Elementary Math for
EL Students
Giving students the tools they need to
succeed in the Mathematics Classroom
Learning mathematics
involves participation in the
mathematical discourse
practices in a classroom or
other mathematical learning
community. — Moschkovich, J.
(2002). A situated and sociocultural
perspective on bilingual mathematics
learners. Mathematical Thinking &
Learning, 4(2&3), 189–212.
Agenda
 9:00-11:45 Break-Out Session
 11:45-12:45 Lunch
 12:45-2:00 Break-Out Session
 2:00-2:30
Question & Answer
It’s the Law!
• All EL Laws are based on the Civil Rights Act of 1964
No person in the United States shall, on the ground of race,
color, or national origin, be excluded from participation in,
be denied the benefits of, or be subjected to discrimination
under any program or activity receiving Federal financial
assistance.
• Same Does NOT mean Equal-Lau v. Nichols (US Supreme
Court Decision 1974)
Equal is providing the skills necessary for each student
to achieve success in the school environment.
• It’s ALL about the Program-Castañeda v. Pickard, 5th Cir.,
1981 648 F.2d 989 (US COURT OF APPEALS)
Sound Theory and Research, Implementation,
Evaluation
• ALL in-Plyler v. Doe (U.S. Supreme Court Decision 1982)
•
Chilling, Registration Process
As a result of the
Dear Colleague
Letter, the
Department of
Education
(January 7, 2015)
has developed a
TOOL KIT for
Educators of
English Learners.
This guidance provides an
outline of the legal obligations of
SEAs and school districts of EL
students under the civil rights
laws. Additionally, the guidance
discusses compliance issues that
frequently arise in OCR and DOJ
investigations under Title VI and
the EEOA and offers approaches
that SEAs and school districts
may use to meet their Federal
obligations to EL Students.
http://www.relnei.org/wp-content/uploads/2015/11/ELLA-12-815-Slides-and-Transcript.pdf (Chapter 1; Page 11)
English Learner Tool Kit
Chapters
•
Identifying All English Learner Students (PDF, 1.5MB)
•
Providing English Learners with a Language Assistance Program (PDF,
800KB)
•
Staffing and Supporting an EL Program (PDF, 921KB)
•
Meaningful Access to Core Curricular, Extra Curricular Programs (PDF,
1.75MB)
•
Creating an Inclusive Environment and Avoiding Unnecessary
Segregation (PDF, 910KB)
•
Addressing English Learners with Disabilities (PDF, 1.27MB)
•
Serving English Learners who Opt-Out of EL Programs (PDF, 386KB)
•
Monitoring and Exiting English Learners from EL Programs and
Services (PDF, 1.23MB)
•
Evaluating the Effectiveness of a Districts EL Program (PDF, 907KB)
•
Ensuring Meaningful Communication with Limited English Proficient
Parents (PDF, 1.26MB)
Chapter 2
• Recommendations:
 Ensure there is an explicit focus on building
academic literacy and cultivating English
language development.
 Ensure that all teachers of ELs have access to
high-quality professional development that
provides differentiated instructional strategies.
 Include instruction aligned to state ELP
standards and grade-level content standards.
Chapter 3
• Recommendations:
 Support Oral Language Development
 Explicitly Teach Academic English
 Value Cultural Diversity
Chapter 3 continued
• Incorporate effective instructional practices for ELs
 Planning and Preparations
•
•
•
•
Bilingual dictionaries, or a word-to-word translator device
Design personal academic dictionaries
Parents as multicultural resources
Resources available in students’ home languages
 Instruction
• Leveled readers appropriate to students’ English proficiency
level
• Opportunities to read text in students’ home languages
• Pair ELs of the same language
 Assessment
• Formative assessments
Chapter 4 (ELs and CCRS – Math)
• Regular and active participation in the classroom –
not only reading and listening but also discussing,
explaining, writing, representing, and presenting – is
critical to the success of ELs in mathematics
 ELs should understand the text of word problems before
they attempt to solve them Ex.: the “Three Reads
Strategy”-1) Understand the story context 2) Identify the
questions, or task 3) Identify important information
 There should be a focus on “mathematical discourse”
and “academic language” Ex.: Opportunities to
communicate mathematically
 Vocabulary instruction is not sufficient for supporting
mathematical communication Ex.: Interactive word wall
with visual representations; Drill and practice is NOT
effective for learning vocabulary.
Activity Break!!
Checking
comprehension and
promoting oral
language
interaction.
WIDA Language Proficiency
Levels
Accommodate Math Instruction
based on English Learners’
Language Proficiency
• Planning and Preparations
 Lesson Plans
 Instruction
• Assessment
 Formative
When planning a lesson…
• Consider the following:
 What is the math goal?
 What is the language goal?
Standards
CCRS
WIDA
*Use multiplication and division within 100 to
solve word problems in situations involving
equal groups, arrays, and measurement
quantities, e.g., by using drawings, and
equations with a symbol for the unknown
number to represent the problem. [3-OA3]
*Solve two-step word problems using the four
operations. Represent these problems using
equations with a letter standing for the
unknown quantity. Assess the reasonableness
of answers using mental computation and
estimation strategies including rounding. (This
standard is limited to problems posed with
whole numbers and having whole number
answers; students should know how to
preform operations in the conventional order
when there are no parentheses to specify a
particular order.) [3-OA8]
English language
learners
communicate
information, ideas
and concepts
necessary for
academic
success in the
content area of
Mathematics.
 What vocabulary needs to be taught explicitly?
 What is the purpose for language: to describe;
to categorize; to hypothesize; to sequence; to
compare and contrast?
 What strategies will you use?
Objectives
Content
M.3.3.1: Demonstrate computational
understanding of multiplication and division by
solving authentic problems with multiple
representations using drawings, words, and/or
numbers.
M.3.3.2: Identify key vocabulary words to solve
multiplication and division word problems.
Examples: times, every, at this rate, each, per,
equal/equally, in all, total.
M.3.3.6: Represent repeated addition,
subtraction, and equal groups using
manipulatives.
M.3.8.5: Solve addition and subtraction
problems, including word problems, involving
one-and two digit numbers with and without
regrouping, using multiple strategies.
M.3.8.7: Represent multiplication and division
with manipulatives.
Language
Students will be able to
demonstrate solving word
problems using multiple
representations for each
part of a multi-step
problem-discussing,
noting, presenting, and
writing their mathematic
learning using: interactive
math wall, visual
vocabulary,
manipulatives,
informational PPT, anchor
charts, and math journal.
 How will you differentiate lesson for various
language proficiencies?
 Are opportunities for discussion built in?
Proficiency
Differenti
ated
Instructio
n
Level 1
Demonstrate
solving word
problems using
multiplication
strategies by
reading the
Listening problem in L1
Speaking and/or use
Reading pictures,
Writing drawings and
selected words
to participate in
the creation of
a group*
anchor chart
and individual
journal entry.
Level 2
Level 3
Level 4
Level 5
Demonstrate
solving word
problems using
multiplication
strategies by
reading the
problem in L1
and/or use
pictures,
selected words
and simple
sentence
frames to
participate in
the creation of
a group*
anchor chart
and individual
journal entry.
Demonstrate
solving word
problems using
multiplication
strategies by
reading word
problems
supported with
pictures and
use key,
technical
vocabulary in
simple
paragraph
frames to
participate in
the creation of
a group*
anchor chart
and individual
journal entry.
Demonstrate
solving word
problems using
multiplication
strategies by
reading word
problems
supported with
pictures and
use key,
technical
vocabulary in
expanded
sentence form
to participate in
the creation of
a group*
anchor chart
and individual
journal entry.
Demonstrate
solving word
problems using
multiplication
strategies by
reading word
problems
supported with
pictures and
use contentspecific
vocabulary in
complex
sentence form
to participate in
the creation of
a group*
anchor chart
and individual
journal entry.
Standards
CCRS
WIDA
Use multiplication and division within 100 to solve word problems in situations
involving equal groups, arrays, and measurement quantities, e.g., by using
drawings, and equations with a symbol for the unknown number to represent
the problem. [3-OA3]
Solve two-step word problems using the four operations. Represent these
problems using equations with a letter standing for the unknown quantity.
Assess the reasonableness of answers using mental computation and
estimation strategies including rounding. (This standard is limited to problems
posed with whole numbers and having whole number answers; students
should know how to preform operations in the conventional order when
there are no parentheses to specify a particular order.) [3-OA8]
Objectives
English language learners communicate
information, ideas and concepts
necessary for academic success in the
content area of Mathematics.
Content
Language
M.3.3.1: Demonstrate computational understanding of multiplication and
division by solving authentic problems with multiple representations using
drawings, words, and/or numbers.
M.3.3.2: Identify key vocabulary words to solve multiplication and division
word problems. Examples: times, every, at this rate, each, per, equal/equally,
in all, total.
M.3.3.6: Represent repeated addition, subtraction, and equal groups using
manipulatives.
M.3.8.5: Solve addition and subtraction problems, including word problems,
involving one-and two digit numbers with and without regrouping, using
multiple strategies.
M.3.8.7: Represent multiplication and division with manipulatives.
Students will be able to demonstrate
solving word problems using multiple
representations for each part of a multistep problem-discussing, noting,
presenting, and writing their mathematic
learning using: interactive math wall,
visual vocabulary, manipulatives,
informational PPT, anchor charts, and
math journal.
Proficiency
Level 1
Level 2
Level 3
Level 4
Level 5
Differentiated
Instruction
Demonstrate solving
word problems using
multiplication strategies
by reading the problem
in L1 and/or use pictures,
drawings and selected
words to participate in
the creation of a group
anchor chart and
individual journal entry.
Demonstrate solving
word problems using
multiplication strategies
by reading the problem
in L1 and/or use pictures,
selected words and
simple sentence frames
to participate in the
creation of a group
anchor chart and
individual journal entry.
Demonstrate solving
word problems using
multiplication strategies
by reading word
problems supported with
pictures and use key,
technical vocabulary in
simple paragraph frames
to participate in the
creation of a group
anchor chart and
individual journal entry.
Demonstrate solving
word problems using
multiplication strategies
by reading word
problems supported with
pictures and use key,
technical vocabulary in
expanded sentence
form to participate in the
creation of a group
anchor chart and
individual journal entry.
Demonstrate solving
word problems using
multiplication strategies
by reading word
problems supported with
pictures and use
content-specific
vocabulary in complex
sentence form to
participate in the
creation of a group
anchor chart and
individual journal entry.
Listening
Speaking
Reading
Writing
*
When planning for group activities, groups
require structuring that is heterogeneous in
nature-each group requires a student who can
model appropriate English-speaking skills in
order to support English learners in speaking
and writing during the sharing and production
process.
Building an Academic Language Community
Begin the first day of school:
• Immerse ELs in an environment filled with words-both written and
spoken. Speak and write academic terms, and expect students
to use the same words in response to questions and in discussion.
• Encourage students to experience and use language in the
context of collaborative activity and problem-solving. Model the
use of academic terms during instruction, and expect students
to respond using the same vocabulary.
Building an Academic Language Community
•
Ensure that every student pays attention to spoken and written
words, and support them as they begin to use those words.
Help students build understanding of the meanings of these
academic terms by providing visual cues, realia, and support
within the classroom environment.
•
Model, and remind students, to look at the speaker when they
are presenting-whether it is the teacher or a classmate.
•
Begin by pairing students for presentations, providing ELs the
opportunity to communicate with a peer if they struggle, in
order to build confidence.
•
Create an environment where differing ideas and opinions are
viewed as a cooperative practice; positive and valued, as this
contributes to building higher levels of thinking about math.
Vocabulary Break!
Polysemy
Use Your Frayer Organizer
Building Background
Alabama: Southern Devil Scorpion
The “Three Reads Method” of addressing word
problems:
First Read: Understand the story context.
Use pictures and have the students identify
words in the text
Second Read: Identifying the question or task.
A multi-step problem needs to be broken into
parts-each part may require a different task, or
ask a connecting question.
Third Read: Identifying important information.
What information is needed to solve the
problem? Breaking task down into numbered
steps.
Frayer Model Graphic Organizer
for students to identify definitions, characteristics, and examples of a
concept
Co-Constructed Word Banks
Word banks that students and teachers
construct together during work on a task, that
is then used for that task
How Many?
When we multiply we write a number
sentence called an equation.
multiplicand
multiplier
product
Partner Share and Group Share
Have students
participate and
practice discourse
with a partner and as
members of a group.
Sentence Starters and Frames:
Sentence stems that students complete to express their
mathematical thinking
This picture helped me.
I noticed this pattern_______________________.
These key words helped me:__________,
__________,_____________.
I used ______________________ to
help me understand the problem.
I agree with _______________
because___________________.
I thought about this problem in a
different way, and I can
explain:______________________.
Where do I begin?
Level One:
How many?
1.
90 scorpions
- 3 scorpions
How many?
2.
8 scorpions
X 2 pincers
How many?
3.
8 groups
X 4 students
8 scorpions
X 6 legs
8 scorpions
X 8 pincers and legs
Where do I begin?
Level Two:
How many scorpions do not live in Arizona?
1.
90 scorpions
- 3 scorpions
There are 8 scorpions. How many pincers? How many legs?
How many pincers and legs?
2.
8 scorpions
X2 pincers
How many students saw
The scorpions ?
3.
8 groups
X 4 students
8 scorpions
X6 legs
8 scorpions
X 8 pincers and legs
Where do I begin?
Level Three:
How many kinds of scorpions do not live in Arizona?
1.
90 scorpions
- 3 scorpions
Students saw 8 scorpions. What math sentences tell how many
pincers and how many legs? How many pincers and legs?
2.
8 scorpions
X2 pincers
There are 8 groups of
4 students
How many students saw
the scorpions ?
3.
8 groups
X 4 students
8 scorpions
X6 legs
8 scorpions
X 8 pincers and legs
“For English Learners to
succeed in learning
mathematics, they need
to be more productive in
mathematics
classrooms—reasoning
more, speaking more,
writing more, drawing
more.” —Personal communication from
Maria Santos, Former Director, New York City
Office of English Language Learners
Checklist for Scaffolding Learning:
 Breaking task down into steps
 Highlighting key vocabulary and phrases
the teacher can use to present the
language of math
 Labeled tables with explanations
 Deleting unnecessary words
 Using simple sentences rather than
complex ones
 Simplifying non-subject-specific vocabulary
Even if the math is NOT contained in a word
problem, the language must always be
supported.
The Go to
Strategies
http://midcentralcoop.org/uploads/go-tostrategies%20(1).pdf
Graffiti
As a group, use symbols, drawings,
shapes and colors, alongside words
and quotations, constructing a
graphic of how you will implement
your learning when engaging your
students in mathematic thinking within
your classroom.
Your group will explain the meanings
of the symbols, drawings, shapes and
colors used in a presentation for the
class.
State ESL Coaches
• Debbie Baeder
[email protected]
• Michele Lee
[email protected]
• Robin Stutts
[email protected]
• Krista Whatley
[email protected]
We appreciate your input. Please go to the link
below to participate in the SAMUEL II Evaluation.
Thank you.
https://www.surveymonkey.com/r/MG5HQYC
References
Castañeda v. Pickard, 648 F.2d 989 (5th Cir. 1981).
Echevarria, J., Vogt, M.E., & Short, D. (2008). Making content comprehensible for
English learners: The SIOP Model (3rd ed.). Boston: Allyn & Bacon.
Echevarria, J., Vogt, M.E., & Short, D. (2010). The SIOP Model for teaching
mathematics to English learners. Boston: Allyn & Bacon.
Fairbairn, S., & Jones-Vo, S. (2010). Differentiating instruction and assessment for
English language learners. Philadelphia: Caslon Publishing.
Hill, J. D., & Miller, K. B. (2013). Classroom instruction that works with English
language learners (2nd ed.). Alexandria, VA: ASCD.
Lau v. Nichols. 414 U.S. 563. (1974).
Levine, L. N., Lukens, L., & Smallwood, B. A. (2013). The GO TO strategies:
Scaffolding options for teachers of English language learners, K-12. For Project
EXCELL, a partnership between the University of Missouri- Kansas City and North
Kansas City Schools, funded by the US Department of Education, PR Number
T195N070316. Available online at www.cal.org/excell.
Plyler v. Doe. 457 U.S. 202. (1982).
U.S. Department of Education, Office for Civil Rights, & U.S. Department of Justice.
(2015, January). Dear colleague letter: English learner students and limited English
proficient parents. Retrieved from http://www2.
ed.gov/about/offices/list/ocr/letters/colleague-el-201501.pdf
U.S. Department of Education, Office of English Language Acquisition. English
Learner Tool Kit. Retrieved from http://www2.ed.gov/about/offices/list/oela/englishlearner-toolkit/index.html
Pattichis, S. (2012). Beyond good teaching: Advancing mathematics education
for ELLs. Reston, VA: National Council of Teachers of Mathematics.