Math Strategies for the Middle School English Language

1
Math Strategies for the Middle School English
Language Learner

• Presented by
• Debbie Dethrage
• Becky Chairez

2
Math Teachers Ten Commandments

• Thou shalt teach the student first then math.
• Thou shalt be sensitive when teaching math.
• Thou shalt build the students self esteem in
  math.
• Thou shalt differentiate instruction in math.
• Thou shalt model respect during math instruction.
• Thou shalt use different approaches until the
  students understand.
• Thou shalt check for individual understanding.
• Thou shalt address any special needs.
• Thou shalt model discipline.
• Thou shalt count thy blessings.
• Donald Edge Ellen Freedman

3
Guiding Principles

• Meaning is not in words on a page, but
  constructed by reader. (schema)
• Prior knowledge is a most important variable.
• Comprehension depends on metacognition.
• Reading and writing are integrally related.
• Learning is a social process and increases with
  collaboration.

4
See Handout
5
Hows Your Schema?
The questions that poultrymen face as they raise
chickens from incubation to adult life are not
easy to answer. Both farmers and merchants can
become concerned when health problems such as
coccidiosis arise any time after the egg stage to
later life. Experts recommend that young chicks
should have plenty of sunshine and nutritious
food for healthy growth. Banties and geese should
not share the same barnyard or even sleep in the
same roost. They may be afraid of the dark.
6
Federal and State Requirements

• U.S. Supreme Court ruling Lau v. Michaels 1974
• Suit by Chinese parents in San Francisco leads to
  ruling that identical education does not
• constitute equal education under the Civil rights
  Act. School districts must take
• affirmative steps to overcome educational
  barriers faced by non-English speaking
• students.
• What does it say? What does it mean?
• _________________________________ _______________
  _________________
• _________________________________ _______________
  _________________
• _________________________________ _______________
  _________________
• _________________________________ _______________
  _________________

See Handout
7
Federal and State Requirements

• Commissioners Rules Concerning Limited English
  Proficient Students March 1999 update Section
  89.1210. Program Content and Design.
• (a.) The district (the teacher) shall modify
  the instruction, pacing, and materials to ensure
  that limited English proficient students have
  full opportunity to master the essential
  knowledge and skills of the required curriculum.
• What does it say? What does it mean?
• _________________________________ _______________
  _________________
• _________________________________ _______________
  _________________
• _________________________________ _______________
  _________________
• _________________________________ _______________
  _________________

See Handout
8
Second Language Acquisition
Monitor
Motivation
Natural Order
Affective Filter
Comprehensible Input
(Krashen 1985)
9
Second Language Acquisition Terms (from Steven
Krashen)

• Language acquisition natural, subconscious
  process of soaking up a language and culture as
  when children learn their first language.
• Language learning formal, conscious process of
  learning grammar, vocabulary, and rules.
• Comprehensible input new language along with
  clues as to what the language means.
• Affective filter emotional states such as
  anxiety or low self-esteem which create a barrier
  to effective language acquisition.
• Monitor conscious application of rules to make
  corrections while speaking or writing requires
  knowledge of rules, attention focused on
  correctness, and time to apply the rules.

10
Stages of Language Proficiency
See Handout
11
Stages of Language Proficiency
See Handout
12
Non-Linguistic Difficulties

• Concept Formation Two Levels
• With word problems ESL students must conceptually
  process both the language and the mathematical
  problem before a solution can be reached.
• The student must be able to use English as a
  vehicle of thought and to solve the problem in
  English, a language students may not understand
  perfectly at this point in their education.

13
Non Linguistic Difficulties

• Cultural differences in the use of decimals and
  commas in fractions or in the strategies students
  use to solve word problems.

8
32
4
32
4
0 8
5.00 R5,00
14
Non-Linguistic Difficulties

• Cultural Background
• Differences in math symbols or in the use, and
  differences in study or problem-solving
  procedures.
• U.S. System Some Spanish-Speaking
  Countries
• fractions metric
• inches, miles, every unit is divided
  by 10
• quarts, pounds,
• etc.
• 4,232 4.232
• 1,258,125 1.258.125
• 4-1/2 4.5 4,5
• OTHERS?

15
Activity Mathematics Literacy Game
16
Mathematics Literacy Game

• 1. The quotient of a number n and 7
• 2. 7 divided by a number n
• 3. 7 times a number n
• 4. The product of 7 and a number n
• 5. The difference between 7 and n
• 6. 7 subtracted from a number n
• 7. 7 is greater than a number n

17
Mathematics Literacy Game

• 8. The sum of a number n and 7
• 9. 7 less than a number n
• 10. 7 is less than a number n
• 11. A number n is less than 7
• 12. The difference between n and 7
• 13. A number n is decreased by 7
• 14. 7 more than a number n
• 15. A number n increased by 7

18
Students struggle with

• Organizing ideas as they read.
• Making meaningful connections.
• Persevering through reading material.
• Mathematics
• Tackling vocabulary.
• Decoding symbols.
• Reading at the text level.
• Understanding text organization.

19
Language Skills in the Content Area of Math TEKS
Connections
See Handout
20
Why Writing in Mathematics?

• New classrooms
• Reading and writing are essential to problem
  solving and concept development.
• Incorporates key ideas from standards.
• Writing to learn in mathematics
• Enhances development of problem solving and
  reasoning
• Promotes metacognition
• Makes connections and integrates new concepts
  with prior knowledge.
• Motivates students
• Facilitates assessment

21
Think-Pair-Share
Think about and share your concerns for writing
in the mathematics classroom and/or your
questions about writing in mathematics.
22
Article Jigsaw Reading In The Mathematics
Classroom by Reehm Long
Expert Group Become an expert on your assigned
reading. Record the key points.
Home Group Each expert will explain his/her key
points and their implication for the English
language learner in the mathematics classroom.
See Handout
23
Vocabulary?
24
Effective Vocabulary Instruction

• Introduces and uses words in meaningful contexts.
• Connects new concepts with prior knowledge.
• Requires repetition.
• Targets learning styles.
• Nonlinguistic representations
• Students own explanations

25
Vocabulary Strategies

• Contribute to reading comprehension.
• Develop understanding of terms that may be major
  concepts.
• Introduce unfamiliar terms.
• Make meaningful connections between terms.
• Improve range and specificity in writing.
• Help students communicate more effectively.
• Types of strategies that can be used with
  students
• List-Group-Label
• Frayer Model
• Concept Definition Mapping
• Concept Circles

26
Vocabulary Development

• List-Group-Label (How does it work?)
• Write a content-area term on the board or on an
  overhead transparency. Explain to students that
  this term has something to do with the next unit
  (or chapters).
• Ask students to generate words and phrases that
  they associate with this term. As students
  volunteer responses, they will stimulate others
  in the class to contribute their ideas.
• After you have developed a list of 15-30 words or
  phrases, ask students to consider what the words
  have in common and to organize them into
  categories. Remind them that these categories
  should identify significant relationships among
  the terms, and that the relationships should
  extend their learning. Grouping words by their
  initial letter, for example, is not an activity
  that identifies a mathematically significant
  relationship.

27
Vocabulary Development List-Group-Label

• This strategy is very effective in assessing
  students prior knowledge and classification
  skills.
• Use class discussions as an opportunity to
  broaden students understanding of the concepts
  generated from the activity and illustrate how to
  apply this understanding when solving problems.

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Vocabulary Development List/Group/Label

• Activity
• In your groups, generate
• a list of terms for the word
• MEASUREMENT

29
Sample List-Group-Label
STUDENT-GENERATED LIST weight height meter len
gth foot pound mile width tape
measure circumference area perimeter scale rad
ius distance ruler age quart time temperature
cup yard kilogram thermometer
CATEGORIZE Units of Measure Things You
Measure Tools for Measurement foot
weight tape measure pound age scale yard
height cup quart circumference ruler meter
radius thermometer mile area kilogram dis
tance time length width perimeter t
emperature
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Vocabulary Quiz

• Directions In each of the six blanks, fill in
  the subject or content area that includes all the
  terms listed below it.
• 1. ___________________ 2.
  ___________________ 3. ____________________
• Parallelogram deciliter mean
• Rectangle kilogram median
• Triangle centimeter range
• Decagon millimeter mode
• Hexagon meter bimodal
• Rhombus milligram
• 4. ___________________ 5.
  ___________________ 6. ____________________

coefficient hyfrolated adagio variable cantifo
rmed pianissimo functions trussiles largo pol
ynomial gabriolation a tempo linear mislets
mezzo forte standard form crestibule lento
See Handout
31
Vocabulary Quiz Answers
1. Polygons 2. Lengths of Measurement 3.
Measure of Central Tendency 4. Equations 5.
Nonsense Words 6. Musical Terms
32
Frayer Model
Vocabulary Word
33
Frayer Model
34
Frayer Model

• Activity
• Create your own and be prepare to share with the
  whole group.

35
Concept Definition Mapping
Number Concept Fraction with Denominator 100 (per
hundred)
Percents can be written in fraction or decimal
form.
Ratio
Additive when base is same 70 of 130 50 of
130 20 of 130
Fraction
n of A is the same as A of n
Percents
Benchmark percents 10 25 50
Interest Rates
Test Scores
Discounts
36
Concept Circles
37
Concept Circles

• Activity
• Choose a topic or vocabulary word in mathematics
  and
• create your own
• Concept Circle.

38
Manipulative and Movement
39
Example of Manipulative Use
40
Are there any issues with the wording of TAKS
questions for the English language learner?
41
Analysis of TAKS Questions (6th Grade)

• 6 Miss Carusos car travels an average of
• 22 miles per gallon of gasoline. The gas tank
• holds 12 gallons. How would you find the
• number of miles Miss Caruso can drive on
• 1 full tank of gasoline?
• F Add the cars average mileage in miles per
• gallon to the number of gallons the tank
• can hold
• G Subtract the number of gallons the tank
• can hold from the cars average mileage in
• miles per gallon
• H Multiply the cars average mileage in
• miles per gallon by the number of gallons
• the tank can hold
• J Divide the cars average mileage in miles
• per gallon by the number of gallons the
• tank can hold

24 Felicia went shopping for clothes. She
bought a pair of jeans priced at 28.00, a
sweater priced at 32.50, and a belt priced at
18.75. If there was an 8.75 tax on clothing
items, which procedure could be used to find
the amount of tax Felicia paid? F Multiply the
tax rate by the sum of the prices of the clothing
items G Add the prices of the clothing items to
the tax rate H Add the prices of the clothing
items J Multiply the tax rate by the price of
the most expensive clothing item
See Handout
42
Analysis of TAKS Questions(7th Grade)

• 13 The table below shows the favorite sports of
• the students at Tompkins Middle School.

37 Which problem situation matches the equation
below? x - 4.72 5.28 A Sergios lunch cost
4.72. He received 5.28 in change when he paid
the bill. What is x, the amount of money he gave
the cashier? B Yvette cycled 4.72 kilometers in a
race. The winning cyclists time was 5.28 seconds
faster than Yvettes. What is x, the time in
seconds it took Yvette to finish the race? C
Janice and Maura measured the wingspans of
butterflies in science class. Janices butterfly
had a wingspan of 4.72 centimeters, and Mauras
butterfly had a wingspan of 5.28 centimeters.
What is x, the average length of a butterflys
wingspan? D Mrs. Castro paid 4.72 for a jar of
iced-tea mix that was originally priced at 5.28.
What is x, the amount of money that Mrs. Castro
saved altogether?
Based on the information in the table, which of
the following is a reasonable assumption? A
About 3 times as many students like cycling as
volleyball. B Swimming is almost twice as popular
as basketball. C About 2 times as many students
like swimming as volleyball. D Volleyball is the
most popular sport.
See Handout
43
Analysis of TAKS Questions(8th Grade)

• 17 Mr. Elliott designed a flower garden in the
• shape of a square. He plans to build a
• walkway through the garden, as shown below.

15 Regular pentagon MNPQR is similar to pentagon
TUVWX.
What scale factor was used to dilate regular
pentagon MNPQR to pentagon TUVWX? A 0.4 B 1.8 C
2.5 D 4.2
Which is closest to the length of the walkway? A
36 ft B 24 ft C 17 ft D 13 ft
See Handout
44
Foldables
These structures can be used to organize parts to
whole by providing topics, definitions, examples,
situations, and /or pictures for easy access to
content knowledge and skills.
45
Foldables Provide

• Novelty and fun for all student
• Can be use as a study aid
• Serves as a good vocabulary builder/word bank
• Utilizes a tactile approach that is recommended
  for struggling learners
• Can use pictures in place of print

46

• Activity
• Create Your Own Foldables

47
Anticipation Guide

• Type of Strategy Informational Text
• Why would you use it?
• Activate and assess prior knowledge.
• Focus reading.
• Motivate reluctant readers.
• Identify misconceptions.
• How do you use it?
• Mathematics examples

See Handout
48
Anticipation Guide
See Handout
49
K-W-L

• Type of Strategy Informational Text
• Why would you use it?
• Activate prior knowledge.
• Organize thoughts.
• Focus on topic.
• Set purpose for reading.
• Check for misconceptions.
• How do you use it?
• Mathematics examples

50
K-N-W-S (K-W-L for Word Problems)

• Type of Strategy
• Informational Text
• Why and when would you use it?
• Activate prior knowledge
• Analyze and plan problem solving
• Organize information
• Check for misconceptions
• How do you use it?
• See example

51
Model K-N-W-S (For Problem Solving)
Video Heaven rents movies for 3 each per night.
They also offer a video club plan. The plan
costs 100 per year and allows unlimited rentals
at 1 per movie per night plus two free rentals
per month. How many movies must you rent in a
year to make the video club worthwhile?
See Handout
52

• Using the cloze strategy

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Using cloze strategy to make your own math
problem.
The entire Palmer family went to an amusement
park. There are ____ members in the family, ____
children and ____ adults. Childrens tickets cost
____ and adult tickets cost ____ each. The
family spent a total of ____ for tickets.
See Handout
54
Additional Strategies for Math

• Teach all the comparison words necessary
• Help students prepare a card file of number words
• Rewrite story problems in simpler English
• Limit the number of problems to be worked
• Check a student reading skills in English through
  informal assessment of word problems
• Use highlighted books
• Give special mathematical meaning for words
  commonly used in English
• Have students prepare their own glossaries of
  math terms used in math context
• Encourage use of diagrams and drawings
• Give a problem requiring several steps to solve

55
SIOP Language /Content Objectives (Differentiated
Instructional Plan)
See Handout
56
Math Cognates

• Equivalentes-equivalent
• Racionales-rational
• Probabilidad-probability
• Modelos-models
• Modo-mode
• Patrones-patterns
• Circulo-circle
• Angulos-angles

See Handout
57
View Stand and Deliver Video(PMI Chart
Activity)
See Handout
58
Synectics

• Teaching the English language learner is like
  sailing a boat because you go where the wind
  blows, but you give it directions.

59
Synectics

• Activity
• Use the stem below and create
• your own saying!
• Teaching the English language
• learner is like ____________ because
  ___________________________.

60
Commitment
Consider the strategies you have learned about
during this workshop. List three or four that you
like and think you could use in your instruction
to help with student understanding.
As a result of this workshop, pledge to use at
least one of the strategies you listed during the
next 20 days of classroom instruction.
61
Thank you!

• Please fill out the evaluation form. Your
  thoughtful comments are appreciated.
• Debbie Dethrage
• Region 10 ESC
• [phone]
• dethraged_at_esc10.ednet10.net
• Becky Chairez
• Region 10 ESC
• (972) 348-
• chairezb_at_esc10.ednet10.net

62
Resources

• Dinah Zikes Big Book of Math Graphics Every
  Teacher Needs! (ISBN 1-882796-13-6)
• How To Evaluate Progress In Problem Solving, by
  Randall Charles (ISBN 0-87353-241-4)
• Illustrated Math Dictionary, Judith de Klerk
  (ISBN 0-673-59959-0)
• Teaching Elementary Math A Problem-Solving
  Approach, Ruben D. Schwieger (ISBN 0-8273-8164-6)
• Making Content Comprehensible for English
  Learners, Jana Echevarria (ISBN 0-205-38641-5)
• The CALLA Handbook, Anna Uhl Chamot (ISBN
  0-201-53963-2)
• Sheltered Instruction in the Middle School math
  and Science
• Module 1