of concern from teachers or
  administrators

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Focus on Math

• Given that the girls would have to take the math
  TAKS test, classroom teacher, aide, computer lab,
  and Khmer primary language support tutor focused
  on math instruction
• Computer lab
• Started out on Kindergarten level
• Completed up to beginning of 2nd grade level by
  end of the school year
• Math instruction
• Classroom teacher pulled worksheets from
  supplemental math books at lower grade levels
• Started a Kindergarten level
• Doing some 5th grade-level work by end of the
  year
• Most math work was solving simple word problems
  with basic arithmetic
• Math concepts Nitha and Bora struggled with and
  which teacher and aide found too difficult to
  explain in English saved for the Khmer primary
  language support tutor
• Nitha, When you explain it in Khmer to us, its
  so easy!

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Examples of Student Math Work

• 2-Digit Addition with Regrouping
• Adam found 91 small twigs and 29 larger twigs for
  the campfire. How many twigs did he find all
  together?
• 2-Digit Subtraction with Regrouping
• Jennifer sold 72 candy bars. Patti sold 56 candy
  bars. How many more candy bars did Jennifer sell?
  (Subtraction Story Problems, p. 4)
• 1-Digit by 2-Digit Multiplication
• Daniel has 3 cases to hold his toy trucks. Each
  case holds 18 trucks. How many trucks can Daniel
  store in his cases? (More Multiplication Story
  Problems, p. 15)

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Examples of Student Math Work

• 2-Digit by 1-Digit Division (no remainder)
• Jason swam 81 laps over a 9-day period. If he
  swam the same distance every day, how many laps
  did he swim each day?
• Money Addition Problems with Decimals (and
  regrouping)
• Jaric saw a bottle of shampoo that cost 1.72. He
  also saw conditioner that cost 1.18. If he
  purchased both items, what would the sum be?
• Adding Fractions with Common Denominators
• Luis used 1/4 cup of paste in one tray and 2/4
  cup in the other. How much paste did he use
  altogether?

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Math instruction

• Much of the focus was on helping Nitha and Bora
  circle the numbers needed for the equation, and
  identify the clue words which signaled which
  operation to use
• Addition - sum, total, in all
• Subtraction - difference, are left, how many more
  
• Worksheets completed
• Simple sentence structure (syntax)
• Only number needed for equation given
• Most only required one operation
• Most worksheets only focussed on a single
  operation (addition, subtraction, etc.)
• Girls discovered the could get right answers
  without actually reading or understanding the
  story problem

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5th Grade Math Texas Essential Knowledge Skills

• Within a well-balanced mathematics curriculum,
  the primary focal points at Grade 5 are comparing
  and contrasting lengths, area, and volume of
  geometric shapes and solids representing and
  interpreting data in graphs, charts, and tables
  and applying whole number operations in a variety
  of contexts.

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Difficulty of the 5th Grade Math TAKS Test for
Nitha and Bora

• 44 Questions
• Questions differed substantially from types of
  questions Nitha and Bora had been learning to
  solve
• i.e., Word problems requiring straight
  computation to lead to obtain a single answer
• Only 6 out of 44 were of this type, but still
  different as most
• Required logical reasoning and multiple steps and
  more than one operation to complete
• Extra information given which is not needed to
  solve the problem
• Rather than single digit answers, students had to
  select from complex answers which demonstrated
  mathematical thinking

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Example of 5th grade Math test item

• A track team ran 4 miles in 36 minutes. Which
  shows how to find the number of minutes it would
  take the track team to run 20 miles?
• A 36 4 19, so 9 x 20 180 minutes
• B 4 x 9 36, so 9 x 36 324 minutes
• C 36 4 9, so 4 x 36 144 minutes
• D 4 x 5 20, so 5 x 20 100 minutes

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Difficulty of the 5th Grade Math TAKS Test for
Nitha and Bora

• Nearly half (20) of the problems required the use
  and interpretation of graphs, tables, charts, and
  illustrations to solve problem
• Nitha and Bora had little practice with questions
  of this type
• TAKS contained concepts and skills beyond what
  they were able to learn six months before the test

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Nitha and Boras Math Work vs. Grade 5 TAKS Math
Test
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Nitha and Boras Math Work vs. Grade 5 TAKS Math
Test
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Nitha and Boras Math Work vs. Grade 5 TAKS Math
Test
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Nitha and Boras Math Work vs. Grade 5 TAKS Math
Test
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Nitha and Boras Math Work vs. Grade 5 TAKS Math
Test
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Difficulty of TAKS TestLinguistic Challenges
Number of Words
36
Difficulty of TAKS TestLinguistic Challenges

• Linguistic Analysis
• Web Vocabulary Profiler
• Words reported in three groups
• First thousand most common words
• First 500 function and content words
• Second 500 content words
• Second thousand most common words
• Academic words
• The 550 words that are frequent in academic texts
  across subjects

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Lexical Demands of Student Math Worksheets vs.
5th Grade Math TAKS
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Difficulty of TAKS TestLinguistic Challenges

• Demand for specific math vocabulary knowledge in
  particular, on the Math TAKS test are much higher
  than those Nitha and Bora encountered on their
  worksheets
• Math-specific academic words
• digit, rectangular, congruent, parallel,
  transformation, and diagram and many others
• Clue words (to signal operation) that Nitha and
  Bora practiced did not help them on TAKS
• Only one problem contained similar clue words

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Clue words Had (have) left
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Difficulty of TAKS TestLinguistic Challenges

• Many questions gave more information than needed
  to solve problem
• ex Barts drama club put on a play. There were
  843 people in the audience. Each ticket to the
  play cost 8. The audience was seated in 3
  sections. If each section had the same number of
  people in it, how many people were in each
  section?
• Unlike worksheets, Nitha and Bora would really
  have to be able to read and understand all the
  words to answer correctly
• 17 of 44 TAKS questions had answers that
  contained words rather than only numbers
• In some problem, students would have to convert a
  word in the problem to a number in order to get
  the correct answer.
• ex two problems required students to know that
  dozen 12
• Words with common meanings which may be known to
  ELLs, but which have different meanings within
  the math register
• Ex face, table, feet, sum (some), product, fair,
  volume, figure, point, even, odd, translation,
  place (as in place value), and ruler

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Difficulty of TAKS TestLinguistic Challenges

• 91 of student worksheets questions had simple
  Subject-Verb-Object sentence structure
• Ex Juan has 10 carrots.
• Less than 75 of the TAKS questions had
  Subject-Verb-Object sentence structure
• TAKS test questions much more syntactically
  complex than the work Nitha and Bora did in class
• Ex What is the least number of boxes he can buy
  so that each fifth-grader gets at least 1
  ice-cream bar?
• Questions with Negation
• Which is NOT a way to find how much money Leanne
  spends on lunches each week?

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(No Transcript)
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Students performance on TAKS

• Linguistically Accommodated Test Math TAKS
• What linguistic accommodations?
• Same test as everyone elsein English
• No Khmer translation allowed
• No Khmer dictionary allowed
• No Khmer glossary allowed
• Took test in small group
• That didnt help much
• Teacher could read questions aloud if they asked
• Didnt ask (why would they?)
• Nitha 6 out of 44 Bora 7 out of 44 correct
• Nitha actually the smarter one in math and tried
  harder than Bora
• Angry she scored lower than Bora
• When taking the test, Bora bubbled in 5 bubbles
  in a row, and yelled out BINGO!
• Student who randomly guessed got higher score
  than student who actually tried

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Conclusions

• Nitha and Bora were bright, hard working students
• Top students in their home village in Cambodia
• Rogers Intermediate did everything it could to
  help Nitha and Bora
• Differentiated classroom instruction
• Daily ESL instruction
• Substantial daily individualized instruction from
  aide
• Extra computer lab support
• Weekly Khmer primary language support
• FAILURE Sometimes your best, just isnt good
  enough
• Despite bright students and dedicated school
  doing everything it could, it still wasnt enough
  to meet the states expectation that Nitha and
  Bora would pass the 5th grade Math TAKS

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Conclusions

• Bush and others
• To say poor, minority and LEP students cannot
  perform well on tests is to exhibit the soft
  bigotry of low expectations
• My response
• To expect newly arrived LEP students from third
  world countries with poor education systems to
  perform on same tests at same level as
  English-fluent peers exibits the hard
  discrimination of unrealistic expectations

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Implications

• NCLB must be made more reasonable for ELL
  students
• Math test just as heavy linguistically as reading
  test
• Exclusion should be extended to math tests for
  newly arrived ELLs
• Policy must be able to account for students
  previous opportunities to learn material on test
• Cant just assume theyve been in US schools
  since Kindergarten
• Accommodations dont work
• No research to show which ones do
• Best to simply exlude ELLs until they become
  proficient in English
• Use alternative assessments which measure ELLs
  growth over time
• Instead of test-prep focus, provide intensive ESL
  and sheltered content-area instruction instead
• Once students are proficient in English, can take
  test without the problem of trying to provide
  accommodations which dont really work