Teaching Secondary Mathematics

1
Teaching Secondary Mathematics
to Second Language Learners
2
Workshop Overview
O v e r v i e w

• Purpose of workshop
• Organization of the TEKS
• Importance of Implementation of TEKS
• Selected Strategies and Activities

3
Purpose
The primary goal is to ensure that all students
experience high levels of academic success.
This guide provides professional development
with information about second language learners
and effective content area instruction.
4
Agenda

• Organization of TEKS document
• Strategies for teaching mathematics to second
  language learners
• Summary

5
The Legislative Background
House Bill 72 mandates a state curriculum
Essential Elements (EEs) First review of EEs
on a mandated five-year cycle Senate Bill No. 1
requires the state to develop Essential
Knowledge and Skills for all students State
Board of Education approves TEKS Texas
Essential Knowledge and Skills
1984
1992
1995
1997
6
TEKS Format Mathematics K-12
Subchapter A. Elementary Subchapter B. Middle
School Grades 6, 7, 8 Subchapter C. High
School Algebra I, II, Geometry, Precalculus,
Mathematical Models with Applications Subchap
ter D. Other High School Mathematics
Courses Independent Study in
Mathematics Advanced Placement (AP)
Statistics Advanced Placement (AP) Calculus
(AB) Advanced Placement (AP) Calculus (BC) IB
Mathematical Studies Subsidiary Level IB
Mathematical Methods Subsidiary Level IB
Advanced Mathematics Subsidiary Level Concurrent
Enrollment in College Courses
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Organization of the TEKS
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TEKS Strands for Mathematics K-12

• Number, Operations and
• Quantitative Reasoning
• Patterns, Relationships, and
• Algebra Thinking
• Measurement
• Geometry and Spatial Reasoning
• Probability and Statistics

9
K-W-L Handout
Teaching Mathematics to Second Language Learners
W
L
K
What I Want to Know About
What I Learned
What I Know
(Ogle, 1986)
10
The Student Languages Spoken
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Common Language
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Who is the second language learner?
Over half a million in the state
Bok!
Bonjour
Sat siri akal
Hola
Hello!
Sallam
Ibaulachi
Asalaam alequm
Nî hâo!
13
Who Are Secondary Newcomer and Linguistically
Different Youth? 1. One in six of all youths who
are 14 to 19 in the United States either speaks a
language other than English at home, was born in
a foreign country, or both. 2. The majority of
newcomer and linguistically different youth are
native-born. 3. Hispanics, ages 14-19,
constitutes about half of all youth who are
linguistically different, foreign-born, or both.
Mexico is the country of birth of the majority of
Hispanic newcomers. There were about 381,000
Mexican-born young people 15 to 19 in the United
States in 1990. Newcomers from Mexico, El
Salvador, Guatemala, Nicaragua, and Honduras
constitute larger proportions of the school-age
population than they do of the adult
population. 4. The former Soviet Union, Iran,
Germany, Portugal, and Poland are the principal
birthplaces of foreign-born linguistically
different non-Hispanic white youth. Youth born
in the United Kingdom and Canada are the largest
groups among non-Hispanic white newcomers born in
English-speaking countries. 5. Vietnam, the
Philippines, and Korea are the principal
birthplaces of young newcomers from Asia. 6.
Asians and Pacific Islanders are the third
largest group among newcomer and linguistically
different youth. Dorothy Waggoner
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Second Language Learner
(2) For students whose first language is other
than English, the native language serves as the
foundation for English language acquisition.
Cognitive skills transfer from one language to
another, and students literate in their first
language will apply these skills and other
academic proficiencies to the second language.
(A) The development of receptive
(listening/reading) and expressive
(speaking/writing) skills in second language
learners may be at different stages. In some
instances, second language learners undergo
silent periods of varying durations when they
first begin to learn a new language. Students
often understand more than they can produce and
may repeat words in sentences that they do not
entirely understand. Second language learners
may also draw upon the resources of their
language and culture as they acquire a new
language and culture. (B) It is important to
understand that limited knowledge of English
structure and vocabulary is neither related to
the students intellectual capabilities nor their
ability to use higher-order thinking skills.
Literacy development across the content areas is
essential in building academic skills in a second
language and can accelerate the learning of both
English language skills and higher-order thinking
skills.
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Students English Proficiency
The content area of math can serve as a vehicle
for
English language acquisition. These are the
levels of
language proficiency.
(A) Beginning
(B) Intermediate
(C) Advanced
(D) Additional first
language and/or
academic needs
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• Let students explore--ask questions, develop
  their own explanations
• Play the role of coach
• Ask open-ended questions.
• Support the different learning styles of your
  students.
• Continually assess how well your students are
  learning

GETTING STARTED
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ESL Strategies
Strategies for Teaching
Second Language Learners
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ESL Strategies in the Classroom
Classroom Strategies
MOTIVATION
BACKGROUND KNOWLEDGE
CONCEPT DEVELOPMENT
ASSESSMENT
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Motivating Students
MOTIVATION
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Activity
Name_______________________________ Reasons
ESL Students May Be Reticent to Ask or Answer
Questions During Class 1. 2. 3. ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
4. 5. 6. 7. 8. 9. 10. 11. 12.
Kate Kinsella, San Francisco State
University, 3/99
Focused Listing
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Activity
Language to Express Opinions
think guess infer conclude believe predict specula
te speculate imagine presume hypothesize deduce I
would venture to say that. . . It occurs to me
that . . . In my opinion, . . . It seems to me
that . . . Example response I speculate that
many ESL students are reticent to participate in
group work because they dont perceive any
pedagogical merits in the activity. I_____________
________that_______________________________ I__
___________________that___________________________
____ I_____________________that________________
_______________
Kate Kinsella, San Francisco
State University, 3/99
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Background Knowledge
Strategies that I use or know
How to assess or build
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Background Knowledge
BACKGROUND KNOWLEDGE
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Concept Development
VOCABULARY
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Vocabulary Activity
Visual Verbal Word Association Modified Version
Scaffold
Providing contextual supports for meaning,
instruction and assessment
Using literature to scaffold students language
development
Write a sentence on the back of the card using
this vocabulary word.
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Vocabulary Activity
Visual Verbal Word Association Modified Version
Vocabulary Term
Visual Association
Personal Association
Definition
Write a sentence on the back of the card using
this vocabulary word.
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Instructional Language
2 x 5 11
Make language and Math Comprehensible
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TEKS
Materials Textbook Supplemental
materials Visuals Graphics Manipulatives
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Technology
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Technology
Instruction Construction Classroom
Activity Teacher centered Learner
centered Didactic Interactive Teacher
role Fact teller Collaborator Always
expert Sometimes learner Student
role Listener Collaborator Always
learner Sometimes expert Instructional
emphasis Facts Relationships Memorization Inquiry
invention Concept of knowledge Accumulation T
ransformation of facts of facts Demonstration
of success Quantity Quality of understanding A
ssessment Norm referenced Criterion referenced
Multiple-choice items Portfolios and
performances Technology use Drill and
practice Communication, collaboration,
information access, expression
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Technology
How technology is used in the math classroom
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Video
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Assessment
ASSESSMENT
Traditional
Alternative
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Assessment Activity
2 x 5 11
Traditional
Alternative
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Alternative Assessment
Examples of Alternative Assessment
? Experiments/Demonstrations ? Teacher
Observations ? Portfolio ? Text Retelling ?
Interviews ? Oral Reports ? Journals
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Planning a Unit
Determine
Plan
Identify
Select
List
Evaluate
1. Select topic. 2. Identify key concepts. 3.
List student expectations. 4. Determine focus
for unit. 5. Select appropriate activities. 6.
Identify strategies that facilitate
understanding 7. Select appropriate
assessment. 8. Evaluate lesson and if the
activities were effective.
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Working Model of Instructional Plan
Concept Strand
Teaching Strategies
Vocabulary
Manipulatives
Learning Styles
Curriculum Integration
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Working Model of Instructional Plan
Concept Strand Functions TEKS the student
understands how algebra can be used to express
generalizations and recognizes and uses the power
of symbols to represent situations.
Vocabulary pattern variable predict constant t
able independent equation dependent linear power
expression perimeter
Teaching Strategies 1. Students recreate
toothpick design in order to predict the number
of toothpicks for the 6th triangle. Students
formulate a linear expression to predict the
number of toothpicks for the nth triangle. 2.
Students construct hexagon pattern using pattern
blocks. 3. Students will create a table in the
calculator and find out what the perimeter will
be for the 15th hexagon, formulate a linear
expression and graph the equation to show its
linearity.
Manipulatives toothpicks pattern blocks TI
82 calculator overhead calculator

• Learning Styles
• kinesthetic
• visual - model pattern construction, development
  of table development of linear expression, on
  overhead projector
• auditory - provide verbal explanations along with
  written or visual cues

Curriculum Integration language arts students
write rule for linear expression in words
students operationally define linear expression,
variable, constant
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Working Model of Instructional Plan
Concept Strand Geometric Patterns TEKS the
student identifies, analyzes and describes
patterns from right triangles the student
develops, extends and uses the Pythagorean Theorem
Vocabulary leg hypotenuse measure right
triangle relationship segment congruent
Teaching Strategies 1. Students will draw 3
different triangles and use a ruler to measure
all three sides. Ask students to color legs blue
and hypotenuse red, and draw in the symbol
indicating that these are right triangles. Then
have students look for a pattern/relationship
among the sides. 2. Students will use a paper
folding activity to develop the Pythagorean
Theorem (Explain, using diagrams, then model)
Manipulatives paper ruler colored
pencils

• Learning Styles
• kinesthetic
• visual - model paper folding on overhead
  projector
• auditory - provide verbal explanations along with
  written or visual cues

Curriculum Integration language arts students
refer to the diagram and explain why the drawing
is an illustration of the Pythagorean Theorem.
40
K-W-L Handout
Teaching Mathematics to Second Language Learners
W
L
K
What I Want to Know About
What I Learned
What I Know
(Ogle, 1986)
41
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